Copyright	Copyright (C) 2006-2018 Bjorn Buckwalter
License	BSD3
Maintainer	bjorn@buckwalter.se
Stability	Stable
Portability	GHC only
Safe Haskell	None
Language	Haskell2010

Numeric.Units.Dimensional.Prelude

Description

Summary

This module supplies a convenient set of imports for working with the dimensional package, including aliases for common Quantitys and Dimensions, and a comprehensive set of SI units and units accepted for use with the SI.

It re-exports the Prelude, hiding arithmetic functions whose names collide with the dimensionally-typed versions supplied by this package.

Synopsis

class HasDynamicDimension a => HasDimension a where
- dimension :: a -> Dimension'
data Dimension' = Dim' !Int !Int !Int !Int !Int !Int !Int
type KnownDimension (d :: Dimension) = HasDimension (Proxy d)
type Cbrt d = NRoot d Pos3
type Sqrt d = NRoot d Pos2
type family NRoot (d :: Dimension) (x :: TypeInt) where ...
type family (d :: Dimension) ^ (x :: TypeInt) where ...
type Recip (d :: Dimension) = DOne / d
type family (a :: Dimension) / (d :: Dimension) where ...
type family (a :: Dimension) * (b :: Dimension) where ...
type DLuminousIntensity = Dim Zero Zero Zero Zero Zero Zero Pos1
type DAmountOfSubstance = Dim Zero Zero Zero Zero Zero Pos1 Zero
type DThermodynamicTemperature = Dim Zero Zero Zero Zero Pos1 Zero Zero
type DElectricCurrent = Dim Zero Zero Zero Pos1 Zero Zero Zero
type DTime = Dim Zero Zero Pos1 Zero Zero Zero Zero
type DMass = Dim Zero Pos1 Zero Zero Zero Zero Zero
type DLength = Dim Pos1 Zero Zero Zero Zero Zero Zero
type DOne = Dim Zero Zero Zero Zero Zero Zero Zero
data Dimension = Dim TypeInt TypeInt TypeInt TypeInt TypeInt TypeInt TypeInt
data Metricality
- = Metric
- | NonMetric
class KnownVariant (v :: Variant) where
- data Dimensional v :: Dimension -> Type -> Type
type Quantity = SQuantity One
type Unit (m :: Metricality) = Dimensional (DUnit m)
siUnit :: forall d a. (KnownDimension d, Num a) => Unit NonMetric d a
showIn :: (Show a, Fractional a) => Unit m d a -> Quantity d a -> String
type LuminousIntensity = Quantity DLuminousIntensity
type AmountOfSubstance = Quantity DAmountOfSubstance
type ThermodynamicTemperature = Quantity DThermodynamicTemperature
type ElectricCurrent = Quantity DElectricCurrent
type Time = Quantity DTime
type Mass = Quantity DMass
type Length = Quantity DLength
type Dimensionless = Quantity DOne
name :: Unit m d a -> UnitName m
exactValue :: Unit m d a -> ExactPi
weaken :: Unit m d a -> Unit NonMetric d a
strengthen :: Unit m d a -> Maybe (Unit Metric d a)
exactify :: Unit m d a -> Unit m d ExactPi
(*~) :: Num a => a -> Unit m d a -> Quantity d a
(/~) :: Fractional a => Quantity d a -> Unit m d a -> a
(*) :: (KnownVariant v1, KnownVariant v2, KnownVariant (v1 * v2), Num a) => Dimensional v1 d1 a -> Dimensional v2 d2 a -> Dimensional (v1 * v2) (d1 * d2) a
(/) :: (KnownVariant v1, KnownVariant v2, KnownVariant (v1 / v2), Fractional a) => Dimensional v1 d1 a -> Dimensional v2 d2 a -> Dimensional (v1 / v2) (d1 / d2) a
recip :: Fractional a => Quantity d a -> Quantity (Recip d) a
(^) :: (Fractional a, KnownTypeInt i, KnownVariant v, KnownVariant (Weaken v)) => Dimensional v d1 a -> Proxy i -> Dimensional (Weaken v) (d1 ^ i) a
negate :: Num a => Quantity d a -> Quantity d a
(+) :: Num a => Quantity d a -> Quantity d a -> Quantity d a
(-) :: Num a => Quantity d a -> Quantity d a -> Quantity d a
abs :: Num a => Quantity d a -> Quantity d a
signum :: Num a => Quantity d a -> Dimensionless a
nroot :: (KnownTypeInt n, Floating a) => Proxy n -> Quantity d a -> Quantity (NRoot d n) a
sqrt :: Floating a => Quantity d a -> Quantity (Sqrt d) a
cbrt :: Floating a => Quantity d a -> Quantity (Cbrt d) a
(^/) :: (KnownTypeInt n, Floating a) => Quantity d a -> Proxy n -> Quantity (NRoot d n) a
(*~~) :: (Functor f, Num a) => f a -> Unit m d a -> f (Quantity d a)
(/~~) :: forall f m d a. (Functor f, Fractional a) => f (Quantity d a) -> Unit m d a -> f a
sum :: (Num a, Foldable f) => f (Quantity d a) -> Quantity d a
product :: (Num a, Foldable f) => f (Dimensionless a) -> Dimensionless a
mean :: (Fractional a, Foldable f) => f (Quantity d a) -> Quantity d a
dimensionlessLength :: (Num a, Foldable f) => f b -> Dimensionless a
nFromTo :: (Fractional a, Integral b) => Quantity d a -> Quantity d a -> b -> [Quantity d a]
exp :: Floating a => Dimensionless a -> Dimensionless a
log :: Floating a => Dimensionless a -> Dimensionless a
sin :: Floating a => Dimensionless a -> Dimensionless a
cos :: Floating a => Dimensionless a -> Dimensionless a
tan :: Floating a => Dimensionless a -> Dimensionless a
asin :: Floating a => Dimensionless a -> Dimensionless a
acos :: Floating a => Dimensionless a -> Dimensionless a
atan :: Floating a => Dimensionless a -> Dimensionless a
sinh :: Floating a => Dimensionless a -> Dimensionless a
cosh :: Floating a => Dimensionless a -> Dimensionless a
tanh :: Floating a => Dimensionless a -> Dimensionless a
asinh :: Floating a => Dimensionless a -> Dimensionless a
acosh :: Floating a => Dimensionless a -> Dimensionless a
atanh :: Floating a => Dimensionless a -> Dimensionless a
log1p :: Floating a => Dimensionless a -> Dimensionless a
expm1 :: Floating a => Dimensionless a -> Dimensionless a
log1pexp :: Floating a => Dimensionless a -> Dimensionless a
log1mexp :: Floating a => Dimensionless a -> Dimensionless a
(**) :: Floating a => Dimensionless a -> Dimensionless a -> Dimensionless a
logBase :: Floating a => Dimensionless a -> Dimensionless a -> Dimensionless a
atan2 :: RealFloat a => Quantity d a -> Quantity d a -> Dimensionless a
one :: Num a => Unit NonMetric DOne a
_0 :: Num a => Quantity d a
_1 :: Num a => Dimensionless a
_2 :: Num a => Dimensionless a
_3 :: Num a => Dimensionless a
_4 :: Num a => Dimensionless a
_5 :: Num a => Dimensionless a
_6 :: Num a => Dimensionless a
_7 :: Num a => Dimensionless a
_8 :: Num a => Dimensionless a
_9 :: Num a => Dimensionless a
pi :: Floating a => Dimensionless a
tau :: Floating a => Dimensionless a
changeRep :: (KnownVariant v, Real a, Fractional b) => Dimensional v d a -> Dimensional v d b
changeRepApproximate :: (KnownVariant v, Floating b) => Dimensional v d ExactPi -> Dimensional v d b
asLens :: Fractional a => Unit m d a -> forall f. Functor f => (a -> f a) -> Quantity d a -> f (Quantity d a)
mkUnitR :: Floating a => UnitName m -> ExactPi -> Unit m1 d a -> Unit m d a
mkUnitQ :: Fractional a => UnitName m -> Rational -> Unit m1 d a -> Unit m d a
mkUnitZ :: Num a => UnitName m -> Integer -> Unit m1 d a -> Unit m d a
module Numeric.Units.Dimensional.Quantities
module Numeric.Units.Dimensional.SIUnits
pos5 :: Proxy Pos5
pos4 :: Proxy Pos4
pos3 :: Proxy Pos3
pos2 :: Proxy Pos2
pos1 :: Proxy Pos1
zero :: Proxy Zero
neg1 :: Proxy Neg1
neg2 :: Proxy Neg2
neg3 :: Proxy Neg3
neg4 :: Proxy Neg4
neg5 :: Proxy Neg5
class Category (cat :: k -> k -> Type) where
- id :: cat a a
- (.) :: cat b c -> cat a b -> cat a c
maximum :: (Foldable t, Ord a) => t a -> a
minimum :: (Foldable t, Ord a) => t a -> a
(++) :: [a] -> [a] -> [a]
seq :: a -> b -> b
filter :: (a -> Bool) -> [a] -> [a]
zip :: [a] -> [b] -> [(a, b)]
print :: Show a => a -> IO ()
fst :: (a, b) -> a
snd :: (a, b) -> b
otherwise :: Bool
map :: (a -> b) -> [a] -> [b]
($) :: (a -> b) -> a -> b
fromIntegral :: (Integral a, Num b) => a -> b
realToFrac :: (Real a, Fractional b) => a -> b
class Bounded a where
- minBound :: a
- maxBound :: a
class Enum a where
- succ :: a -> a
- pred :: a -> a
- toEnum :: Int -> a
- fromEnum :: a -> Int
- enumFrom :: a -> [a]
- enumFromThen :: a -> a -> [a]
- enumFromTo :: a -> a -> [a]
- enumFromThenTo :: a -> a -> a -> [a]
class Eq a where
- (==) :: a -> a -> Bool
- (/=) :: a -> a -> Bool
class Fractional a => Floating a
class Num a => Fractional a where
- fromRational :: Rational -> a
class (Real a, Enum a) => Integral a where
- quot :: a -> a -> a
- rem :: a -> a -> a
- div :: a -> a -> a
- mod :: a -> a -> a
- quotRem :: a -> a -> (a, a)
- divMod :: a -> a -> (a, a)
- toInteger :: a -> Integer
class Applicative m => Monad (m :: Type -> Type) where
- (>>=) :: m a -> (a -> m b) -> m b
- (>>) :: m a -> m b -> m b
- return :: a -> m a
- fail :: String -> m a
class Functor (f :: Type -> Type) where
- fmap :: (a -> b) -> f a -> f b
- (<$) :: a -> f b -> f a
class Num a where
- fromInteger :: Integer -> a
class Eq a => Ord a where
- compare :: a -> a -> Ordering
- (<) :: a -> a -> Bool
- (<=) :: a -> a -> Bool
- (>) :: a -> a -> Bool
- (>=) :: a -> a -> Bool
- max :: a -> a -> a
- min :: a -> a -> a
class Read a where
- readsPrec :: Int -> ReadS a
- readList :: ReadS [a]
class (Num a, Ord a) => Real a where
- toRational :: a -> Rational
class (RealFrac a, Floating a) => RealFloat a where
- floatRadix :: a -> Integer
- floatDigits :: a -> Int
- floatRange :: a -> (Int, Int)
- decodeFloat :: a -> (Integer, Int)
- encodeFloat :: Integer -> Int -> a
- exponent :: a -> Int
- significand :: a -> a
- scaleFloat :: Int -> a -> a
- isNaN :: a -> Bool
- isInfinite :: a -> Bool
- isDenormalized :: a -> Bool
- isNegativeZero :: a -> Bool
- isIEEE :: a -> Bool
class (Real a, Fractional a) => RealFrac a where
- properFraction :: Integral b => a -> (b, a)
- truncate :: Integral b => a -> b
- round :: Integral b => a -> b
- ceiling :: Integral b => a -> b
- floor :: Integral b => a -> b
class Show a where
- showsPrec :: Int -> a -> ShowS
- show :: a -> String
- showList :: [a] -> ShowS
class Functor f => Applicative (f :: Type -> Type) where
- pure :: a -> f a
- (<*>) :: f (a -> b) -> f a -> f b
- (*>) :: f a -> f b -> f b
- (<*) :: f a -> f b -> f a
class Foldable (t :: Type -> Type) where
- foldMap :: Monoid m => (a -> m) -> t a -> m
- foldr :: (a -> b -> b) -> b -> t a -> b
- foldl :: (b -> a -> b) -> b -> t a -> b
- foldr1 :: (a -> a -> a) -> t a -> a
- foldl1 :: (a -> a -> a) -> t a -> a
- null :: t a -> Bool
- length :: t a -> Int
- elem :: Eq a => a -> t a -> Bool
class (Functor t, Foldable t) => Traversable (t :: Type -> Type) where
- traverse :: Applicative f => (a -> f b) -> t a -> f (t b)
- sequenceA :: Applicative f => t (f a) -> f (t a)
- mapM :: Monad m => (a -> m b) -> t a -> m (t b)
- sequence :: Monad m => t (m a) -> m (t a)
class Semigroup a where
- (<>) :: a -> a -> a
class Semigroup a => Monoid a where
- mempty :: a
- mappend :: a -> a -> a
- mconcat :: [a] -> a
data Bool
- = False
- | True
data Char
data Double
data Float
data Int
data Integer
data Maybe a
- = Nothing
- | Just a
data Ordering
- = LT
- | EQ
- | GT
type Rational = Ratio Integer
data IO a
data Word
data Either a b
- = Left a
- | Right b
readIO :: Read a => String -> IO a
readLn :: Read a => IO a
appendFile :: FilePath -> String -> IO ()
writeFile :: FilePath -> String -> IO ()
readFile :: FilePath -> IO String
interact :: (String -> String) -> IO ()
getContents :: IO String
getLine :: IO String
getChar :: IO Char
putStrLn :: String -> IO ()
putStr :: String -> IO ()
putChar :: Char -> IO ()
ioError :: IOError -> IO a
type FilePath = String
userError :: String -> IOError
type IOError = IOException
notElem :: (Foldable t, Eq a) => a -> t a -> Bool
all :: Foldable t => (a -> Bool) -> t a -> Bool
any :: Foldable t => (a -> Bool) -> t a -> Bool
or :: Foldable t => t Bool -> Bool
and :: Foldable t => t Bool -> Bool
concatMap :: Foldable t => (a -> [b]) -> t a -> [b]
concat :: Foldable t => t [a] -> [a]
sequence_ :: (Foldable t, Monad m) => t (m a) -> m ()
mapM_ :: (Foldable t, Monad m) => (a -> m b) -> t a -> m ()
unwords :: [String] -> String
words :: String -> [String]
unlines :: [String] -> String
lines :: String -> [String]
read :: Read a => String -> a
reads :: Read a => ReadS a
either :: (a -> c) -> (b -> c) -> Either a b -> c
lex :: ReadS String
readParen :: Bool -> ReadS a -> ReadS a
type ReadS a = String -> [(a, String)]
(<$>) :: Functor f => (a -> b) -> f a -> f b
lcm :: Integral a => a -> a -> a
gcd :: Integral a => a -> a -> a
(^^) :: (Fractional a, Integral b) => a -> b -> a
odd :: Integral a => a -> Bool
even :: Integral a => a -> Bool
showParen :: Bool -> ShowS -> ShowS
showString :: String -> ShowS
showChar :: Char -> ShowS
shows :: Show a => a -> ShowS
type ShowS = String -> String
unzip3 :: [(a, b, c)] -> ([a], [b], [c])
unzip :: [(a, b)] -> ([a], [b])
zipWith3 :: (a -> b -> c -> d) -> [a] -> [b] -> [c] -> [d]
zipWith :: (a -> b -> c) -> [a] -> [b] -> [c]
zip3 :: [a] -> [b] -> [c] -> [(a, b, c)]
(!!) :: [a] -> Int -> a
lookup :: Eq a => a -> [(a, b)] -> Maybe b
reverse :: [a] -> [a]
break :: (a -> Bool) -> [a] -> ([a], [a])
span :: (a -> Bool) -> [a] -> ([a], [a])
splitAt :: Int -> [a] -> ([a], [a])
drop :: Int -> [a] -> [a]
take :: Int -> [a] -> [a]
dropWhile :: (a -> Bool) -> [a] -> [a]
takeWhile :: (a -> Bool) -> [a] -> [a]
cycle :: [a] -> [a]
replicate :: Int -> a -> [a]
repeat :: a -> [a]
iterate :: (a -> a) -> a -> [a]
scanr1 :: (a -> a -> a) -> [a] -> [a]
scanr :: (a -> b -> b) -> b -> [a] -> [b]
scanl1 :: (a -> a -> a) -> [a] -> [a]
scanl :: (b -> a -> b) -> b -> [a] -> [b]
init :: [a] -> [a]
last :: [a] -> a
tail :: [a] -> [a]
head :: [a] -> a
maybe :: b -> (a -> b) -> Maybe a -> b
uncurry :: (a -> b -> c) -> (a, b) -> c
curry :: ((a, b) -> c) -> a -> b -> c
subtract :: Num a => a -> a -> a
asTypeOf :: a -> a -> a
until :: (a -> Bool) -> (a -> a) -> a -> a
($!) :: (a -> b) -> a -> b
flip :: (a -> b -> c) -> b -> a -> c
const :: a -> b -> a
(=<<) :: Monad m => (a -> m b) -> m a -> m b
type String = [Char]
undefined :: HasCallStack => a
errorWithoutStackTrace :: [Char] -> a
error :: HasCallStack => [Char] -> a
(&&) :: Bool -> Bool -> Bool
(||) :: Bool -> Bool -> Bool
not :: Bool -> Bool

Documentation

class HasDynamicDimension a => HasDimension a where Source #

Dimensional values inhabit this class, which allows access to a term-level representation of their dimension.

Methods

dimension :: a -> Dimension' Source #

Obtains a term-level representation of a value's dimension.

Instances

HasDimension Dimension' Source #
Instance details Defined in Numeric.Units.Dimensional.Dimensions.TermLevel Methods dimension :: Dimension' -> Dimension' Source #
HasDimension AnyUnit Source #
Instance details Defined in Numeric.Units.Dimensional.Dynamic Methods dimension :: AnyUnit -> Dimension' Source #
HasDimension (AnyQuantity a) Source #
Instance details Defined in Numeric.Units.Dimensional.Dynamic Methods dimension :: AnyQuantity a -> Dimension' Source #
(KnownTypeInt l, KnownTypeInt m, KnownTypeInt t, KnownTypeInt i, KnownTypeInt th, KnownTypeInt n, KnownTypeInt j) => HasDimension (Proxy (Dim l m t i th n j)) Source #
Instance details Defined in Numeric.Units.Dimensional.Dimensions.TypeLevel Methods dimension :: Proxy (Dim l m t i th n j) -> Dimension' Source #
KnownDimension d => HasDimension (Dimensional v d a) Source #
Instance details Defined in Numeric.Units.Dimensional.Internal Methods dimension :: Dimensional v d a -> Dimension' Source #

data Dimension' Source #

A physical dimension, encoded as 7 integers, representing a factorization of the dimension into the 7 SI base dimensions. By convention they are stored in the same order as in the Dimension data kind.

Constructors

Dim' !Int !Int !Int !Int !Int !Int !Int

Instances

Eq Dimension' Source #
Instance details Defined in Numeric.Units.Dimensional.Dimensions.TermLevel Methods (==) :: Dimension' -> Dimension' -> Bool # (/=) :: Dimension' -> Dimension' -> Bool #
Data Dimension' Source #
Instance details Defined in Numeric.Units.Dimensional.Dimensions.TermLevel Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Dimension' -> c Dimension' # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Dimension' # toConstr :: Dimension' -> Constr # dataTypeOf :: Dimension' -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c Dimension') # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Dimension') # gmapT :: (forall b. Data b => b -> b) -> Dimension' -> Dimension' # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Dimension' -> r # gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Dimension' -> r # gmapQ :: (forall d. Data d => d -> u) -> Dimension' -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> Dimension' -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Dimension' -> m Dimension' # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Dimension' -> m Dimension' # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Dimension' -> m Dimension' #
Ord Dimension' Source #
Instance details Defined in Numeric.Units.Dimensional.Dimensions.TermLevel Methods compare :: Dimension' -> Dimension' -> Ordering # (<) :: Dimension' -> Dimension' -> Bool # (<=) :: Dimension' -> Dimension' -> Bool # (>) :: Dimension' -> Dimension' -> Bool # (>=) :: Dimension' -> Dimension' -> Bool # max :: Dimension' -> Dimension' -> Dimension' # min :: Dimension' -> Dimension' -> Dimension' #
Show Dimension' Source #
Instance details Defined in Numeric.Units.Dimensional.Dimensions.TermLevel Methods showsPrec :: Int -> Dimension' -> ShowS # show :: Dimension' -> String # showList :: [Dimension'] -> ShowS #
Generic Dimension' Source #
Instance details Defined in Numeric.Units.Dimensional.Dimensions.TermLevel Associated Types type Rep Dimension' :: Type -> Type # Methods from :: Dimension' -> Rep Dimension' x # to :: Rep Dimension' x -> Dimension' #
Semigroup Dimension' Source #
Instance details Defined in Numeric.Units.Dimensional.Dimensions.TermLevel Methods (<>) :: Dimension' -> Dimension' -> Dimension' # sconcat :: NonEmpty Dimension' -> Dimension' # stimes :: Integral b => b -> Dimension' -> Dimension' #
Monoid Dimension' Source #	The monoid of dimensions under multiplication.
Instance details Defined in Numeric.Units.Dimensional.Dimensions.TermLevel Methods mempty :: Dimension' # mappend :: Dimension' -> Dimension' -> Dimension' # mconcat :: [Dimension'] -> Dimension' #
NFData Dimension' Source #
Instance details Defined in Numeric.Units.Dimensional.Dimensions.TermLevel Methods rnf :: Dimension' -> () #
HasDimension Dimension' Source #
Instance details Defined in Numeric.Units.Dimensional.Dimensions.TermLevel Methods dimension :: Dimension' -> Dimension' Source #
HasDynamicDimension Dimension' Source #
Instance details Defined in Numeric.Units.Dimensional.Dimensions.TermLevel Methods dynamicDimension :: Dimension' -> DynamicDimension Source #
type Rep Dimension' Source #
Instance details Defined in Numeric.Units.Dimensional.Dimensions.TermLevel type Rep Dimension' = D1 (MetaData "Dimension'" "Numeric.Units.Dimensional.Dimensions.TermLevel" "dimensional-1.3-7Gh1mp5ZBGaGfkDr7lUYf2" False) (C1 (MetaCons "Dim'" PrefixI False) ((S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) (Rec0 Int) :: (S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) (Rec0 Int) :: S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) (Rec0 Int))) :: ((S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) (Rec0 Int) :: S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) (Rec0 Int)) :: (S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) (Rec0 Int) :: S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) (Rec0 Int)))))

type KnownDimension (d :: Dimension) = HasDimension (Proxy d) Source #

A KnownDimension is one for which we can construct a term-level representation. Each validly constructed type of kind Dimension has a KnownDimension instance.

While KnownDimension is a constraint synonym, the presence of KnownDimension d in a context allows use of dimension :: Proxy d -> Dimension'.

type Cbrt d = NRoot d Pos3 Source #

Cube root is a special case of NRoot with order 3.

type Sqrt d = NRoot d Pos2 Source #

Square root is a special case of NRoot with order 2.

type family NRoot (d :: Dimension) (x :: TypeInt) where ... Source #

Roots of dimensions corresponds to division of the base dimensions' exponents by the order of the root.

Equations

NRoot DOne x = DOne
NRoot d Pos1 = d
NRoot (Dim l m t i th n j) x = Dim (l / x) (m / x) (t / x) (i / x) (th / x) (n / x) (j / x)

type family (d :: Dimension) ^ (x :: TypeInt) where ... infixr 8 Source #

Powers of dimensions corresponds to multiplication of the base dimensions' exponents by the exponent.

We limit ourselves to integer powers of Dimensionals as fractional powers make little physical sense.

Equations

DOne ^ x = DOne
d ^ Zero = DOne
d ^ Pos1 = d
(Dim l m t i th n j) ^ x = Dim (l * x) (m * x) (t * x) (i * x) (th * x) (n * x) (j * x)

type Recip (d :: Dimension) = DOne / d Source #

The reciprocal of a dimension is defined as the result of dividing DOne by it, or of negating each of the base dimensions' exponents.

type family (a :: Dimension) / (d :: Dimension) where ... infixl 7 Source #

Division of dimensions corresponds to subtraction of the base dimensions' exponents.

Equations

d / DOne = d
d / d = DOne
(Dim l m t i th n j) / (Dim l' m' t' i' th' n' j') = Dim (l - l') (m - m') (t - t') (i - i') (th - th') (n - n') (j - j')

type family (a :: Dimension) * (b :: Dimension) where ... infixl 7 Source #

Multiplication of dimensions corresponds to adding of the base dimensions' exponents.

Equations

DOne * d = d
d * DOne = d
(Dim l m t i th n j) * (Dim l' m' t' i' th' n' j') = Dim (l + l') (m + m') (t + t') (i + i') (th + th') (n + n') (j + j')

type DLuminousIntensity = Dim Zero Zero Zero Zero Zero Zero Pos1 Source #

type DAmountOfSubstance = Dim Zero Zero Zero Zero Zero Pos1 Zero Source #

type DThermodynamicTemperature = Dim Zero Zero Zero Zero Pos1 Zero Zero Source #

type DElectricCurrent = Dim Zero Zero Zero Pos1 Zero Zero Zero Source #

type DTime = Dim Zero Zero Pos1 Zero Zero Zero Zero Source #

type DMass = Dim Zero Pos1 Zero Zero Zero Zero Zero Source #

type DLength = Dim Pos1 Zero Zero Zero Zero Zero Zero Source #

type DOne = Dim Zero Zero Zero Zero Zero Zero Zero Source #

The type-level dimension of dimensionless values.

data Dimension Source #

Represents a physical dimension in the basis of the 7 SI base dimensions, where the respective dimensions are represented by type variables using the following convention:

l: Length
m: Mass
t: Time
i: Electric current
th: Thermodynamic temperature
n: Amount of substance
j: Luminous intensity

For the equivalent term-level representation, see Dimension'

Constructors

Dim TypeInt TypeInt TypeInt TypeInt TypeInt TypeInt TypeInt

Instances

(KnownTypeInt l, KnownTypeInt m, KnownTypeInt t, KnownTypeInt i, KnownTypeInt th, KnownTypeInt n, KnownTypeInt j) => HasDimension (Proxy (Dim l m t i th n j)) Source #
Instance details Defined in Numeric.Units.Dimensional.Dimensions.TypeLevel Methods dimension :: Proxy (Dim l m t i th n j) -> Dimension' Source #
(KnownTypeInt l, KnownTypeInt m, KnownTypeInt t, KnownTypeInt i, KnownTypeInt th, KnownTypeInt n, KnownTypeInt j) => HasDynamicDimension (Proxy (Dim l m t i th n j)) Source #
Instance details Defined in Numeric.Units.Dimensional.Dimensions.TypeLevel Methods dynamicDimension :: Proxy (Dim l m t i th n j) -> DynamicDimension Source #

data Metricality Source #

Encodes whether a unit is a metric unit, that is, whether it can be combined with a metric prefix to form a related unit.

Constructors

Metric	Capable of receiving a metric prefix.
NonMetric	Incapable of receiving a metric prefix.

Instances

Eq Metricality Source #
Instance details Defined in Numeric.Units.Dimensional.Variants Methods (==) :: Metricality -> Metricality -> Bool # (/=) :: Metricality -> Metricality -> Bool #
Data Metricality Source #
Instance details Defined in Numeric.Units.Dimensional.Variants Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Metricality -> c Metricality # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Metricality # toConstr :: Metricality -> Constr # dataTypeOf :: Metricality -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c Metricality) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Metricality) # gmapT :: (forall b. Data b => b -> b) -> Metricality -> Metricality # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Metricality -> r # gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Metricality -> r # gmapQ :: (forall d. Data d => d -> u) -> Metricality -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> Metricality -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Metricality -> m Metricality # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Metricality -> m Metricality # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Metricality -> m Metricality #
Ord Metricality Source #
Instance details Defined in Numeric.Units.Dimensional.Variants Methods compare :: Metricality -> Metricality -> Ordering # (<) :: Metricality -> Metricality -> Bool # (<=) :: Metricality -> Metricality -> Bool # (>) :: Metricality -> Metricality -> Bool # (>=) :: Metricality -> Metricality -> Bool # max :: Metricality -> Metricality -> Metricality # min :: Metricality -> Metricality -> Metricality #
Generic Metricality Source #
Instance details Defined in Numeric.Units.Dimensional.Variants Associated Types type Rep Metricality :: Type -> Type # Methods from :: Metricality -> Rep Metricality x # to :: Rep Metricality x -> Metricality #
NFData Metricality Source #
Instance details Defined in Numeric.Units.Dimensional.Variants Methods rnf :: Metricality -> () #
type Rep Metricality Source #
Instance details Defined in Numeric.Units.Dimensional.Variants type Rep Metricality = D1 (MetaData "Metricality" "Numeric.Units.Dimensional.Variants" "dimensional-1.3-7Gh1mp5ZBGaGfkDr7lUYf2" False) (C1 (MetaCons "Metric" PrefixI False) (U1 :: Type -> Type) :+: C1 (MetaCons "NonMetric" PrefixI False) (U1 :: Type -> Type))

class KnownVariant (v :: Variant) Source #

A KnownVariant is one whose term-level Dimensional values we can represent with an associated data family instance and manipulate with certain functions, not all of which are exported from the package.

Each validly constructed type of kind Variant has a KnownVariant instance.

Minimal complete definition

extractValue, extractName, injectValue, dmap

Associated Types

data Dimensional v :: Dimension -> Type -> Type Source #

A dimensional value, either a Quantity or a Unit, parameterized by its Dimension and representation.

Instances

KnownVariant (DQuantity s) Source #
Instance details Defined in Numeric.Units.Dimensional.Internal Associated Types data Dimensional (DQuantity s) a b :: Type Source # type ScaleFactor (DQuantity s) :: ExactPi' Methods extractValue :: Dimensional (DQuantity s) d a -> (a, Maybe ExactPi) extractName :: Dimensional (DQuantity s) d a -> Maybe (UnitName NonMetric) injectValue :: Maybe (UnitName NonMetric) -> (a, Maybe ExactPi) -> Dimensional (DQuantity s) d a dmap :: (a1 -> a2) -> Dimensional (DQuantity s) d a1 -> Dimensional (DQuantity s) d a2 Source #
Typeable m => KnownVariant (DUnit m) Source #
Instance details Defined in Numeric.Units.Dimensional.Internal Associated Types data Dimensional (DUnit m) a b :: Type Source # type ScaleFactor (DUnit m) :: ExactPi' Methods extractValue :: Dimensional (DUnit m) d a -> (a, Maybe ExactPi) extractName :: Dimensional (DUnit m) d a -> Maybe (UnitName NonMetric) injectValue :: Maybe (UnitName NonMetric) -> (a, Maybe ExactPi) -> Dimensional (DUnit m) d a dmap :: (a1 -> a2) -> Dimensional (DUnit m) d a1 -> Dimensional (DUnit m) d a2 Source #

type Quantity = SQuantity One Source #

A dimensional quantity.

type Unit (m :: Metricality) = Dimensional (DUnit m) Source #

A unit of measurement.

siUnit :: forall d a. (KnownDimension d, Num a) => Unit NonMetric d a Source #

A polymorphic Unit which can be used in place of the coherent SI base unit of any dimension. This allows polymorphic quantity creation and destruction without exposing the Dimensional constructor.

showIn :: (Show a, Fractional a) => Unit m d a -> Quantity d a -> String Source #

Shows the value of a Quantity expressed in a specified Unit of the same Dimension.

Uses non-breaking spaces between the value and the unit, and within the unit name.

>>> putStrLn $ showIn watt $ (37 *~ volt) * (4 *~ ampere)
148.0 W

type LuminousIntensity = Quantity DLuminousIntensity Source #

type AmountOfSubstance = Quantity DAmountOfSubstance Source #

type ThermodynamicTemperature = Quantity DThermodynamicTemperature Source #

type ElectricCurrent = Quantity DElectricCurrent Source #

type Time = Quantity DTime Source #

type Mass = Quantity DMass Source #

type Length = Quantity DLength Source #

type Dimensionless = Quantity DOne Source #

name :: Unit m d a -> UnitName m Source #

Extracts the UnitName of a Unit.

exactValue :: Unit m d a -> ExactPi Source #

Extracts the exact value of a Unit, expressed in terms of the SI coherent derived unit (see siUnit) of the same Dimension.

Note that the actual value may in some cases be approximate, for example if the unit is defined by experiment.

weaken :: Unit m d a -> Unit NonMetric d a Source #

Discards potentially unwanted type level information about a Unit.

strengthen :: Unit m d a -> Maybe (Unit Metric d a) Source #

Attempts to convert a Unit which may or may not be Metric to one which is certainly Metric.

exactify :: Unit m d a -> Unit m d ExactPi Source #

Forms the exact version of a Unit.

(*~) :: Num a => a -> Unit m d a -> Quantity d a infixl 7 Source #

Forms a Quantity by multipliying a number and a unit.

(/~) :: Fractional a => Quantity d a -> Unit m d a -> a infixl 7 Source #

Divides a Quantity by a Unit of the same physical dimension, obtaining the numerical value of the quantity expressed in that unit.

(*) :: (KnownVariant v1, KnownVariant v2, KnownVariant (v1 * v2), Num a) => Dimensional v1 d1 a -> Dimensional v2 d2 a -> Dimensional (v1 * v2) (d1 * d2) a infixl 7 Source #

Multiplies two Quantitys or two Units.

The intimidating type signature captures the similarity between these operations and ensures that composite Units are NonMetric.

(/) :: (KnownVariant v1, KnownVariant v2, KnownVariant (v1 / v2), Fractional a) => Dimensional v1 d1 a -> Dimensional v2 d2 a -> Dimensional (v1 / v2) (d1 / d2) a infixl 7 Source #

Divides one Quantity by another or one Unit by another.

The intimidating type signature captures the similarity between these operations and ensures that composite Units are NotPrefixable.

recip :: Fractional a => Quantity d a -> Quantity (Recip d) a Source #

Forms the reciprocal of a Quantity, which has the reciprocal dimension.

>>> recip $ 47 *~ hertz
2.127659574468085e-2 s

(^) :: (Fractional a, KnownTypeInt i, KnownVariant v, KnownVariant (Weaken v)) => Dimensional v d1 a -> Proxy i -> Dimensional (Weaken v) (d1 ^ i) a infixr 8 Source #

Raises a Quantity or Unit to an integer power.

Because the power chosen impacts the Dimension of the result, it is necessary to supply a type-level representation of the exponent in the form of a Proxy to some TypeInt. Convenience values pos1, pos2, neg1, ... are supplied by the Numeric.NumType.DK.Integers module. The most commonly used ones are also reexported by Numeric.Units.Dimensional.Prelude.

The intimidating type signature captures the similarity between these operations and ensures that composite Units are NotPrefixable.

negate :: Num a => Quantity d a -> Quantity d a Source #

Negates the value of a Quantity.

(+) :: Num a => Quantity d a -> Quantity d a -> Quantity d a infixl 6 Source #

Adds two Quantitys.

(-) :: Num a => Quantity d a -> Quantity d a -> Quantity d a infixl 6 Source #

Subtracts one Quantity from another.

abs :: Num a => Quantity d a -> Quantity d a Source #

Takes the absolute value of a Quantity.

signum :: Num a => Quantity d a -> Dimensionless a Source #

Takes the sign of a Quantity. The functions abs and signum satisy the law that:

abs x * signum x == x

The sign is either negate _1 (negative), _0 (zero), or _1 (positive).

nroot :: (KnownTypeInt n, Floating a) => Proxy n -> Quantity d a -> Quantity (NRoot d n) a Source #

Computes the nth root of a Quantity using **.

The NRoot type family will prevent application of this operator where the result would have a fractional dimension or where n is zero.

Because the root chosen impacts the Dimension of the result, it is necessary to supply a type-level representation of the root in the form of a Proxy to some TypeInt. Convenience values pos1, pos2, neg1, ... are supplied by the Numeric.NumType.DK.Integers module. The most commonly used ones are also reexported by Numeric.Units.Dimensional.Prelude.

n must not be zero. Negative roots are defined such that nroot (Proxy :: Proxy (Negate n)) x == nroot (Proxy :: Proxy n) (recip x).

Also available in operator form, see ^/.

sqrt :: Floating a => Quantity d a -> Quantity (Sqrt d) a Source #

Computes the square root of a Quantity using **.

The NRoot type family will prevent application where the supplied quantity does not have a square dimension.

(x :: Area Double) >= _0 ==> sqrt x == nroot pos2 x

cbrt :: Floating a => Quantity d a -> Quantity (Cbrt d) a Source #

Computes the cube root of a Quantity using **.

The NRoot type family will prevent application where the supplied quantity does not have a cubic dimension.

(x :: Volume Double) >= _0 ==> cbrt x == nroot pos3 x

(^/) :: (KnownTypeInt n, Floating a) => Quantity d a -> Proxy n -> Quantity (NRoot d n) a infixr 8 Source #

Computes the nth root of a Quantity using **.

The NRoot type family will prevent application of this operator where the result would have a fractional dimension or where n is zero.

Because the root chosen impacts the Dimension of the result, it is necessary to supply a type-level representation of the root in the form of a Proxy to some TypeInt. Convenience values pos1, pos2, neg1, ... are supplied by the Numeric.NumType.DK.Integers module. The most commonly used ones are also reexported by Numeric.Units.Dimensional.Prelude.

Also available in prefix form, see nroot.

(*~~) :: (Functor f, Num a) => f a -> Unit m d a -> f (Quantity d a) infixl 7 Source #

Applies *~ to all values in a functor.

(/~~) :: forall f m d a. (Functor f, Fractional a) => f (Quantity d a) -> Unit m d a -> f a infixl 7 Source #

Applies /~ to all values in a functor.

sum :: (Num a, Foldable f) => f (Quantity d a) -> Quantity d a Source #

The sum of all elements in a foldable structure.

>>> sum ([] :: [Mass Double])
0.0 kg

>>> sum [12.4 *~ meter, 1 *~ foot]
12.7048 m

product :: (Num a, Foldable f) => f (Dimensionless a) -> Dimensionless a Source #

The product of all elements in a foldable structure.

>>> product ([] :: [Dimensionless Double])
1.0

>>> product [pi, _4, 0.36 *~ one]
4.523893421169302

mean :: (Fractional a, Foldable f) => f (Quantity d a) -> Quantity d a Source #

The arithmetic mean of all elements in a foldable structure.

>>> mean [pi, _7]
5.070796326794897

dimensionlessLength :: (Num a, Foldable f) => f b -> Dimensionless a Source #

The length of the foldable data structure as a Dimensionless. This can be useful for purposes of e.g. calculating averages.

>>> dimensionlessLength ["foo", "bar"]
2

nFromTo Source #

Arguments

:: (Fractional a, Integral b)
=> Quantity d a	The initial value.
-> Quantity d a	The final value.
-> b	The number of intermediate values. If less than one, no intermediate values will result.
-> [Quantity d a]

Returns a list of quantities between given bounds.

n <= 0 ==> nFromTo (x :: Mass Double) (y :: Mass Double) n == [x, y]

(x :: Length Double) <= (y :: Length Double) ==> all (\z -> x <= z && z <= y) (nFromTo x y n)

>>> nFromTo _0 _3 2
[0.0,1.0,2.0,3.0]

>>> nFromTo _1 _0 7
[1.0,0.875,0.75,0.625,0.5,0.375,0.25,0.125,0.0]

>>> nFromTo _0 _1 (-5)
[0.0,1.0]

exp :: Floating a => Dimensionless a -> Dimensionless a Source #

log :: Floating a => Dimensionless a -> Dimensionless a Source #

sin :: Floating a => Dimensionless a -> Dimensionless a Source #

cos :: Floating a => Dimensionless a -> Dimensionless a Source #

tan :: Floating a => Dimensionless a -> Dimensionless a Source #

asin :: Floating a => Dimensionless a -> Dimensionless a Source #

acos :: Floating a => Dimensionless a -> Dimensionless a Source #

atan :: Floating a => Dimensionless a -> Dimensionless a Source #

sinh :: Floating a => Dimensionless a -> Dimensionless a Source #

cosh :: Floating a => Dimensionless a -> Dimensionless a Source #

tanh :: Floating a => Dimensionless a -> Dimensionless a Source #

asinh :: Floating a => Dimensionless a -> Dimensionless a Source #

acosh :: Floating a => Dimensionless a -> Dimensionless a Source #

atanh :: Floating a => Dimensionless a -> Dimensionless a Source #

log1p :: Floating a => Dimensionless a -> Dimensionless a Source #

expm1 :: Floating a => Dimensionless a -> Dimensionless a Source #

log1pexp :: Floating a => Dimensionless a -> Dimensionless a Source #

log1mexp :: Floating a => Dimensionless a -> Dimensionless a Source #

(**) :: Floating a => Dimensionless a -> Dimensionless a -> Dimensionless a infixr 8 Source #

Raises a dimensionless quantity to a dimensionless power.

logBase :: Floating a => Dimensionless a -> Dimensionless a -> Dimensionless a Source #

Takes the logarithm of the second argument in the base of the first.

>>> logBase _2 _8
3.0

atan2 :: RealFloat a => Quantity d a -> Quantity d a -> Dimensionless a Source #

The standard two argument arctangent function. Since it interprets its two arguments in comparison with one another, the input may have any dimension.

>>> atan2 _0 _1
0.0

>>> atan2 _1 _0
1.5707963267948966

>>> atan2 _0 (negate _1)
3.141592653589793

>>> atan2 (negate _1) _0
-1.5707963267948966

one :: Num a => Unit NonMetric DOne a Source #

The unit one has dimension DOne and is the base unit of dimensionless values.

As detailed in 7.10 "Values of quantities expressed simply as numbers: the unit one, symbol 1" of [1] the unit one generally does not appear in expressions. However, for us it is necessary to use one as we would any other unit to perform the "boxing" of dimensionless values.

_0 :: Num a => Quantity d a Source #

The constant for zero is polymorphic, allowing it to express zero Length or Capacitance or Velocity etc, in addition to the Dimensionless value zero.

_1 :: Num a => Dimensionless a Source #

_2 :: Num a => Dimensionless a Source #

_3 :: Num a => Dimensionless a Source #

_4 :: Num a => Dimensionless a Source #

_5 :: Num a => Dimensionless a Source #

_6 :: Num a => Dimensionless a Source #

_7 :: Num a => Dimensionless a Source #

_8 :: Num a => Dimensionless a Source #

_9 :: Num a => Dimensionless a Source #

pi :: Floating a => Dimensionless a Source #

tau :: Floating a => Dimensionless a Source #

Twice pi.

For background on tau see http://tauday.com/tau-manifesto (but also feel free to review http://www.thepimanifesto.com).

changeRep :: (KnownVariant v, Real a, Fractional b) => Dimensional v d a -> Dimensional v d b Source #

Convenient conversion between numerical types while retaining dimensional information.

>>> let x = (37 :: Rational) *~ poundMass
>>> changeRep x :: Mass Double
16.78291769 kg

changeRepApproximate :: (KnownVariant v, Floating b) => Dimensional v d ExactPi -> Dimensional v d b Source #

Convenient conversion from exactly represented values while retaining dimensional information.

asLens :: Fractional a => Unit m d a -> forall f. Functor f => (a -> f a) -> Quantity d a -> f (Quantity d a) Source #

Converts a Unit into a lens from Quantitys to values.

mkUnitR :: Floating a => UnitName m -> ExactPi -> Unit m1 d a -> Unit m d a Source #

Forms a new atomic Unit by specifying its UnitName and its definition as a multiple of another Unit.

Use this variant when the scale factor of the resulting unit is irrational or Approximate. See mkUnitQ for when it is rational and mkUnitZ for when it is an integer.

Note that supplying zero as a definining quantity is invalid, as the library relies upon units forming a group under multiplication.

Supplying negative defining quantities is allowed and handled gracefully, but is discouraged on the grounds that it may be unexpected by other readers.

mkUnitQ :: Fractional a => UnitName m -> Rational -> Unit m1 d a -> Unit m d a Source #

Forms a new atomic Unit by specifying its UnitName and its definition as a multiple of another Unit.

Use this variant when the scale factor of the resulting unit is rational. See mkUnitZ for when it is an integer and mkUnitR for the general case.

For more information see mkUnitR.

mkUnitZ :: Num a => UnitName m -> Integer -> Unit m1 d a -> Unit m d a Source #

Forms a new atomic Unit by specifying its UnitName and its definition as a multiple of another Unit.

Use this variant when the scale factor of the resulting unit is an integer. See mkUnitQ for when it is rational and mkUnitR for the general case.

For more information see mkUnitR.

module Numeric.Units.Dimensional.Quantities

module Numeric.Units.Dimensional.SIUnits

pos5 :: Proxy Pos5 #

pos4 :: Proxy Pos4 #

pos3 :: Proxy Pos3 #

pos2 :: Proxy Pos2 #

pos1 :: Proxy Pos1 #

zero :: Proxy Zero #

neg1 :: Proxy Neg1 #

neg2 :: Proxy Neg2 #

neg3 :: Proxy Neg3 #

neg4 :: Proxy Neg4 #

neg5 :: Proxy Neg5 #

class Category (cat :: k -> k -> Type) where #

A class for categories. Instances should satisfy the laws

f . id  =  f  -- (right identity)
id . f  =  f  -- (left identity)
f . (g . h)  =  (f . g) . h  -- (associativity)

Methods

id :: cat a a #

the identity morphism

(.) :: cat b c -> cat a b -> cat a c infixr 9 #

morphism composition

Instances

Category (Coercion :: k -> k -> Type)	Since: base-4.7.0.0
Instance details Defined in Control.Category Methods id :: Coercion a a # (.) :: Coercion b c -> Coercion a b -> Coercion a c #
Category ((:~:) :: k -> k -> Type)	Since: base-4.7.0.0
Instance details Defined in Control.Category Methods id :: a :~: a # (.) :: (b :~: c) -> (a :~: b) -> a :~: c #
Category ((:~~:) :: k -> k -> Type)	Since: base-4.10.0.0
Instance details Defined in Control.Category Methods id :: a :~~: a # (.) :: (b :~~: c) -> (a :~~: b) -> a :~~: c #
Category ((->) :: Type -> Type -> Type)	Since: base-3.0
Instance details Defined in Control.Category Methods id :: a -> a # (.) :: (b -> c) -> (a -> b) -> a -> c #

maximum :: (Foldable t, Ord a) => t a -> a #

The largest element of a non-empty structure.

minimum :: (Foldable t, Ord a) => t a -> a #

The least element of a non-empty structure.

(++) :: [a] -> [a] -> [a] infixr 5 #

Append two lists, i.e.,

[x1, ..., xm] ++ [y1, ..., yn] == [x1, ..., xm, y1, ..., yn]
[x1, ..., xm] ++ [y1, ...] == [x1, ..., xm, y1, ...]

If the first list is not finite, the result is the first list.

seq :: a -> b -> b #

The value of seq a b is bottom if a is bottom, and otherwise equal to b. In other words, it evaluates the first argument a to weak head normal form (WHNF). seq is usually introduced to improve performance by avoiding unneeded laziness.

A note on evaluation order: the expression seq a b does not guarantee that a will be evaluated before b. The only guarantee given by seq is that the both a and b will be evaluated before seq returns a value. In particular, this means that b may be evaluated before a. If you need to guarantee a specific order of evaluation, you must use the function pseq from the "parallel" package.

filter :: (a -> Bool) -> [a] -> [a] #

filter, applied to a predicate and a list, returns the list of those elements that satisfy the predicate; i.e.,

filter p xs = [ x | x <- xs, p x]

zip :: [a] -> [b] -> [(a, b)] #

zip takes two lists and returns a list of corresponding pairs.

zip [1, 2] ['a', 'b'] = [(1, 'a'), (2, 'b')]

If one input list is short, excess elements of the longer list are discarded:

zip [1] ['a', 'b'] = [(1, 'a')]
zip [1, 2] ['a'] = [(1, 'a')]

zip is right-lazy:

zip [] _|_ = []
zip _|_ [] = _|_

print :: Show a => a -> IO () #

The print function outputs a value of any printable type to the standard output device. Printable types are those that are instances of class Show; print converts values to strings for output using the show operation and adds a newline.

For example, a program to print the first 20 integers and their powers of 2 could be written as:

main = print ([(n, 2^n) | n <- [0..19]])

fst :: (a, b) -> a #

Extract the first component of a pair.

snd :: (a, b) -> b #

Extract the second component of a pair.

otherwise :: Bool #

otherwise is defined as the value True. It helps to make guards more readable. eg.

 f x | x < 0     = ...
     | otherwise = ...

map :: (a -> b) -> [a] -> [b] #

map f xs is the list obtained by applying f to each element of xs, i.e.,

map f [x1, x2, ..., xn] == [f x1, f x2, ..., f xn]
map f [x1, x2, ...] == [f x1, f x2, ...]

($) :: (a -> b) -> a -> b infixr 0 #

Application operator. This operator is redundant, since ordinary application (f x) means the same as (f $ x). However, $ has low, right-associative binding precedence, so it sometimes allows parentheses to be omitted; for example:

f $ g $ h x  =  f (g (h x))

It is also useful in higher-order situations, such as map ($ 0) xs, or zipWith ($) fs xs.

Note that ($) is levity-polymorphic in its result type, so that foo $ True where foo :: Bool -> Int# is well-typed

fromIntegral :: (Integral a, Num b) => a -> b #

general coercion from integral types

realToFrac :: (Real a, Fractional b) => a -> b #

general coercion to fractional types

class Bounded a where #

The Bounded class is used to name the upper and lower limits of a type. Ord is not a superclass of Bounded since types that are not totally ordered may also have upper and lower bounds.

The Bounded class may be derived for any enumeration type; minBound is the first constructor listed in the data declaration and maxBound is the last. Bounded may also be derived for single-constructor datatypes whose constituent types are in Bounded.

Methods

minBound :: a #

maxBound :: a #

Instances

Bounded Bool	Since: base-2.1
Instance details Defined in GHC.Enum Methods minBound :: Bool # maxBound :: Bool #
Bounded Char	Since: base-2.1
Instance details Defined in GHC.Enum Methods minBound :: Char # maxBound :: Char #
Bounded Int	Since: base-2.1
Instance details Defined in GHC.Enum Methods minBound :: Int # maxBound :: Int #
Bounded Int8	Since: base-2.1
Instance details Defined in GHC.Int Methods minBound :: Int8 # maxBound :: Int8 #
Bounded Int16	Since: base-2.1
Instance details Defined in GHC.Int Methods minBound :: Int16 # maxBound :: Int16 #
Bounded Int32	Since: base-2.1
Instance details Defined in GHC.Int Methods minBound :: Int32 # maxBound :: Int32 #
Bounded Int64	Since: base-2.1
Instance details Defined in GHC.Int Methods minBound :: Int64 # maxBound :: Int64 #
Bounded Ordering	Since: base-2.1
Instance details Defined in GHC.Enum Methods minBound :: Ordering # maxBound :: Ordering #
Bounded Word	Since: base-2.1
Instance details Defined in GHC.Enum Methods minBound :: Word # maxBound :: Word #
Bounded Word8	Since: base-2.1
Instance details Defined in GHC.Word Methods minBound :: Word8 # maxBound :: Word8 #
Bounded Word16	Since: base-2.1
Instance details Defined in GHC.Word Methods minBound :: Word16 # maxBound :: Word16 #
Bounded Word32	Since: base-2.1
Instance details Defined in GHC.Word Methods minBound :: Word32 # maxBound :: Word32 #
Bounded Word64	Since: base-2.1
Instance details Defined in GHC.Word Methods minBound :: Word64 # maxBound :: Word64 #
Bounded VecCount	Since: base-4.10.0.0
Instance details Defined in GHC.Enum Methods minBound :: VecCount # maxBound :: VecCount #
Bounded VecElem	Since: base-4.10.0.0
Instance details Defined in GHC.Enum Methods minBound :: VecElem # maxBound :: VecElem #
Bounded ()	Since: base-2.1
Instance details Defined in GHC.Enum Methods minBound :: () # maxBound :: () #
Bounded All	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods minBound :: All # maxBound :: All #
Bounded Any	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods minBound :: Any # maxBound :: Any #
Bounded Associativity	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods minBound :: Associativity # maxBound :: Associativity #
Bounded SourceUnpackedness	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods minBound :: SourceUnpackedness # maxBound :: SourceUnpackedness #
Bounded SourceStrictness	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods minBound :: SourceStrictness # maxBound :: SourceStrictness #
Bounded DecidedStrictness	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods minBound :: DecidedStrictness # maxBound :: DecidedStrictness #
Bounded CChar
Instance details Defined in Foreign.C.Types Methods minBound :: CChar # maxBound :: CChar #
Bounded CSChar
Instance details Defined in Foreign.C.Types Methods minBound :: CSChar # maxBound :: CSChar #
Bounded CUChar
Instance details Defined in Foreign.C.Types Methods minBound :: CUChar # maxBound :: CUChar #
Bounded CShort
Instance details Defined in Foreign.C.Types Methods minBound :: CShort # maxBound :: CShort #
Bounded CUShort
Instance details Defined in Foreign.C.Types Methods minBound :: CUShort # maxBound :: CUShort #
Bounded CInt
Instance details Defined in Foreign.C.Types Methods minBound :: CInt # maxBound :: CInt #
Bounded CUInt
Instance details Defined in Foreign.C.Types Methods minBound :: CUInt # maxBound :: CUInt #
Bounded CLong
Instance details Defined in Foreign.C.Types Methods minBound :: CLong # maxBound :: CLong #
Bounded CULong
Instance details Defined in Foreign.C.Types Methods minBound :: CULong # maxBound :: CULong #
Bounded CLLong
Instance details Defined in Foreign.C.Types Methods minBound :: CLLong # maxBound :: CLLong #
Bounded CULLong
Instance details Defined in Foreign.C.Types Methods minBound :: CULLong # maxBound :: CULLong #
Bounded CBool
Instance details Defined in Foreign.C.Types Methods minBound :: CBool # maxBound :: CBool #
Bounded CPtrdiff
Instance details Defined in Foreign.C.Types Methods minBound :: CPtrdiff # maxBound :: CPtrdiff #
Bounded CSize
Instance details Defined in Foreign.C.Types Methods minBound :: CSize # maxBound :: CSize #
Bounded CWchar
Instance details Defined in Foreign.C.Types Methods minBound :: CWchar # maxBound :: CWchar #
Bounded CSigAtomic
Instance details Defined in Foreign.C.Types Methods minBound :: CSigAtomic # maxBound :: CSigAtomic #
Bounded CIntPtr
Instance details Defined in Foreign.C.Types Methods minBound :: CIntPtr # maxBound :: CIntPtr #
Bounded CUIntPtr
Instance details Defined in Foreign.C.Types Methods minBound :: CUIntPtr # maxBound :: CUIntPtr #
Bounded CIntMax
Instance details Defined in Foreign.C.Types Methods minBound :: CIntMax # maxBound :: CIntMax #
Bounded CUIntMax
Instance details Defined in Foreign.C.Types Methods minBound :: CUIntMax # maxBound :: CUIntMax #
Bounded WordPtr
Instance details Defined in Foreign.Ptr Methods minBound :: WordPtr # maxBound :: WordPtr #
Bounded IntPtr
Instance details Defined in Foreign.Ptr Methods minBound :: IntPtr # maxBound :: IntPtr #
Bounded a => Bounded (Min a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods minBound :: Min a # maxBound :: Min a #
Bounded a => Bounded (Max a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods minBound :: Max a # maxBound :: Max a #
Bounded a => Bounded (First a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods minBound :: First a # maxBound :: First a #
Bounded a => Bounded (Last a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods minBound :: Last a # maxBound :: Last a #
Bounded m => Bounded (WrappedMonoid m)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods minBound :: WrappedMonoid m # maxBound :: WrappedMonoid m #
Bounded a => Bounded (Identity a)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Identity Methods minBound :: Identity a # maxBound :: Identity a #
Bounded a => Bounded (Dual a)	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods minBound :: Dual a # maxBound :: Dual a #
Bounded a => Bounded (Sum a)	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods minBound :: Sum a # maxBound :: Sum a #
Bounded a => Bounded (Product a)	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods minBound :: Product a # maxBound :: Product a #
(Bounded a, Bounded b) => Bounded (a, b)	Since: base-2.1
Instance details Defined in GHC.Enum Methods minBound :: (a, b) # maxBound :: (a, b) #
Bounded (Proxy t)	Since: base-4.7.0.0
Instance details Defined in Data.Proxy Methods minBound :: Proxy t # maxBound :: Proxy t #
(Bounded a, Bounded b, Bounded c) => Bounded (a, b, c)	Since: base-2.1
Instance details Defined in GHC.Enum Methods minBound :: (a, b, c) # maxBound :: (a, b, c) #
Bounded a => Bounded (Const a b)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Const Methods minBound :: Const a b # maxBound :: Const a b #
(Applicative f, Bounded a) => Bounded (Ap f a)	Since: base-4.12.0.0
Instance details Defined in Data.Monoid Methods minBound :: Ap f a # maxBound :: Ap f a #
Coercible a b => Bounded (Coercion a b)	Since: base-4.7.0.0
Instance details Defined in Data.Type.Coercion Methods minBound :: Coercion a b # maxBound :: Coercion a b #
a ~ b => Bounded (a :~: b)	Since: base-4.7.0.0
Instance details Defined in Data.Type.Equality Methods minBound :: a :~: b # maxBound :: a :~: b #
Bounded a => Bounded (SQuantity s d a) Source #
Instance details Defined in Numeric.Units.Dimensional.Internal Methods minBound :: SQuantity s d a # maxBound :: SQuantity s d a #
(Bounded a, Bounded b, Bounded c, Bounded d) => Bounded (a, b, c, d)	Since: base-2.1
Instance details Defined in GHC.Enum Methods minBound :: (a, b, c, d) # maxBound :: (a, b, c, d) #
a ~~ b => Bounded (a :~~: b)	Since: base-4.10.0.0
Instance details Defined in Data.Type.Equality Methods minBound :: a :~~: b # maxBound :: a :~~: b #
(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e) => Bounded (a, b, c, d, e)	Since: base-2.1
Instance details Defined in GHC.Enum Methods minBound :: (a, b, c, d, e) # maxBound :: (a, b, c, d, e) #
(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f) => Bounded (a, b, c, d, e, f)	Since: base-2.1
Instance details Defined in GHC.Enum Methods minBound :: (a, b, c, d, e, f) # maxBound :: (a, b, c, d, e, f) #
(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g) => Bounded (a, b, c, d, e, f, g)	Since: base-2.1
Instance details Defined in GHC.Enum Methods minBound :: (a, b, c, d, e, f, g) # maxBound :: (a, b, c, d, e, f, g) #
(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h) => Bounded (a, b, c, d, e, f, g, h)	Since: base-2.1
Instance details Defined in GHC.Enum Methods minBound :: (a, b, c, d, e, f, g, h) # maxBound :: (a, b, c, d, e, f, g, h) #
(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i) => Bounded (a, b, c, d, e, f, g, h, i)	Since: base-2.1
Instance details Defined in GHC.Enum Methods minBound :: (a, b, c, d, e, f, g, h, i) # maxBound :: (a, b, c, d, e, f, g, h, i) #
(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i, Bounded j) => Bounded (a, b, c, d, e, f, g, h, i, j)	Since: base-2.1
Instance details Defined in GHC.Enum Methods minBound :: (a, b, c, d, e, f, g, h, i, j) # maxBound :: (a, b, c, d, e, f, g, h, i, j) #
(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i, Bounded j, Bounded k) => Bounded (a, b, c, d, e, f, g, h, i, j, k)	Since: base-2.1
Instance details Defined in GHC.Enum Methods minBound :: (a, b, c, d, e, f, g, h, i, j, k) # maxBound :: (a, b, c, d, e, f, g, h, i, j, k) #
(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i, Bounded j, Bounded k, Bounded l) => Bounded (a, b, c, d, e, f, g, h, i, j, k, l)	Since: base-2.1
Instance details Defined in GHC.Enum Methods minBound :: (a, b, c, d, e, f, g, h, i, j, k, l) # maxBound :: (a, b, c, d, e, f, g, h, i, j, k, l) #
(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i, Bounded j, Bounded k, Bounded l, Bounded m) => Bounded (a, b, c, d, e, f, g, h, i, j, k, l, m)	Since: base-2.1
Instance details Defined in GHC.Enum Methods minBound :: (a, b, c, d, e, f, g, h, i, j, k, l, m) # maxBound :: (a, b, c, d, e, f, g, h, i, j, k, l, m) #
(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i, Bounded j, Bounded k, Bounded l, Bounded m, Bounded n) => Bounded (a, b, c, d, e, f, g, h, i, j, k, l, m, n)	Since: base-2.1
Instance details Defined in GHC.Enum Methods minBound :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) # maxBound :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) #
(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i, Bounded j, Bounded k, Bounded l, Bounded m, Bounded n, Bounded o) => Bounded (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o)	Since: base-2.1
Instance details Defined in GHC.Enum Methods minBound :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) # maxBound :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) #

class Enum a where #

Class Enum defines operations on sequentially ordered types.

The enumFrom... methods are used in Haskell's translation of arithmetic sequences.

Instances of Enum may be derived for any enumeration type (types whose constructors have no fields). The nullary constructors are assumed to be numbered left-to-right by fromEnum from 0 through n-1. See Chapter 10 of the Haskell Report for more details.

For any type that is an instance of class Bounded as well as Enum, the following should hold:

The calls succ maxBound and pred minBound should result in a runtime error.
fromEnum and toEnum should give a runtime error if the result value is not representable in the result type. For example, toEnum 7 :: Bool is an error.
enumFrom and enumFromThen should be defined with an implicit bound, thus:

   enumFrom     x   = enumFromTo     x maxBound
   enumFromThen x y = enumFromThenTo x y bound
     where
       bound | fromEnum y >= fromEnum x = maxBound
             | otherwise                = minBound

Minimal complete definition

toEnum, fromEnum

Methods

succ :: a -> a #

the successor of a value. For numeric types, succ adds 1.

pred :: a -> a #

the predecessor of a value. For numeric types, pred subtracts 1.

toEnum :: Int -> a #

Convert from an Int.

fromEnum :: a -> Int #

Convert to an Int. It is implementation-dependent what fromEnum returns when applied to a value that is too large to fit in an Int.

enumFrom :: a -> [a] #

Used in Haskell's translation of [n..] with [n..] = enumFrom n, a possible implementation being enumFrom n = n : enumFrom (succ n). For example:

```
enumFrom 4 :: [Integer] = [4,5,6,7,...]
```

enumFrom 6 :: [Int] = [6,7,8,9,...,maxBound :: Int]

enumFromThen :: a -> a -> [a] #

Used in Haskell's translation of [n,n'..] with [n,n'..] = enumFromThen n n', a possible implementation being enumFromThen n n' = n : n' : worker (f x) (f x n'), worker s v = v : worker s (s v), x = fromEnum n' - fromEnum n and f n y | n > 0 = f (n - 1) (succ y) | n < 0 = f (n + 1) (pred y) | otherwise = y For example:

enumFromThen 4 6 :: [Integer] = [4,6,8,10...]

enumFromThen 6 2 :: [Int] = [6,2,-2,-6,...,minBound :: Int]

enumFromTo :: a -> a -> [a] #

Used in Haskell's translation of [n..m] with [n..m] = enumFromTo n m, a possible implementation being enumFromTo n m | n <= m = n : enumFromTo (succ n) m | otherwise = []. For example:

```
enumFromTo 6 10 :: [Int] = [6,7,8,9,10]
```
```
enumFromTo 42 1 :: [Integer] = []
```

enumFromThenTo :: a -> a -> a -> [a] #

Used in Haskell's translation of [n,n'..m] with [n,n'..m] = enumFromThenTo n n' m, a possible implementation being enumFromThenTo n n' m = worker (f x) (c x) n m, x = fromEnum n' - fromEnum n, c x = bool (>=) ((x 0) f n y | n > 0 = f (n - 1) (succ y) | n < 0 = f (n + 1) (pred y) | otherwise = y and worker s c v m | c v m = v : worker s c (s v) m | otherwise = [] For example:

enumFromThenTo 4 2 -6 :: [Integer] = [4,2,0,-2,-4,-6]

```
enumFromThenTo 6 8 2 :: [Int] = []
```

Instances

Enum Bool	Since: base-2.1
Instance details Defined in GHC.Enum Methods succ :: Bool -> Bool # pred :: Bool -> Bool # toEnum :: Int -> Bool # fromEnum :: Bool -> Int # enumFrom :: Bool -> [Bool] # enumFromThen :: Bool -> Bool -> [Bool] # enumFromTo :: Bool -> Bool -> [Bool] # enumFromThenTo :: Bool -> Bool -> Bool -> [Bool] #
Enum Char	Since: base-2.1
Instance details Defined in GHC.Enum Methods succ :: Char -> Char # pred :: Char -> Char # toEnum :: Int -> Char # fromEnum :: Char -> Int # enumFrom :: Char -> [Char] # enumFromThen :: Char -> Char -> [Char] # enumFromTo :: Char -> Char -> [Char] # enumFromThenTo :: Char -> Char -> Char -> [Char] #
Enum Int	Since: base-2.1
Instance details Defined in GHC.Enum Methods succ :: Int -> Int # pred :: Int -> Int # toEnum :: Int -> Int # fromEnum :: Int -> Int # enumFrom :: Int -> [Int] # enumFromThen :: Int -> Int -> [Int] # enumFromTo :: Int -> Int -> [Int] # enumFromThenTo :: Int -> Int -> Int -> [Int] #
Enum Int8	Since: base-2.1
Instance details Defined in GHC.Int Methods succ :: Int8 -> Int8 # pred :: Int8 -> Int8 # toEnum :: Int -> Int8 # fromEnum :: Int8 -> Int # enumFrom :: Int8 -> [Int8] # enumFromThen :: Int8 -> Int8 -> [Int8] # enumFromTo :: Int8 -> Int8 -> [Int8] # enumFromThenTo :: Int8 -> Int8 -> Int8 -> [Int8] #
Enum Int16	Since: base-2.1
Instance details Defined in GHC.Int Methods succ :: Int16 -> Int16 # pred :: Int16 -> Int16 # toEnum :: Int -> Int16 # fromEnum :: Int16 -> Int # enumFrom :: Int16 -> [Int16] # enumFromThen :: Int16 -> Int16 -> [Int16] # enumFromTo :: Int16 -> Int16 -> [Int16] # enumFromThenTo :: Int16 -> Int16 -> Int16 -> [Int16] #
Enum Int32	Since: base-2.1
Instance details Defined in GHC.Int Methods succ :: Int32 -> Int32 # pred :: Int32 -> Int32 # toEnum :: Int -> Int32 # fromEnum :: Int32 -> Int # enumFrom :: Int32 -> [Int32] # enumFromThen :: Int32 -> Int32 -> [Int32] # enumFromTo :: Int32 -> Int32 -> [Int32] # enumFromThenTo :: Int32 -> Int32 -> Int32 -> [Int32] #
Enum Int64	Since: base-2.1
Instance details Defined in GHC.Int Methods succ :: Int64 -> Int64 # pred :: Int64 -> Int64 # toEnum :: Int -> Int64 # fromEnum :: Int64 -> Int # enumFrom :: Int64 -> [Int64] # enumFromThen :: Int64 -> Int64 -> [Int64] # enumFromTo :: Int64 -> Int64 -> [Int64] # enumFromThenTo :: Int64 -> Int64 -> Int64 -> [Int64] #
Enum Integer	Since: base-2.1
Instance details Defined in GHC.Enum Methods succ :: Integer -> Integer # pred :: Integer -> Integer # toEnum :: Int -> Integer # fromEnum :: Integer -> Int # enumFrom :: Integer -> [Integer] # enumFromThen :: Integer -> Integer -> [Integer] # enumFromTo :: Integer -> Integer -> [Integer] # enumFromThenTo :: Integer -> Integer -> Integer -> [Integer] #
Enum Natural	Since: base-4.8.0.0
Instance details Defined in GHC.Enum Methods succ :: Natural -> Natural # pred :: Natural -> Natural # toEnum :: Int -> Natural # fromEnum :: Natural -> Int # enumFrom :: Natural -> [Natural] # enumFromThen :: Natural -> Natural -> [Natural] # enumFromTo :: Natural -> Natural -> [Natural] # enumFromThenTo :: Natural -> Natural -> Natural -> [Natural] #
Enum Ordering	Since: base-2.1
Instance details Defined in GHC.Enum Methods succ :: Ordering -> Ordering # pred :: Ordering -> Ordering # toEnum :: Int -> Ordering # fromEnum :: Ordering -> Int # enumFrom :: Ordering -> [Ordering] # enumFromThen :: Ordering -> Ordering -> [Ordering] # enumFromTo :: Ordering -> Ordering -> [Ordering] # enumFromThenTo :: Ordering -> Ordering -> Ordering -> [Ordering] #
Enum Word	Since: base-2.1
Instance details Defined in GHC.Enum Methods succ :: Word -> Word # pred :: Word -> Word # toEnum :: Int -> Word # fromEnum :: Word -> Int # enumFrom :: Word -> [Word] # enumFromThen :: Word -> Word -> [Word] # enumFromTo :: Word -> Word -> [Word] # enumFromThenTo :: Word -> Word -> Word -> [Word] #
Enum Word8	Since: base-2.1
Instance details Defined in GHC.Word Methods succ :: Word8 -> Word8 # pred :: Word8 -> Word8 # toEnum :: Int -> Word8 # fromEnum :: Word8 -> Int # enumFrom :: Word8 -> [Word8] # enumFromThen :: Word8 -> Word8 -> [Word8] # enumFromTo :: Word8 -> Word8 -> [Word8] # enumFromThenTo :: Word8 -> Word8 -> Word8 -> [Word8] #
Enum Word16	Since: base-2.1
Instance details Defined in GHC.Word Methods succ :: Word16 -> Word16 # pred :: Word16 -> Word16 # toEnum :: Int -> Word16 # fromEnum :: Word16 -> Int # enumFrom :: Word16 -> [Word16] # enumFromThen :: Word16 -> Word16 -> [Word16] # enumFromTo :: Word16 -> Word16 -> [Word16] # enumFromThenTo :: Word16 -> Word16 -> Word16 -> [Word16] #
Enum Word32	Since: base-2.1
Instance details Defined in GHC.Word Methods succ :: Word32 -> Word32 # pred :: Word32 -> Word32 # toEnum :: Int -> Word32 # fromEnum :: Word32 -> Int # enumFrom :: Word32 -> [Word32] # enumFromThen :: Word32 -> Word32 -> [Word32] # enumFromTo :: Word32 -> Word32 -> [Word32] # enumFromThenTo :: Word32 -> Word32 -> Word32 -> [Word32] #
Enum Word64	Since: base-2.1
Instance details Defined in GHC.Word Methods succ :: Word64 -> Word64 # pred :: Word64 -> Word64 # toEnum :: Int -> Word64 # fromEnum :: Word64 -> Int # enumFrom :: Word64 -> [Word64] # enumFromThen :: Word64 -> Word64 -> [Word64] # enumFromTo :: Word64 -> Word64 -> [Word64] # enumFromThenTo :: Word64 -> Word64 -> Word64 -> [Word64] #
Enum VecCount	Since: base-4.10.0.0
Instance details Defined in GHC.Enum Methods succ :: VecCount -> VecCount # pred :: VecCount -> VecCount # toEnum :: Int -> VecCount # fromEnum :: VecCount -> Int # enumFrom :: VecCount -> [VecCount] # enumFromThen :: VecCount -> VecCount -> [VecCount] # enumFromTo :: VecCount -> VecCount -> [VecCount] # enumFromThenTo :: VecCount -> VecCount -> VecCount -> [VecCount] #
Enum VecElem	Since: base-4.10.0.0
Instance details Defined in GHC.Enum Methods succ :: VecElem -> VecElem # pred :: VecElem -> VecElem # toEnum :: Int -> VecElem # fromEnum :: VecElem -> Int # enumFrom :: VecElem -> [VecElem] # enumFromThen :: VecElem -> VecElem -> [VecElem] # enumFromTo :: VecElem -> VecElem -> [VecElem] # enumFromThenTo :: VecElem -> VecElem -> VecElem -> [VecElem] #
Enum ()	Since: base-2.1
Instance details Defined in GHC.Enum Methods succ :: () -> () # pred :: () -> () # toEnum :: Int -> () # fromEnum :: () -> Int # enumFrom :: () -> [()] # enumFromThen :: () -> () -> [()] # enumFromTo :: () -> () -> [()] # enumFromThenTo :: () -> () -> () -> [()] #
Enum Associativity	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods succ :: Associativity -> Associativity # pred :: Associativity -> Associativity # toEnum :: Int -> Associativity # fromEnum :: Associativity -> Int # enumFrom :: Associativity -> [Associativity] # enumFromThen :: Associativity -> Associativity -> [Associativity] # enumFromTo :: Associativity -> Associativity -> [Associativity] # enumFromThenTo :: Associativity -> Associativity -> Associativity -> [Associativity] #
Enum SourceUnpackedness	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods succ :: SourceUnpackedness -> SourceUnpackedness # pred :: SourceUnpackedness -> SourceUnpackedness # toEnum :: Int -> SourceUnpackedness # fromEnum :: SourceUnpackedness -> Int # enumFrom :: SourceUnpackedness -> [SourceUnpackedness] # enumFromThen :: SourceUnpackedness -> SourceUnpackedness -> [SourceUnpackedness] # enumFromTo :: SourceUnpackedness -> SourceUnpackedness -> [SourceUnpackedness] # enumFromThenTo :: SourceUnpackedness -> SourceUnpackedness -> SourceUnpackedness -> [SourceUnpackedness] #
Enum SourceStrictness	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods succ :: SourceStrictness -> SourceStrictness # pred :: SourceStrictness -> SourceStrictness # toEnum :: Int -> SourceStrictness # fromEnum :: SourceStrictness -> Int # enumFrom :: SourceStrictness -> [SourceStrictness] # enumFromThen :: SourceStrictness -> SourceStrictness -> [SourceStrictness] # enumFromTo :: SourceStrictness -> SourceStrictness -> [SourceStrictness] # enumFromThenTo :: SourceStrictness -> SourceStrictness -> SourceStrictness -> [SourceStrictness] #
Enum DecidedStrictness	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods succ :: DecidedStrictness -> DecidedStrictness # pred :: DecidedStrictness -> DecidedStrictness # toEnum :: Int -> DecidedStrictness # fromEnum :: DecidedStrictness -> Int # enumFrom :: DecidedStrictness -> [DecidedStrictness] # enumFromThen :: DecidedStrictness -> DecidedStrictness -> [DecidedStrictness] # enumFromTo :: DecidedStrictness -> DecidedStrictness -> [DecidedStrictness] # enumFromThenTo :: DecidedStrictness -> DecidedStrictness -> DecidedStrictness -> [DecidedStrictness] #
Enum CChar
Instance details Defined in Foreign.C.Types Methods succ :: CChar -> CChar # pred :: CChar -> CChar # toEnum :: Int -> CChar # fromEnum :: CChar -> Int # enumFrom :: CChar -> [CChar] # enumFromThen :: CChar -> CChar -> [CChar] # enumFromTo :: CChar -> CChar -> [CChar] # enumFromThenTo :: CChar -> CChar -> CChar -> [CChar] #
Enum CSChar
Instance details Defined in Foreign.C.Types Methods succ :: CSChar -> CSChar # pred :: CSChar -> CSChar # toEnum :: Int -> CSChar # fromEnum :: CSChar -> Int # enumFrom :: CSChar -> [CSChar] # enumFromThen :: CSChar -> CSChar -> [CSChar] # enumFromTo :: CSChar -> CSChar -> [CSChar] # enumFromThenTo :: CSChar -> CSChar -> CSChar -> [CSChar] #
Enum CUChar
Instance details Defined in Foreign.C.Types Methods succ :: CUChar -> CUChar # pred :: CUChar -> CUChar # toEnum :: Int -> CUChar # fromEnum :: CUChar -> Int # enumFrom :: CUChar -> [CUChar] # enumFromThen :: CUChar -> CUChar -> [CUChar] # enumFromTo :: CUChar -> CUChar -> [CUChar] # enumFromThenTo :: CUChar -> CUChar -> CUChar -> [CUChar] #
Enum CShort
Instance details Defined in Foreign.C.Types Methods succ :: CShort -> CShort # pred :: CShort -> CShort # toEnum :: Int -> CShort # fromEnum :: CShort -> Int # enumFrom :: CShort -> [CShort] # enumFromThen :: CShort -> CShort -> [CShort] # enumFromTo :: CShort -> CShort -> [CShort] # enumFromThenTo :: CShort -> CShort -> CShort -> [CShort] #
Enum CUShort
Instance details Defined in Foreign.C.Types Methods succ :: CUShort -> CUShort # pred :: CUShort -> CUShort # toEnum :: Int -> CUShort # fromEnum :: CUShort -> Int # enumFrom :: CUShort -> [CUShort] # enumFromThen :: CUShort -> CUShort -> [CUShort] # enumFromTo :: CUShort -> CUShort -> [CUShort] # enumFromThenTo :: CUShort -> CUShort -> CUShort -> [CUShort] #
Enum CInt
Instance details Defined in Foreign.C.Types Methods succ :: CInt -> CInt # pred :: CInt -> CInt # toEnum :: Int -> CInt # fromEnum :: CInt -> Int # enumFrom :: CInt -> [CInt] # enumFromThen :: CInt -> CInt -> [CInt] # enumFromTo :: CInt -> CInt -> [CInt] # enumFromThenTo :: CInt -> CInt -> CInt -> [CInt] #
Enum CUInt
Instance details Defined in Foreign.C.Types Methods succ :: CUInt -> CUInt # pred :: CUInt -> CUInt # toEnum :: Int -> CUInt # fromEnum :: CUInt -> Int # enumFrom :: CUInt -> [CUInt] # enumFromThen :: CUInt -> CUInt -> [CUInt] # enumFromTo :: CUInt -> CUInt -> [CUInt] # enumFromThenTo :: CUInt -> CUInt -> CUInt -> [CUInt] #
Enum CLong
Instance details Defined in Foreign.C.Types Methods succ :: CLong -> CLong # pred :: CLong -> CLong # toEnum :: Int -> CLong # fromEnum :: CLong -> Int # enumFrom :: CLong -> [CLong] # enumFromThen :: CLong -> CLong -> [CLong] # enumFromTo :: CLong -> CLong -> [CLong] # enumFromThenTo :: CLong -> CLong -> CLong -> [CLong] #
Enum CULong
Instance details Defined in Foreign.C.Types Methods succ :: CULong -> CULong # pred :: CULong -> CULong # toEnum :: Int -> CULong # fromEnum :: CULong -> Int # enumFrom :: CULong -> [CULong] # enumFromThen :: CULong -> CULong -> [CULong] # enumFromTo :: CULong -> CULong -> [CULong] # enumFromThenTo :: CULong -> CULong -> CULong -> [CULong] #
Enum CLLong
Instance details Defined in Foreign.C.Types Methods succ :: CLLong -> CLLong # pred :: CLLong -> CLLong # toEnum :: Int -> CLLong # fromEnum :: CLLong -> Int # enumFrom :: CLLong -> [CLLong] # enumFromThen :: CLLong -> CLLong -> [CLLong] # enumFromTo :: CLLong -> CLLong -> [CLLong] # enumFromThenTo :: CLLong -> CLLong -> CLLong -> [CLLong] #
Enum CULLong
Instance details Defined in Foreign.C.Types Methods succ :: CULLong -> CULLong # pred :: CULLong -> CULLong # toEnum :: Int -> CULLong # fromEnum :: CULLong -> Int # enumFrom :: CULLong -> [CULLong] # enumFromThen :: CULLong -> CULLong -> [CULLong] # enumFromTo :: CULLong -> CULLong -> [CULLong] # enumFromThenTo :: CULLong -> CULLong -> CULLong -> [CULLong] #
Enum CBool
Instance details Defined in Foreign.C.Types Methods succ :: CBool -> CBool # pred :: CBool -> CBool # toEnum :: Int -> CBool # fromEnum :: CBool -> Int # enumFrom :: CBool -> [CBool] # enumFromThen :: CBool -> CBool -> [CBool] # enumFromTo :: CBool -> CBool -> [CBool] # enumFromThenTo :: CBool -> CBool -> CBool -> [CBool] #
Enum CFloat
Instance details Defined in Foreign.C.Types Methods succ :: CFloat -> CFloat # pred :: CFloat -> CFloat # toEnum :: Int -> CFloat # fromEnum :: CFloat -> Int # enumFrom :: CFloat -> [CFloat] # enumFromThen :: CFloat -> CFloat -> [CFloat] # enumFromTo :: CFloat -> CFloat -> [CFloat] # enumFromThenTo :: CFloat -> CFloat -> CFloat -> [CFloat] #
Enum CDouble
Instance details Defined in Foreign.C.Types Methods succ :: CDouble -> CDouble # pred :: CDouble -> CDouble # toEnum :: Int -> CDouble # fromEnum :: CDouble -> Int # enumFrom :: CDouble -> [CDouble] # enumFromThen :: CDouble -> CDouble -> [CDouble] # enumFromTo :: CDouble -> CDouble -> [CDouble] # enumFromThenTo :: CDouble -> CDouble -> CDouble -> [CDouble] #
Enum CPtrdiff
Instance details Defined in Foreign.C.Types Methods succ :: CPtrdiff -> CPtrdiff # pred :: CPtrdiff -> CPtrdiff # toEnum :: Int -> CPtrdiff # fromEnum :: CPtrdiff -> Int # enumFrom :: CPtrdiff -> [CPtrdiff] # enumFromThen :: CPtrdiff -> CPtrdiff -> [CPtrdiff] # enumFromTo :: CPtrdiff -> CPtrdiff -> [CPtrdiff] # enumFromThenTo :: CPtrdiff -> CPtrdiff -> CPtrdiff -> [CPtrdiff] #
Enum CSize
Instance details Defined in Foreign.C.Types Methods succ :: CSize -> CSize # pred :: CSize -> CSize # toEnum :: Int -> CSize # fromEnum :: CSize -> Int # enumFrom :: CSize -> [CSize] # enumFromThen :: CSize -> CSize -> [CSize] # enumFromTo :: CSize -> CSize -> [CSize] # enumFromThenTo :: CSize -> CSize -> CSize -> [CSize] #
Enum CWchar
Instance details Defined in Foreign.C.Types Methods succ :: CWchar -> CWchar # pred :: CWchar -> CWchar # toEnum :: Int -> CWchar # fromEnum :: CWchar -> Int # enumFrom :: CWchar -> [CWchar] # enumFromThen :: CWchar -> CWchar -> [CWchar] # enumFromTo :: CWchar -> CWchar -> [CWchar] # enumFromThenTo :: CWchar -> CWchar -> CWchar -> [CWchar] #
Enum CSigAtomic
Instance details Defined in Foreign.C.Types Methods succ :: CSigAtomic -> CSigAtomic # pred :: CSigAtomic -> CSigAtomic # toEnum :: Int -> CSigAtomic # fromEnum :: CSigAtomic -> Int # enumFrom :: CSigAtomic -> [CSigAtomic] # enumFromThen :: CSigAtomic -> CSigAtomic -> [CSigAtomic] # enumFromTo :: CSigAtomic -> CSigAtomic -> [CSigAtomic] # enumFromThenTo :: CSigAtomic -> CSigAtomic -> CSigAtomic -> [CSigAtomic] #
Enum CClock
Instance details Defined in Foreign.C.Types Methods succ :: CClock -> CClock # pred :: CClock -> CClock # toEnum :: Int -> CClock # fromEnum :: CClock -> Int # enumFrom :: CClock -> [CClock] # enumFromThen :: CClock -> CClock -> [CClock] # enumFromTo :: CClock -> CClock -> [CClock] # enumFromThenTo :: CClock -> CClock -> CClock -> [CClock] #
Enum CTime
Instance details Defined in Foreign.C.Types Methods succ :: CTime -> CTime # pred :: CTime -> CTime # toEnum :: Int -> CTime # fromEnum :: CTime -> Int # enumFrom :: CTime -> [CTime] # enumFromThen :: CTime -> CTime -> [CTime] # enumFromTo :: CTime -> CTime -> [CTime] # enumFromThenTo :: CTime -> CTime -> CTime -> [CTime] #
Enum CUSeconds
Instance details Defined in Foreign.C.Types Methods succ :: CUSeconds -> CUSeconds # pred :: CUSeconds -> CUSeconds # toEnum :: Int -> CUSeconds # fromEnum :: CUSeconds -> Int # enumFrom :: CUSeconds -> [CUSeconds] # enumFromThen :: CUSeconds -> CUSeconds -> [CUSeconds] # enumFromTo :: CUSeconds -> CUSeconds -> [CUSeconds] # enumFromThenTo :: CUSeconds -> CUSeconds -> CUSeconds -> [CUSeconds] #
Enum CSUSeconds
Instance details Defined in Foreign.C.Types Methods succ :: CSUSeconds -> CSUSeconds # pred :: CSUSeconds -> CSUSeconds # toEnum :: Int -> CSUSeconds # fromEnum :: CSUSeconds -> Int # enumFrom :: CSUSeconds -> [CSUSeconds] # enumFromThen :: CSUSeconds -> CSUSeconds -> [CSUSeconds] # enumFromTo :: CSUSeconds -> CSUSeconds -> [CSUSeconds] # enumFromThenTo :: CSUSeconds -> CSUSeconds -> CSUSeconds -> [CSUSeconds] #
Enum CIntPtr
Instance details Defined in Foreign.C.Types Methods succ :: CIntPtr -> CIntPtr # pred :: CIntPtr -> CIntPtr # toEnum :: Int -> CIntPtr # fromEnum :: CIntPtr -> Int # enumFrom :: CIntPtr -> [CIntPtr] # enumFromThen :: CIntPtr -> CIntPtr -> [CIntPtr] # enumFromTo :: CIntPtr -> CIntPtr -> [CIntPtr] # enumFromThenTo :: CIntPtr -> CIntPtr -> CIntPtr -> [CIntPtr] #
Enum CUIntPtr
Instance details Defined in Foreign.C.Types Methods succ :: CUIntPtr -> CUIntPtr # pred :: CUIntPtr -> CUIntPtr # toEnum :: Int -> CUIntPtr # fromEnum :: CUIntPtr -> Int # enumFrom :: CUIntPtr -> [CUIntPtr] # enumFromThen :: CUIntPtr -> CUIntPtr -> [CUIntPtr] # enumFromTo :: CUIntPtr -> CUIntPtr -> [CUIntPtr] # enumFromThenTo :: CUIntPtr -> CUIntPtr -> CUIntPtr -> [CUIntPtr] #
Enum CIntMax
Instance details Defined in Foreign.C.Types Methods succ :: CIntMax -> CIntMax # pred :: CIntMax -> CIntMax # toEnum :: Int -> CIntMax # fromEnum :: CIntMax -> Int # enumFrom :: CIntMax -> [CIntMax] # enumFromThen :: CIntMax -> CIntMax -> [CIntMax] # enumFromTo :: CIntMax -> CIntMax -> [CIntMax] # enumFromThenTo :: CIntMax -> CIntMax -> CIntMax -> [CIntMax] #
Enum CUIntMax
Instance details Defined in Foreign.C.Types Methods succ :: CUIntMax -> CUIntMax # pred :: CUIntMax -> CUIntMax # toEnum :: Int -> CUIntMax # fromEnum :: CUIntMax -> Int # enumFrom :: CUIntMax -> [CUIntMax] # enumFromThen :: CUIntMax -> CUIntMax -> [CUIntMax] # enumFromTo :: CUIntMax -> CUIntMax -> [CUIntMax] # enumFromThenTo :: CUIntMax -> CUIntMax -> CUIntMax -> [CUIntMax] #
Enum WordPtr
Instance details Defined in Foreign.Ptr Methods succ :: WordPtr -> WordPtr # pred :: WordPtr -> WordPtr # toEnum :: Int -> WordPtr # fromEnum :: WordPtr -> Int # enumFrom :: WordPtr -> [WordPtr] # enumFromThen :: WordPtr -> WordPtr -> [WordPtr] # enumFromTo :: WordPtr -> WordPtr -> [WordPtr] # enumFromThenTo :: WordPtr -> WordPtr -> WordPtr -> [WordPtr] #
Enum IntPtr
Instance details Defined in Foreign.Ptr Methods succ :: IntPtr -> IntPtr # pred :: IntPtr -> IntPtr # toEnum :: Int -> IntPtr # fromEnum :: IntPtr -> Int # enumFrom :: IntPtr -> [IntPtr] # enumFromThen :: IntPtr -> IntPtr -> [IntPtr] # enumFromTo :: IntPtr -> IntPtr -> [IntPtr] # enumFromThenTo :: IntPtr -> IntPtr -> IntPtr -> [IntPtr] #
Integral a => Enum (Ratio a)	Since: base-2.0.1
Instance details Defined in GHC.Real Methods succ :: Ratio a -> Ratio a # pred :: Ratio a -> Ratio a # toEnum :: Int -> Ratio a # fromEnum :: Ratio a -> Int # enumFrom :: Ratio a -> [Ratio a] # enumFromThen :: Ratio a -> Ratio a -> [Ratio a] # enumFromTo :: Ratio a -> Ratio a -> [Ratio a] # enumFromThenTo :: Ratio a -> Ratio a -> Ratio a -> [Ratio a] #
Enum (Fixed a)	Since: base-2.1
Instance details Defined in Data.Fixed Methods succ :: Fixed a -> Fixed a # pred :: Fixed a -> Fixed a # toEnum :: Int -> Fixed a # fromEnum :: Fixed a -> Int # enumFrom :: Fixed a -> [Fixed a] # enumFromThen :: Fixed a -> Fixed a -> [Fixed a] # enumFromTo :: Fixed a -> Fixed a -> [Fixed a] # enumFromThenTo :: Fixed a -> Fixed a -> Fixed a -> [Fixed a] #
Enum a => Enum (Min a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods succ :: Min a -> Min a # pred :: Min a -> Min a # toEnum :: Int -> Min a # fromEnum :: Min a -> Int # enumFrom :: Min a -> [Min a] # enumFromThen :: Min a -> Min a -> [Min a] # enumFromTo :: Min a -> Min a -> [Min a] # enumFromThenTo :: Min a -> Min a -> Min a -> [Min a] #
Enum a => Enum (Max a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods succ :: Max a -> Max a # pred :: Max a -> Max a # toEnum :: Int -> Max a # fromEnum :: Max a -> Int # enumFrom :: Max a -> [Max a] # enumFromThen :: Max a -> Max a -> [Max a] # enumFromTo :: Max a -> Max a -> [Max a] # enumFromThenTo :: Max a -> Max a -> Max a -> [Max a] #
Enum a => Enum (First a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods succ :: First a -> First a # pred :: First a -> First a # toEnum :: Int -> First a # fromEnum :: First a -> Int # enumFrom :: First a -> [First a] # enumFromThen :: First a -> First a -> [First a] # enumFromTo :: First a -> First a -> [First a] # enumFromThenTo :: First a -> First a -> First a -> [First a] #
Enum a => Enum (Last a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods succ :: Last a -> Last a # pred :: Last a -> Last a # toEnum :: Int -> Last a # fromEnum :: Last a -> Int # enumFrom :: Last a -> [Last a] # enumFromThen :: Last a -> Last a -> [Last a] # enumFromTo :: Last a -> Last a -> [Last a] # enumFromThenTo :: Last a -> Last a -> Last a -> [Last a] #
Enum a => Enum (WrappedMonoid a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods succ :: WrappedMonoid a -> WrappedMonoid a # pred :: WrappedMonoid a -> WrappedMonoid a # toEnum :: Int -> WrappedMonoid a # fromEnum :: WrappedMonoid a -> Int # enumFrom :: WrappedMonoid a -> [WrappedMonoid a] # enumFromThen :: WrappedMonoid a -> WrappedMonoid a -> [WrappedMonoid a] # enumFromTo :: WrappedMonoid a -> WrappedMonoid a -> [WrappedMonoid a] # enumFromThenTo :: WrappedMonoid a -> WrappedMonoid a -> WrappedMonoid a -> [WrappedMonoid a] #
Enum a => Enum (Identity a)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Identity Methods succ :: Identity a -> Identity a # pred :: Identity a -> Identity a # toEnum :: Int -> Identity a # fromEnum :: Identity a -> Int # enumFrom :: Identity a -> [Identity a] # enumFromThen :: Identity a -> Identity a -> [Identity a] # enumFromTo :: Identity a -> Identity a -> [Identity a] # enumFromThenTo :: Identity a -> Identity a -> Identity a -> [Identity a] #
Enum (Proxy s)	Since: base-4.7.0.0
Instance details Defined in Data.Proxy Methods succ :: Proxy s -> Proxy s # pred :: Proxy s -> Proxy s # toEnum :: Int -> Proxy s # fromEnum :: Proxy s -> Int # enumFrom :: Proxy s -> [Proxy s] # enumFromThen :: Proxy s -> Proxy s -> [Proxy s] # enumFromTo :: Proxy s -> Proxy s -> [Proxy s] # enumFromThenTo :: Proxy s -> Proxy s -> Proxy s -> [Proxy s] #
Enum a => Enum (Const a b)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Const Methods succ :: Const a b -> Const a b # pred :: Const a b -> Const a b # toEnum :: Int -> Const a b # fromEnum :: Const a b -> Int # enumFrom :: Const a b -> [Const a b] # enumFromThen :: Const a b -> Const a b -> [Const a b] # enumFromTo :: Const a b -> Const a b -> [Const a b] # enumFromThenTo :: Const a b -> Const a b -> Const a b -> [Const a b] #
Enum (f a) => Enum (Ap f a)	Since: base-4.12.0.0
Instance details Defined in Data.Monoid Methods succ :: Ap f a -> Ap f a # pred :: Ap f a -> Ap f a # toEnum :: Int -> Ap f a # fromEnum :: Ap f a -> Int # enumFrom :: Ap f a -> [Ap f a] # enumFromThen :: Ap f a -> Ap f a -> [Ap f a] # enumFromTo :: Ap f a -> Ap f a -> [Ap f a] # enumFromThenTo :: Ap f a -> Ap f a -> Ap f a -> [Ap f a] #
Enum (f a) => Enum (Alt f a)	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods succ :: Alt f a -> Alt f a # pred :: Alt f a -> Alt f a # toEnum :: Int -> Alt f a # fromEnum :: Alt f a -> Int # enumFrom :: Alt f a -> [Alt f a] # enumFromThen :: Alt f a -> Alt f a -> [Alt f a] # enumFromTo :: Alt f a -> Alt f a -> [Alt f a] # enumFromThenTo :: Alt f a -> Alt f a -> Alt f a -> [Alt f a] #
Coercible a b => Enum (Coercion a b)	Since: base-4.7.0.0
Instance details Defined in Data.Type.Coercion Methods succ :: Coercion a b -> Coercion a b # pred :: Coercion a b -> Coercion a b # toEnum :: Int -> Coercion a b # fromEnum :: Coercion a b -> Int # enumFrom :: Coercion a b -> [Coercion a b] # enumFromThen :: Coercion a b -> Coercion a b -> [Coercion a b] # enumFromTo :: Coercion a b -> Coercion a b -> [Coercion a b] # enumFromThenTo :: Coercion a b -> Coercion a b -> Coercion a b -> [Coercion a b] #
a ~ b => Enum (a :~: b)	Since: base-4.7.0.0
Instance details Defined in Data.Type.Equality Methods succ :: (a :~: b) -> a :~: b # pred :: (a :~: b) -> a :~: b # toEnum :: Int -> a :~: b # fromEnum :: (a :~: b) -> Int # enumFrom :: (a :~: b) -> [a :~: b] # enumFromThen :: (a :~: b) -> (a :~: b) -> [a :~: b] # enumFromTo :: (a :~: b) -> (a :~: b) -> [a :~: b] # enumFromThenTo :: (a :~: b) -> (a :~: b) -> (a :~: b) -> [a :~: b] #
a ~~ b => Enum (a :~~: b)	Since: base-4.10.0.0
Instance details Defined in Data.Type.Equality Methods succ :: (a :~~: b) -> a :~~: b # pred :: (a :~~: b) -> a :~~: b # toEnum :: Int -> a :~~: b # fromEnum :: (a :~~: b) -> Int # enumFrom :: (a :~~: b) -> [a :~~: b] # enumFromThen :: (a :~~: b) -> (a :~~: b) -> [a :~~: b] # enumFromTo :: (a :~~: b) -> (a :~~: b) -> [a :~~: b] # enumFromThenTo :: (a :~~: b) -> (a :~~: b) -> (a :~~: b) -> [a :~~: b] #

class Eq a where #

The Eq class defines equality (==) and inequality (/=). All the basic datatypes exported by the Prelude are instances of Eq, and Eq may be derived for any datatype whose constituents are also instances of Eq.

The Haskell Report defines no laws for Eq. However, == is customarily expected to implement an equivalence relationship where two values comparing equal are indistinguishable by "public" functions, with a "public" function being one not allowing to see implementation details. For example, for a type representing non-normalised natural numbers modulo 100, a "public" function doesn't make the difference between 1 and 201. It is expected to have the following properties:

Reflexivity: x == x = True
Symmetry: x == y = y == x
Transitivity: if x == y && y == z = True, then x == z = True
Substitutivity: if x == y = True and f is a "public" function whose return type is an instance of Eq, then f x == f y = True
Negation: x /= y = not (x == y)

Minimal complete definition: either == or /=.

Minimal complete definition

(==) | (/=)

Methods

(==) :: a -> a -> Bool infix 4 #

(/=) :: a -> a -> Bool infix 4 #

Instances

Eq Bool
Instance details Defined in GHC.Classes Methods (==) :: Bool -> Bool -> Bool # (/=) :: Bool -> Bool -> Bool #
Eq Char
Instance details Defined in GHC.Classes Methods (==) :: Char -> Char -> Bool # (/=) :: Char -> Char -> Bool #
Eq Double	Note that due to the presence of `NaN`, `Double`'s `Eq` instance does not satisfy reflexivity. `>>>` `0/0 == (0/0 :: Double)`False Also note that `Double`'s `Eq` instance does not satisfy substitutivity: `>>>` `0 == (-0 :: Double)`True `>>>` `recip 0 == recip (-0 :: Double)`False
Instance details Defined in GHC.Classes Methods (==) :: Double -> Double -> Bool # (/=) :: Double -> Double -> Bool #
Eq Float	Note that due to the presence of `NaN`, `Float`'s `Eq` instance does not satisfy reflexivity. `>>>` `0/0 == (0/0 :: Float)`False Also note that `Float`'s `Eq` instance does not satisfy substitutivity: `>>>` `0 == (-0 :: Float)`True `>>>` `recip 0 == recip (-0 :: Float)`False
Instance details Defined in GHC.Classes Methods (==) :: Float -> Float -> Bool # (/=) :: Float -> Float -> Bool #
Eq Int
Instance details Defined in GHC.Classes Methods (==) :: Int -> Int -> Bool # (/=) :: Int -> Int -> Bool #
Eq Int8	Since: base-2.1
Instance details Defined in GHC.Int Methods (==) :: Int8 -> Int8 -> Bool # (/=) :: Int8 -> Int8 -> Bool #
Eq Int16	Since: base-2.1
Instance details Defined in GHC.Int Methods (==) :: Int16 -> Int16 -> Bool # (/=) :: Int16 -> Int16 -> Bool #
Eq Int32	Since: base-2.1
Instance details Defined in GHC.Int Methods (==) :: Int32 -> Int32 -> Bool # (/=) :: Int32 -> Int32 -> Bool #
Eq Int64	Since: base-2.1
Instance details Defined in GHC.Int Methods (==) :: Int64 -> Int64 -> Bool # (/=) :: Int64 -> Int64 -> Bool #
Eq Integer
Instance details Defined in GHC.Integer.Type Methods (==) :: Integer -> Integer -> Bool # (/=) :: Integer -> Integer -> Bool #
Eq Natural	Since: base-4.8.0.0
Instance details Defined in GHC.Natural Methods (==) :: Natural -> Natural -> Bool # (/=) :: Natural -> Natural -> Bool #
Eq Ordering
Instance details Defined in GHC.Classes Methods (==) :: Ordering -> Ordering -> Bool # (/=) :: Ordering -> Ordering -> Bool #
Eq Word
Instance details Defined in GHC.Classes Methods (==) :: Word -> Word -> Bool # (/=) :: Word -> Word -> Bool #
Eq Word8	Since: base-2.1
Instance details Defined in GHC.Word Methods (==) :: Word8 -> Word8 -> Bool # (/=) :: Word8 -> Word8 -> Bool #
Eq Word16	Since: base-2.1
Instance details Defined in GHC.Word Methods (==) :: Word16 -> Word16 -> Bool # (/=) :: Word16 -> Word16 -> Bool #
Eq Word32	Since: base-2.1
Instance details Defined in GHC.Word Methods (==) :: Word32 -> Word32 -> Bool # (/=) :: Word32 -> Word32 -> Bool #
Eq Word64	Since: base-2.1
Instance details Defined in GHC.Word Methods (==) :: Word64 -> Word64 -> Bool # (/=) :: Word64 -> Word64 -> Bool #
Eq SomeTypeRep
Instance details Defined in Data.Typeable.Internal Methods (==) :: SomeTypeRep -> SomeTypeRep -> Bool # (/=) :: SomeTypeRep -> SomeTypeRep -> Bool #
Eq ()
Instance details Defined in GHC.Classes Methods (==) :: () -> () -> Bool # (/=) :: () -> () -> Bool #
Eq TyCon
Instance details Defined in GHC.Classes Methods (==) :: TyCon -> TyCon -> Bool # (/=) :: TyCon -> TyCon -> Bool #
Eq Module
Instance details Defined in GHC.Classes Methods (==) :: Module -> Module -> Bool # (/=) :: Module -> Module -> Bool #
Eq TrName
Instance details Defined in GHC.Classes Methods (==) :: TrName -> TrName -> Bool # (/=) :: TrName -> TrName -> Bool #
Eq BigNat
Instance details Defined in GHC.Integer.Type Methods (==) :: BigNat -> BigNat -> Bool # (/=) :: BigNat -> BigNat -> Bool #
Eq Void	Since: base-4.8.0.0
Instance details Defined in Data.Void Methods (==) :: Void -> Void -> Bool # (/=) :: Void -> Void -> Bool #
Eq SpecConstrAnnotation	Since: base-4.3.0.0
Instance details Defined in GHC.Exts Methods (==) :: SpecConstrAnnotation -> SpecConstrAnnotation -> Bool # (/=) :: SpecConstrAnnotation -> SpecConstrAnnotation -> Bool #
Eq Constr	Equality of constructors Since: base-4.0.0.0
Instance details Defined in Data.Data Methods (==) :: Constr -> Constr -> Bool # (/=) :: Constr -> Constr -> Bool #
Eq DataRep	Since: base-4.0.0.0
Instance details Defined in Data.Data Methods (==) :: DataRep -> DataRep -> Bool # (/=) :: DataRep -> DataRep -> Bool #
Eq ConstrRep	Since: base-4.0.0.0
Instance details Defined in Data.Data Methods (==) :: ConstrRep -> ConstrRep -> Bool # (/=) :: ConstrRep -> ConstrRep -> Bool #
Eq Fixity	Since: base-4.0.0.0
Instance details Defined in Data.Data Methods (==) :: Fixity -> Fixity -> Bool # (/=) :: Fixity -> Fixity -> Bool #
Eq Unique
Instance details Defined in Data.Unique Methods (==) :: Unique -> Unique -> Bool # (/=) :: Unique -> Unique -> Bool #
Eq Version	Since: base-2.1
Instance details Defined in Data.Version Methods (==) :: Version -> Version -> Bool # (/=) :: Version -> Version -> Bool #
Eq ThreadId	Since: base-4.2.0.0
Instance details Defined in GHC.Conc.Sync Methods (==) :: ThreadId -> ThreadId -> Bool # (/=) :: ThreadId -> ThreadId -> Bool #
Eq BlockReason	Since: base-4.3.0.0
Instance details Defined in GHC.Conc.Sync Methods (==) :: BlockReason -> BlockReason -> Bool # (/=) :: BlockReason -> BlockReason -> Bool #
Eq ThreadStatus	Since: base-4.3.0.0
Instance details Defined in GHC.Conc.Sync Methods (==) :: ThreadStatus -> ThreadStatus -> Bool # (/=) :: ThreadStatus -> ThreadStatus -> Bool #
Eq AsyncException	Since: base-4.2.0.0
Instance details Defined in GHC.IO.Exception Methods (==) :: AsyncException -> AsyncException -> Bool # (/=) :: AsyncException -> AsyncException -> Bool #
Eq ArrayException	Since: base-4.2.0.0
Instance details Defined in GHC.IO.Exception Methods (==) :: ArrayException -> ArrayException -> Bool # (/=) :: ArrayException -> ArrayException -> Bool #
Eq ExitCode
Instance details Defined in GHC.IO.Exception Methods (==) :: ExitCode -> ExitCode -> Bool # (/=) :: ExitCode -> ExitCode -> Bool #
Eq IOErrorType	Since: base-4.1.0.0
Instance details Defined in GHC.IO.Exception Methods (==) :: IOErrorType -> IOErrorType -> Bool # (/=) :: IOErrorType -> IOErrorType -> Bool #
Eq MaskingState	Since: base-4.3.0.0
Instance details Defined in GHC.IO Methods (==) :: MaskingState -> MaskingState -> Bool # (/=) :: MaskingState -> MaskingState -> Bool #
Eq IOException	Since: base-4.1.0.0
Instance details Defined in GHC.IO.Exception Methods (==) :: IOException -> IOException -> Bool # (/=) :: IOException -> IOException -> Bool #
Eq All	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods (==) :: All -> All -> Bool # (/=) :: All -> All -> Bool #
Eq Any	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods (==) :: Any -> Any -> Bool # (/=) :: Any -> Any -> Bool #
Eq Fixity	Since: base-4.6.0.0
Instance details Defined in GHC.Generics Methods (==) :: Fixity -> Fixity -> Bool # (/=) :: Fixity -> Fixity -> Bool #
Eq Associativity	Since: base-4.6.0.0
Instance details Defined in GHC.Generics Methods (==) :: Associativity -> Associativity -> Bool # (/=) :: Associativity -> Associativity -> Bool #
Eq SourceUnpackedness	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods (==) :: SourceUnpackedness -> SourceUnpackedness -> Bool # (/=) :: SourceUnpackedness -> SourceUnpackedness -> Bool #
Eq SourceStrictness	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods (==) :: SourceStrictness -> SourceStrictness -> Bool # (/=) :: SourceStrictness -> SourceStrictness -> Bool #
Eq DecidedStrictness	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods (==) :: DecidedStrictness -> DecidedStrictness -> Bool # (/=) :: DecidedStrictness -> DecidedStrictness -> Bool #
Eq SomeSymbol	Since: base-4.7.0.0
Instance details Defined in GHC.TypeLits Methods (==) :: SomeSymbol -> SomeSymbol -> Bool # (/=) :: SomeSymbol -> SomeSymbol -> Bool #
Eq SomeNat	Since: base-4.7.0.0
Instance details Defined in GHC.TypeNats Methods (==) :: SomeNat -> SomeNat -> Bool # (/=) :: SomeNat -> SomeNat -> Bool #
Eq CChar
Instance details Defined in Foreign.C.Types Methods (==) :: CChar -> CChar -> Bool # (/=) :: CChar -> CChar -> Bool #
Eq CSChar
Instance details Defined in Foreign.C.Types Methods (==) :: CSChar -> CSChar -> Bool # (/=) :: CSChar -> CSChar -> Bool #
Eq CUChar
Instance details Defined in Foreign.C.Types Methods (==) :: CUChar -> CUChar -> Bool # (/=) :: CUChar -> CUChar -> Bool #
Eq CShort
Instance details Defined in Foreign.C.Types Methods (==) :: CShort -> CShort -> Bool # (/=) :: CShort -> CShort -> Bool #
Eq CUShort
Instance details Defined in Foreign.C.Types Methods (==) :: CUShort -> CUShort -> Bool # (/=) :: CUShort -> CUShort -> Bool #
Eq CInt
Instance details Defined in Foreign.C.Types Methods (==) :: CInt -> CInt -> Bool # (/=) :: CInt -> CInt -> Bool #
Eq CUInt
Instance details Defined in Foreign.C.Types Methods (==) :: CUInt -> CUInt -> Bool # (/=) :: CUInt -> CUInt -> Bool #
Eq CLong
Instance details Defined in Foreign.C.Types Methods (==) :: CLong -> CLong -> Bool # (/=) :: CLong -> CLong -> Bool #
Eq CULong
Instance details Defined in Foreign.C.Types Methods (==) :: CULong -> CULong -> Bool # (/=) :: CULong -> CULong -> Bool #
Eq CLLong
Instance details Defined in Foreign.C.Types Methods (==) :: CLLong -> CLLong -> Bool # (/=) :: CLLong -> CLLong -> Bool #
Eq CULLong
Instance details Defined in Foreign.C.Types Methods (==) :: CULLong -> CULLong -> Bool # (/=) :: CULLong -> CULLong -> Bool #
Eq CBool
Instance details Defined in Foreign.C.Types Methods (==) :: CBool -> CBool -> Bool # (/=) :: CBool -> CBool -> Bool #
Eq CFloat
Instance details Defined in Foreign.C.Types Methods (==) :: CFloat -> CFloat -> Bool # (/=) :: CFloat -> CFloat -> Bool #
Eq CDouble
Instance details Defined in Foreign.C.Types Methods (==) :: CDouble -> CDouble -> Bool # (/=) :: CDouble -> CDouble -> Bool #
Eq CPtrdiff
Instance details Defined in Foreign.C.Types Methods (==) :: CPtrdiff -> CPtrdiff -> Bool # (/=) :: CPtrdiff -> CPtrdiff -> Bool #
Eq CSize
Instance details Defined in Foreign.C.Types Methods (==) :: CSize -> CSize -> Bool # (/=) :: CSize -> CSize -> Bool #
Eq CWchar
Instance details Defined in Foreign.C.Types Methods (==) :: CWchar -> CWchar -> Bool # (/=) :: CWchar -> CWchar -> Bool #
Eq CSigAtomic
Instance details Defined in Foreign.C.Types Methods (==) :: CSigAtomic -> CSigAtomic -> Bool # (/=) :: CSigAtomic -> CSigAtomic -> Bool #
Eq CClock
Instance details Defined in Foreign.C.Types Methods (==) :: CClock -> CClock -> Bool # (/=) :: CClock -> CClock -> Bool #
Eq CTime
Instance details Defined in Foreign.C.Types Methods (==) :: CTime -> CTime -> Bool # (/=) :: CTime -> CTime -> Bool #
Eq CUSeconds
Instance details Defined in Foreign.C.Types Methods (==) :: CUSeconds -> CUSeconds -> Bool # (/=) :: CUSeconds -> CUSeconds -> Bool #
Eq CSUSeconds
Instance details Defined in Foreign.C.Types Methods (==) :: CSUSeconds -> CSUSeconds -> Bool # (/=) :: CSUSeconds -> CSUSeconds -> Bool #
Eq CIntPtr
Instance details Defined in Foreign.C.Types Methods (==) :: CIntPtr -> CIntPtr -> Bool # (/=) :: CIntPtr -> CIntPtr -> Bool #
Eq CUIntPtr
Instance details Defined in Foreign.C.Types Methods (==) :: CUIntPtr -> CUIntPtr -> Bool # (/=) :: CUIntPtr -> CUIntPtr -> Bool #
Eq CIntMax
Instance details Defined in Foreign.C.Types Methods (==) :: CIntMax -> CIntMax -> Bool # (/=) :: CIntMax -> CIntMax -> Bool #
Eq CUIntMax
Instance details Defined in Foreign.C.Types Methods (==) :: CUIntMax -> CUIntMax -> Bool # (/=) :: CUIntMax -> CUIntMax -> Bool #
Eq WordPtr
Instance details Defined in Foreign.Ptr Methods (==) :: WordPtr -> WordPtr -> Bool # (/=) :: WordPtr -> WordPtr -> Bool #
Eq IntPtr
Instance details Defined in Foreign.Ptr Methods (==) :: IntPtr -> IntPtr -> Bool # (/=) :: IntPtr -> IntPtr -> Bool #
Eq Fingerprint	Since: base-4.4.0.0
Instance details Defined in GHC.Fingerprint.Type Methods (==) :: Fingerprint -> Fingerprint -> Bool # (/=) :: Fingerprint -> Fingerprint -> Bool #
Eq SrcLoc	Since: base-4.9.0.0
Instance details Defined in GHC.Stack.Types Methods (==) :: SrcLoc -> SrcLoc -> Bool # (/=) :: SrcLoc -> SrcLoc -> Bool #
Eq ByteArray	Since: primitive-0.6.3.0
Instance details Defined in Data.Primitive.ByteArray Methods (==) :: ByteArray -> ByteArray -> Bool # (/=) :: ByteArray -> ByteArray -> Bool #
Eq Addr
Instance details Defined in Data.Primitive.Types Methods (==) :: Addr -> Addr -> Bool # (/=) :: Addr -> Addr -> Bool #
Eq DynamicDimension Source #
Instance details Defined in Numeric.Units.Dimensional.Dimensions.TermLevel Methods (==) :: DynamicDimension -> DynamicDimension -> Bool # (/=) :: DynamicDimension -> DynamicDimension -> Bool #
Eq Dimension' Source #
Instance details Defined in Numeric.Units.Dimensional.Dimensions.TermLevel Methods (==) :: Dimension' -> Dimension' -> Bool # (/=) :: Dimension' -> Dimension' -> Bool #
Eq InterchangeName Source #
Instance details Defined in Numeric.Units.Dimensional.UnitNames.InterchangeNames Methods (==) :: InterchangeName -> InterchangeName -> Bool # (/=) :: InterchangeName -> InterchangeName -> Bool #
Eq InterchangeNameAuthority Source #
Instance details Defined in Numeric.Units.Dimensional.UnitNames.InterchangeNames Methods (==) :: InterchangeNameAuthority -> InterchangeNameAuthority -> Bool # (/=) :: InterchangeNameAuthority -> InterchangeNameAuthority -> Bool #
Eq Metricality Source #
Instance details Defined in Numeric.Units.Dimensional.Variants Methods (==) :: Metricality -> Metricality -> Bool # (/=) :: Metricality -> Metricality -> Bool #
Eq Prefix Source #
Instance details Defined in Numeric.Units.Dimensional.UnitNames.Internal Methods (==) :: Prefix -> Prefix -> Bool # (/=) :: Prefix -> Prefix -> Bool #
Eq a => Eq [a]
Instance details Defined in GHC.Classes Methods (==) :: [a] -> [a] -> Bool # (/=) :: [a] -> [a] -> Bool #
Eq a => Eq (Maybe a)	Since: base-2.1
Instance details Defined in GHC.Maybe Methods (==) :: Maybe a -> Maybe a -> Bool # (/=) :: Maybe a -> Maybe a -> Bool #
Eq a => Eq (Ratio a)	Since: base-2.1
Instance details Defined in GHC.Real Methods (==) :: Ratio a -> Ratio a -> Bool # (/=) :: Ratio a -> Ratio a -> Bool #
Eq (StablePtr a)	Since: base-2.1
Instance details Defined in GHC.Stable Methods (==) :: StablePtr a -> StablePtr a -> Bool # (/=) :: StablePtr a -> StablePtr a -> Bool #
Eq (Ptr a)	Since: base-2.1
Instance details Defined in GHC.Ptr Methods (==) :: Ptr a -> Ptr a -> Bool # (/=) :: Ptr a -> Ptr a -> Bool #
Eq (FunPtr a)
Instance details Defined in GHC.Ptr Methods (==) :: FunPtr a -> FunPtr a -> Bool # (/=) :: FunPtr a -> FunPtr a -> Bool #
Eq p => Eq (Par1 p)	Since: base-4.7.0.0
Instance details Defined in GHC.Generics Methods (==) :: Par1 p -> Par1 p -> Bool # (/=) :: Par1 p -> Par1 p -> Bool #
Eq (ForeignPtr a)	Since: base-2.1
Instance details Defined in GHC.ForeignPtr Methods (==) :: ForeignPtr a -> ForeignPtr a -> Bool # (/=) :: ForeignPtr a -> ForeignPtr a -> Bool #
Eq a => Eq (Complex a)	Since: base-2.1
Instance details Defined in Data.Complex Methods (==) :: Complex a -> Complex a -> Bool # (/=) :: Complex a -> Complex a -> Bool #
Eq (Fixed a)	Since: base-2.1
Instance details Defined in Data.Fixed Methods (==) :: Fixed a -> Fixed a -> Bool # (/=) :: Fixed a -> Fixed a -> Bool #
Eq a => Eq (Min a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods (==) :: Min a -> Min a -> Bool # (/=) :: Min a -> Min a -> Bool #
Eq a => Eq (Max a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods (==) :: Max a -> Max a -> Bool # (/=) :: Max a -> Max a -> Bool #
Eq a => Eq (First a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods (==) :: First a -> First a -> Bool # (/=) :: First a -> First a -> Bool #
Eq a => Eq (Last a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods (==) :: Last a -> Last a -> Bool # (/=) :: Last a -> Last a -> Bool #
Eq m => Eq (WrappedMonoid m)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods (==) :: WrappedMonoid m -> WrappedMonoid m -> Bool # (/=) :: WrappedMonoid m -> WrappedMonoid m -> Bool #
Eq a => Eq (Option a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods (==) :: Option a -> Option a -> Bool # (/=) :: Option a -> Option a -> Bool #
Eq (StableName a)	Since: base-2.1
Instance details Defined in GHC.StableName Methods (==) :: StableName a -> StableName a -> Bool # (/=) :: StableName a -> StableName a -> Bool #
Eq a => Eq (ZipList a)	Since: base-4.7.0.0
Instance details Defined in Control.Applicative Methods (==) :: ZipList a -> ZipList a -> Bool # (/=) :: ZipList a -> ZipList a -> Bool #
Eq a => Eq (Identity a)	Since: base-4.8.0.0
Instance details Defined in Data.Functor.Identity Methods (==) :: Identity a -> Identity a -> Bool # (/=) :: Identity a -> Identity a -> Bool #
Eq (TVar a)	Since: base-4.8.0.0
Instance details Defined in GHC.Conc.Sync Methods (==) :: TVar a -> TVar a -> Bool # (/=) :: TVar a -> TVar a -> Bool #
Eq (IORef a)	^ Pointer equality. Since: base-4.1.0.0
Instance details Defined in GHC.IORef Methods (==) :: IORef a -> IORef a -> Bool # (/=) :: IORef a -> IORef a -> Bool #
Eq a => Eq (First a)	Since: base-2.1
Instance details Defined in Data.Monoid Methods (==) :: First a -> First a -> Bool # (/=) :: First a -> First a -> Bool #
Eq a => Eq (Last a)	Since: base-2.1
Instance details Defined in Data.Monoid Methods (==) :: Last a -> Last a -> Bool # (/=) :: Last a -> Last a -> Bool #
Eq a => Eq (Dual a)	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods (==) :: Dual a -> Dual a -> Bool # (/=) :: Dual a -> Dual a -> Bool #
Eq a => Eq (Sum a)	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods (==) :: Sum a -> Sum a -> Bool # (/=) :: Sum a -> Sum a -> Bool #
Eq a => Eq (Product a)	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods (==) :: Product a -> Product a -> Bool # (/=) :: Product a -> Product a -> Bool #
Eq a => Eq (Down a)	Since: base-4.6.0.0
Instance details Defined in Data.Ord Methods (==) :: Down a -> Down a -> Bool # (/=) :: Down a -> Down a -> Bool #
Eq (MVar a)	Since: base-4.1.0.0
Instance details Defined in GHC.MVar Methods (==) :: MVar a -> MVar a -> Bool # (/=) :: MVar a -> MVar a -> Bool #
Eq a => Eq (NonEmpty a)	Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods (==) :: NonEmpty a -> NonEmpty a -> Bool # (/=) :: NonEmpty a -> NonEmpty a -> Bool #
(Eq a, PrimUnlifted a) => Eq (UnliftedArray a)
Instance details Defined in Data.Primitive.UnliftedArray Methods (==) :: UnliftedArray a -> UnliftedArray a -> Bool # (/=) :: UnliftedArray a -> UnliftedArray a -> Bool #
(Eq a, Prim a) => Eq (PrimArray a)	Since: primitive-0.6.4.0
Instance details Defined in Data.Primitive.PrimArray Methods (==) :: PrimArray a -> PrimArray a -> Bool # (/=) :: PrimArray a -> PrimArray a -> Bool #
Eq a => Eq (SmallArray a)
Instance details Defined in Data.Primitive.SmallArray Methods (==) :: SmallArray a -> SmallArray a -> Bool # (/=) :: SmallArray a -> SmallArray a -> Bool #
Eq a => Eq (Array a)
Instance details Defined in Data.Primitive.Array Methods (==) :: Array a -> Array a -> Bool # (/=) :: Array a -> Array a -> Bool #
(Prim a, Eq a) => Eq (Vector a)
Instance details Defined in Data.Vector.Primitive Methods (==) :: Vector a -> Vector a -> Bool # (/=) :: Vector a -> Vector a -> Bool #
Eq (NameAtom m) Source #
Instance details Defined in Numeric.Units.Dimensional.UnitNames.Internal Methods (==) :: NameAtom m -> NameAtom m -> Bool # (/=) :: NameAtom m -> NameAtom m -> Bool #
Eq (UnitName m) Source #
Instance details Defined in Numeric.Units.Dimensional.UnitNames.Internal Methods (==) :: UnitName m -> UnitName m -> Bool # (/=) :: UnitName m -> UnitName m -> Bool #
Eq a => Eq (DynQuantity a) Source #
Instance details Defined in Numeric.Units.Dimensional.Dynamic Methods (==) :: DynQuantity a -> DynQuantity a -> Bool # (/=) :: DynQuantity a -> DynQuantity a -> Bool #
Eq a => Eq (AnyQuantity a) Source #
Instance details Defined in Numeric.Units.Dimensional.Dynamic Methods (==) :: AnyQuantity a -> AnyQuantity a -> Bool # (/=) :: AnyQuantity a -> AnyQuantity a -> Bool #
(Eq a, Eq b) => Eq (Either a b)	Since: base-2.1
Instance details Defined in Data.Either Methods (==) :: Either a b -> Either a b -> Bool # (/=) :: Either a b -> Either a b -> Bool #
Eq (V1 p)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods (==) :: V1 p -> V1 p -> Bool # (/=) :: V1 p -> V1 p -> Bool #
Eq (U1 p)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods (==) :: U1 p -> U1 p -> Bool # (/=) :: U1 p -> U1 p -> Bool #
Eq (TypeRep a)	Since: base-2.1
Instance details Defined in Data.Typeable.Internal Methods (==) :: TypeRep a -> TypeRep a -> Bool # (/=) :: TypeRep a -> TypeRep a -> Bool #
(Eq a, Eq b) => Eq (a, b)
Instance details Defined in GHC.Classes Methods (==) :: (a, b) -> (a, b) -> Bool # (/=) :: (a, b) -> (a, b) -> Bool #
(Ix i, Eq e) => Eq (Array i e)	Since: base-2.1
Instance details Defined in GHC.Arr Methods (==) :: Array i e -> Array i e -> Bool # (/=) :: Array i e -> Array i e -> Bool #
Eq a => Eq (Arg a b)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods (==) :: Arg a b -> Arg a b -> Bool # (/=) :: Arg a b -> Arg a b -> Bool #
Eq (Proxy s)	Since: base-4.7.0.0
Instance details Defined in Data.Proxy Methods (==) :: Proxy s -> Proxy s -> Bool # (/=) :: Proxy s -> Proxy s -> Bool #
Eq (STRef s a)	Pointer equality. Since: base-2.1
Instance details Defined in GHC.STRef Methods (==) :: STRef s a -> STRef s a -> Bool # (/=) :: STRef s a -> STRef s a -> Bool #
Eq (MutableUnliftedArray s a)
Instance details Defined in Data.Primitive.UnliftedArray Methods (==) :: MutableUnliftedArray s a -> MutableUnliftedArray s a -> Bool # (/=) :: MutableUnliftedArray s a -> MutableUnliftedArray s a -> Bool #
Eq (SmallMutableArray s a)
Instance details Defined in Data.Primitive.SmallArray Methods (==) :: SmallMutableArray s a -> SmallMutableArray s a -> Bool # (/=) :: SmallMutableArray s a -> SmallMutableArray s a -> Bool #
Eq (MutableArray s a)
Instance details Defined in Data.Primitive.Array Methods (==) :: MutableArray s a -> MutableArray s a -> Bool # (/=) :: MutableArray s a -> MutableArray s a -> Bool #
(Eq1 m, Eq a) => Eq (MaybeT m a)
Instance details Defined in Control.Monad.Trans.Maybe Methods (==) :: MaybeT m a -> MaybeT m a -> Bool # (/=) :: MaybeT m a -> MaybeT m a -> Bool #
(Eq1 m, Eq a) => Eq (ListT m a)
Instance details Defined in Control.Monad.Trans.List Methods (==) :: ListT m a -> ListT m a -> Bool # (/=) :: ListT m a -> ListT m a -> Bool #
Eq (f p) => Eq (Rec1 f p)	Since: base-4.7.0.0
Instance details Defined in GHC.Generics Methods (==) :: Rec1 f p -> Rec1 f p -> Bool # (/=) :: Rec1 f p -> Rec1 f p -> Bool #
Eq (URec (Ptr ()) p)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods (==) :: URec (Ptr ()) p -> URec (Ptr ()) p -> Bool # (/=) :: URec (Ptr ()) p -> URec (Ptr ()) p -> Bool #
Eq (URec Char p)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods (==) :: URec Char p -> URec Char p -> Bool # (/=) :: URec Char p -> URec Char p -> Bool #
Eq (URec Double p)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods (==) :: URec Double p -> URec Double p -> Bool # (/=) :: URec Double p -> URec Double p -> Bool #
Eq (URec Float p)
Instance details Defined in GHC.Generics Methods (==) :: URec Float p -> URec Float p -> Bool # (/=) :: URec Float p -> URec Float p -> Bool #
Eq (URec Int p)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods (==) :: URec Int p -> URec Int p -> Bool # (/=) :: URec Int p -> URec Int p -> Bool #
Eq (URec Word p)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods (==) :: URec Word p -> URec Word p -> Bool # (/=) :: URec Word p -> URec Word p -> Bool #
(Eq a, Eq b, Eq c) => Eq (a, b, c)
Instance details Defined in GHC.Classes Methods (==) :: (a, b, c) -> (a, b, c) -> Bool # (/=) :: (a, b, c) -> (a, b, c) -> Bool #
Eq (STArray s i e)	Since: base-2.1
Instance details Defined in GHC.Arr Methods (==) :: STArray s i e -> STArray s i e -> Bool # (/=) :: STArray s i e -> STArray s i e -> Bool #
Eq a => Eq (Const a b)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Const Methods (==) :: Const a b -> Const a b -> Bool # (/=) :: Const a b -> Const a b -> Bool #
Eq (f a) => Eq (Ap f a)	Since: base-4.12.0.0
Instance details Defined in Data.Monoid Methods (==) :: Ap f a -> Ap f a -> Bool # (/=) :: Ap f a -> Ap f a -> Bool #
Eq (f a) => Eq (Alt f a)	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods (==) :: Alt f a -> Alt f a -> Bool # (/=) :: Alt f a -> Alt f a -> Bool #
Eq (Coercion a b)	Since: base-4.7.0.0
Instance details Defined in Data.Type.Coercion Methods (==) :: Coercion a b -> Coercion a b -> Bool # (/=) :: Coercion a b -> Coercion a b -> Bool #
Eq (a :~: b)	Since: base-4.7.0.0
Instance details Defined in Data.Type.Equality Methods (==) :: (a :~: b) -> (a :~: b) -> Bool # (/=) :: (a :~: b) -> (a :~: b) -> Bool #
(Eq w, Eq1 m, Eq a) => Eq (WriterT w m a)
Instance details Defined in Control.Monad.Trans.Writer.Strict Methods (==) :: WriterT w m a -> WriterT w m a -> Bool # (/=) :: WriterT w m a -> WriterT w m a -> Bool #
(Eq w, Eq1 m, Eq a) => Eq (WriterT w m a)
Instance details Defined in Control.Monad.Trans.Writer.Lazy Methods (==) :: WriterT w m a -> WriterT w m a -> Bool # (/=) :: WriterT w m a -> WriterT w m a -> Bool #
(Eq1 f, Eq a) => Eq (IdentityT f a)
Instance details Defined in Control.Monad.Trans.Identity Methods (==) :: IdentityT f a -> IdentityT f a -> Bool # (/=) :: IdentityT f a -> IdentityT f a -> Bool #
(Eq e, Eq1 m, Eq a) => Eq (ExceptT e m a)
Instance details Defined in Control.Monad.Trans.Except Methods (==) :: ExceptT e m a -> ExceptT e m a -> Bool # (/=) :: ExceptT e m a -> ExceptT e m a -> Bool #
(Eq e, Eq1 m, Eq a) => Eq (ErrorT e m a)
Instance details Defined in Control.Monad.Trans.Error Methods (==) :: ErrorT e m a -> ErrorT e m a -> Bool # (/=) :: ErrorT e m a -> ErrorT e m a -> Bool #
Eq a => Eq (Dimensional (DQuantity s) d a) Source #
Instance details Defined in Numeric.Units.Dimensional.Internal Methods (==) :: Dimensional (DQuantity s) d a -> Dimensional (DQuantity s) d a -> Bool # (/=) :: Dimensional (DQuantity s) d a -> Dimensional (DQuantity s) d a -> Bool #
Eq c => Eq (K1 i c p)	Since: base-4.7.0.0
Instance details Defined in GHC.Generics Methods (==) :: K1 i c p -> K1 i c p -> Bool # (/=) :: K1 i c p -> K1 i c p -> Bool #
(Eq (f p), Eq (g p)) => Eq ((f :+: g) p)	Since: base-4.7.0.0
Instance details Defined in GHC.Generics Methods (==) :: (f :+: g) p -> (f :+: g) p -> Bool # (/=) :: (f :+: g) p -> (f :+: g) p -> Bool #
(Eq (f p), Eq (g p)) => Eq ((f :*: g) p)	Since: base-4.7.0.0
Instance details Defined in GHC.Generics Methods (==) :: (f :: g) p -> (f :: g) p -> Bool # (/=) :: (f :: g) p -> (f :: g) p -> Bool #
(Eq a, Eq b, Eq c, Eq d) => Eq (a, b, c, d)
Instance details Defined in GHC.Classes Methods (==) :: (a, b, c, d) -> (a, b, c, d) -> Bool # (/=) :: (a, b, c, d) -> (a, b, c, d) -> Bool #
(Eq1 f, Eq1 g, Eq a) => Eq (Product f g a)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Product Methods (==) :: Product f g a -> Product f g a -> Bool # (/=) :: Product f g a -> Product f g a -> Bool #
(Eq1 f, Eq1 g, Eq a) => Eq (Sum f g a)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Sum Methods (==) :: Sum f g a -> Sum f g a -> Bool # (/=) :: Sum f g a -> Sum f g a -> Bool #
Eq (a :~~: b)	Since: base-4.10.0.0
Instance details Defined in Data.Type.Equality Methods (==) :: (a :~~: b) -> (a :~~: b) -> Bool # (/=) :: (a :~~: b) -> (a :~~: b) -> Bool #
Eq (f p) => Eq (M1 i c f p)	Since: base-4.7.0.0
Instance details Defined in GHC.Generics Methods (==) :: M1 i c f p -> M1 i c f p -> Bool # (/=) :: M1 i c f p -> M1 i c f p -> Bool #
Eq (f (g p)) => Eq ((f :.: g) p)	Since: base-4.7.0.0
Instance details Defined in GHC.Generics Methods (==) :: (f :.: g) p -> (f :.: g) p -> Bool # (/=) :: (f :.: g) p -> (f :.: g) p -> Bool #
(Eq a, Eq b, Eq c, Eq d, Eq e) => Eq (a, b, c, d, e)
Instance details Defined in GHC.Classes Methods (==) :: (a, b, c, d, e) -> (a, b, c, d, e) -> Bool # (/=) :: (a, b, c, d, e) -> (a, b, c, d, e) -> Bool #
(Eq1 f, Eq1 g, Eq a) => Eq (Compose f g a)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Compose Methods (==) :: Compose f g a -> Compose f g a -> Bool # (/=) :: Compose f g a -> Compose f g a -> Bool #
(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f) => Eq (a, b, c, d, e, f)
Instance details Defined in GHC.Classes Methods (==) :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> Bool # (/=) :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> Bool #
(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g) => Eq (a, b, c, d, e, f, g)
Instance details Defined in GHC.Classes Methods (==) :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) -> Bool # (/=) :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) -> Bool #
(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h) => Eq (a, b, c, d, e, f, g, h)
Instance details Defined in GHC.Classes Methods (==) :: (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) -> Bool # (/=) :: (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) -> Bool #
(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i) => Eq (a, b, c, d, e, f, g, h, i)
Instance details Defined in GHC.Classes Methods (==) :: (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) -> Bool # (/=) :: (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) -> Bool #
(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j) => Eq (a, b, c, d, e, f, g, h, i, j)
Instance details Defined in GHC.Classes Methods (==) :: (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) -> Bool # (/=) :: (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) -> Bool #
(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j, Eq k) => Eq (a, b, c, d, e, f, g, h, i, j, k)
Instance details Defined in GHC.Classes Methods (==) :: (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k) -> Bool # (/=) :: (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k) -> Bool #
(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j, Eq k, Eq l) => Eq (a, b, c, d, e, f, g, h, i, j, k, l)
Instance details Defined in GHC.Classes Methods (==) :: (a, b, c, d, e, f, g, h, i, j, k, l) -> (a, b, c, d, e, f, g, h, i, j, k, l) -> Bool # (/=) :: (a, b, c, d, e, f, g, h, i, j, k, l) -> (a, b, c, d, e, f, g, h, i, j, k, l) -> Bool #
(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j, Eq k, Eq l, Eq m) => Eq (a, b, c, d, e, f, g, h, i, j, k, l, m)
Instance details Defined in GHC.Classes Methods (==) :: (a, b, c, d, e, f, g, h, i, j, k, l, m) -> (a, b, c, d, e, f, g, h, i, j, k, l, m) -> Bool # (/=) :: (a, b, c, d, e, f, g, h, i, j, k, l, m) -> (a, b, c, d, e, f, g, h, i, j, k, l, m) -> Bool #
(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j, Eq k, Eq l, Eq m, Eq n) => Eq (a, b, c, d, e, f, g, h, i, j, k, l, m, n)
Instance details Defined in GHC.Classes Methods (==) :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> Bool # (/=) :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> Bool #
(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j, Eq k, Eq l, Eq m, Eq n, Eq o) => Eq (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o)
Instance details Defined in GHC.Classes Methods (==) :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> Bool # (/=) :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> Bool #

class Fractional a => Floating a #

Trigonometric and hyperbolic functions and related functions.

The Haskell Report defines no laws for Floating. However, '(+)', '(*)' and exp are customarily expected to define an exponential field and have the following properties:

exp (a + b) = @exp a * exp b
exp (fromInteger 0) = fromInteger 1

Minimal complete definition

pi, exp, log, sin, cos, asin, acos, atan, sinh, cosh, asinh, acosh, atanh

Instances

Floating Double	Since: base-2.1
Instance details Defined in GHC.Float Methods pi :: Double # exp :: Double -> Double # log :: Double -> Double # sqrt :: Double -> Double # (**) :: Double -> Double -> Double # logBase :: Double -> Double -> Double # sin :: Double -> Double # cos :: Double -> Double # tan :: Double -> Double # asin :: Double -> Double # acos :: Double -> Double # atan :: Double -> Double # sinh :: Double -> Double # cosh :: Double -> Double # tanh :: Double -> Double # asinh :: Double -> Double # acosh :: Double -> Double # atanh :: Double -> Double # log1p :: Double -> Double # expm1 :: Double -> Double # log1pexp :: Double -> Double # log1mexp :: Double -> Double #
Floating Float	Since: base-2.1
Instance details Defined in GHC.Float Methods pi :: Float # exp :: Float -> Float # log :: Float -> Float # sqrt :: Float -> Float # (**) :: Float -> Float -> Float # logBase :: Float -> Float -> Float # sin :: Float -> Float # cos :: Float -> Float # tan :: Float -> Float # asin :: Float -> Float # acos :: Float -> Float # atan :: Float -> Float # sinh :: Float -> Float # cosh :: Float -> Float # tanh :: Float -> Float # asinh :: Float -> Float # acosh :: Float -> Float # atanh :: Float -> Float # log1p :: Float -> Float # expm1 :: Float -> Float # log1pexp :: Float -> Float # log1mexp :: Float -> Float #
Floating CFloat
Instance details Defined in Foreign.C.Types Methods pi :: CFloat # exp :: CFloat -> CFloat # log :: CFloat -> CFloat # sqrt :: CFloat -> CFloat # (**) :: CFloat -> CFloat -> CFloat # logBase :: CFloat -> CFloat -> CFloat # sin :: CFloat -> CFloat # cos :: CFloat -> CFloat # tan :: CFloat -> CFloat # asin :: CFloat -> CFloat # acos :: CFloat -> CFloat # atan :: CFloat -> CFloat # sinh :: CFloat -> CFloat # cosh :: CFloat -> CFloat # tanh :: CFloat -> CFloat # asinh :: CFloat -> CFloat # acosh :: CFloat -> CFloat # atanh :: CFloat -> CFloat # log1p :: CFloat -> CFloat # expm1 :: CFloat -> CFloat # log1pexp :: CFloat -> CFloat # log1mexp :: CFloat -> CFloat #
Floating CDouble
Instance details Defined in Foreign.C.Types Methods pi :: CDouble # exp :: CDouble -> CDouble # log :: CDouble -> CDouble # sqrt :: CDouble -> CDouble # (**) :: CDouble -> CDouble -> CDouble # logBase :: CDouble -> CDouble -> CDouble # sin :: CDouble -> CDouble # cos :: CDouble -> CDouble # tan :: CDouble -> CDouble # asin :: CDouble -> CDouble # acos :: CDouble -> CDouble # atan :: CDouble -> CDouble # sinh :: CDouble -> CDouble # cosh :: CDouble -> CDouble # tanh :: CDouble -> CDouble # asinh :: CDouble -> CDouble # acosh :: CDouble -> CDouble # atanh :: CDouble -> CDouble # log1p :: CDouble -> CDouble # expm1 :: CDouble -> CDouble # log1pexp :: CDouble -> CDouble # log1mexp :: CDouble -> CDouble #
Floating ExactPi
Instance details Defined in Data.ExactPi Methods pi :: ExactPi # exp :: ExactPi -> ExactPi # log :: ExactPi -> ExactPi # sqrt :: ExactPi -> ExactPi # (**) :: ExactPi -> ExactPi -> ExactPi # logBase :: ExactPi -> ExactPi -> ExactPi # sin :: ExactPi -> ExactPi # cos :: ExactPi -> ExactPi # tan :: ExactPi -> ExactPi # asin :: ExactPi -> ExactPi # acos :: ExactPi -> ExactPi # atan :: ExactPi -> ExactPi # sinh :: ExactPi -> ExactPi # cosh :: ExactPi -> ExactPi # tanh :: ExactPi -> ExactPi # asinh :: ExactPi -> ExactPi # acosh :: ExactPi -> ExactPi # atanh :: ExactPi -> ExactPi # log1p :: ExactPi -> ExactPi # expm1 :: ExactPi -> ExactPi # log1pexp :: ExactPi -> ExactPi # log1mexp :: ExactPi -> ExactPi #
KnownMinCtxt Floating
Instance details Defined in Data.ExactPi.TypeLevel Methods inj :: Floating a => Proxy Floating -> ExactPi -> a
RealFloat a => Floating (Complex a)	Since: base-2.1
Instance details Defined in Data.Complex Methods pi :: Complex a # exp :: Complex a -> Complex a # log :: Complex a -> Complex a # sqrt :: Complex a -> Complex a # (**) :: Complex a -> Complex a -> Complex a # logBase :: Complex a -> Complex a -> Complex a # sin :: Complex a -> Complex a # cos :: Complex a -> Complex a # tan :: Complex a -> Complex a # asin :: Complex a -> Complex a # acos :: Complex a -> Complex a # atan :: Complex a -> Complex a # sinh :: Complex a -> Complex a # cosh :: Complex a -> Complex a # tanh :: Complex a -> Complex a # asinh :: Complex a -> Complex a # acosh :: Complex a -> Complex a # atanh :: Complex a -> Complex a # log1p :: Complex a -> Complex a # expm1 :: Complex a -> Complex a # log1pexp :: Complex a -> Complex a # log1mexp :: Complex a -> Complex a #
Floating a => Floating (Identity a)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Identity Methods pi :: Identity a # exp :: Identity a -> Identity a # log :: Identity a -> Identity a # sqrt :: Identity a -> Identity a # (**) :: Identity a -> Identity a -> Identity a # logBase :: Identity a -> Identity a -> Identity a # sin :: Identity a -> Identity a # cos :: Identity a -> Identity a # tan :: Identity a -> Identity a # asin :: Identity a -> Identity a # acos :: Identity a -> Identity a # atan :: Identity a -> Identity a # sinh :: Identity a -> Identity a # cosh :: Identity a -> Identity a # tanh :: Identity a -> Identity a # asinh :: Identity a -> Identity a # acosh :: Identity a -> Identity a # atanh :: Identity a -> Identity a # log1p :: Identity a -> Identity a # expm1 :: Identity a -> Identity a # log1pexp :: Identity a -> Identity a # log1mexp :: Identity a -> Identity a #
Floating a => Floating (DynQuantity a) Source #
Instance details Defined in Numeric.Units.Dimensional.Dynamic Methods pi :: DynQuantity a # exp :: DynQuantity a -> DynQuantity a # log :: DynQuantity a -> DynQuantity a # sqrt :: DynQuantity a -> DynQuantity a # (**) :: DynQuantity a -> DynQuantity a -> DynQuantity a # logBase :: DynQuantity a -> DynQuantity a -> DynQuantity a # sin :: DynQuantity a -> DynQuantity a # cos :: DynQuantity a -> DynQuantity a # tan :: DynQuantity a -> DynQuantity a # asin :: DynQuantity a -> DynQuantity a # acos :: DynQuantity a -> DynQuantity a # atan :: DynQuantity a -> DynQuantity a # sinh :: DynQuantity a -> DynQuantity a # cosh :: DynQuantity a -> DynQuantity a # tanh :: DynQuantity a -> DynQuantity a # asinh :: DynQuantity a -> DynQuantity a # acosh :: DynQuantity a -> DynQuantity a # atanh :: DynQuantity a -> DynQuantity a # log1p :: DynQuantity a -> DynQuantity a # expm1 :: DynQuantity a -> DynQuantity a # log1pexp :: DynQuantity a -> DynQuantity a # log1mexp :: DynQuantity a -> DynQuantity a #
Floating a => Floating (Const a b)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Const Methods pi :: Const a b # exp :: Const a b -> Const a b # log :: Const a b -> Const a b # sqrt :: Const a b -> Const a b # (**) :: Const a b -> Const a b -> Const a b # logBase :: Const a b -> Const a b -> Const a b # sin :: Const a b -> Const a b # cos :: Const a b -> Const a b # tan :: Const a b -> Const a b # asin :: Const a b -> Const a b # acos :: Const a b -> Const a b # atan :: Const a b -> Const a b # sinh :: Const a b -> Const a b # cosh :: Const a b -> Const a b # tanh :: Const a b -> Const a b # asinh :: Const a b -> Const a b # acosh :: Const a b -> Const a b # atanh :: Const a b -> Const a b # log1p :: Const a b -> Const a b # expm1 :: Const a b -> Const a b # log1pexp :: Const a b -> Const a b # log1mexp :: Const a b -> Const a b #

class Num a => Fractional a where #

Fractional numbers, supporting real division.

The Haskell Report defines no laws for Fractional. However, '(+)' and '(*)' are customarily expected to define a division ring and have the following properties:

recip gives the multiplicative inverse: x * recip x = recip x * x = fromInteger 1

Note that it isn't customarily expected that a type instance of Fractional implement a field. However, all instances in base do.

Methods

fromRational :: Rational -> a #

Conversion from a Rational (that is Ratio Integer). A floating literal stands for an application of fromRational to a value of type Rational, so such literals have type (Fractional a) => a.

Instances

Fractional CFloat
Instance details Defined in Foreign.C.Types Methods (/) :: CFloat -> CFloat -> CFloat # recip :: CFloat -> CFloat # fromRational :: Rational -> CFloat #
Fractional CDouble
Instance details Defined in Foreign.C.Types Methods (/) :: CDouble -> CDouble -> CDouble # recip :: CDouble -> CDouble # fromRational :: Rational -> CDouble #
Fractional ExactPi
Instance details Defined in Data.ExactPi Methods (/) :: ExactPi -> ExactPi -> ExactPi # recip :: ExactPi -> ExactPi # fromRational :: Rational -> ExactPi #
KnownMinCtxt Fractional
Instance details Defined in Data.ExactPi.TypeLevel Methods inj :: Fractional a => Proxy Fractional -> ExactPi -> a
Integral a => Fractional (Ratio a)	Since: base-2.0.1
Instance details Defined in GHC.Real Methods (/) :: Ratio a -> Ratio a -> Ratio a # recip :: Ratio a -> Ratio a # fromRational :: Rational -> Ratio a #
RealFloat a => Fractional (Complex a)	Since: base-2.1
Instance details Defined in Data.Complex Methods (/) :: Complex a -> Complex a -> Complex a # recip :: Complex a -> Complex a # fromRational :: Rational -> Complex a #
HasResolution a => Fractional (Fixed a)	Since: base-2.1
Instance details Defined in Data.Fixed Methods (/) :: Fixed a -> Fixed a -> Fixed a # recip :: Fixed a -> Fixed a # fromRational :: Rational -> Fixed a #
Fractional a => Fractional (Identity a)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Identity Methods (/) :: Identity a -> Identity a -> Identity a # recip :: Identity a -> Identity a # fromRational :: Rational -> Identity a #
Fractional a => Fractional (DynQuantity a) Source #
Instance details Defined in Numeric.Units.Dimensional.Dynamic Methods (/) :: DynQuantity a -> DynQuantity a -> DynQuantity a # recip :: DynQuantity a -> DynQuantity a # fromRational :: Rational -> DynQuantity a #
Fractional a => Fractional (Const a b)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Const Methods (/) :: Const a b -> Const a b -> Const a b # recip :: Const a b -> Const a b # fromRational :: Rational -> Const a b #

class (Real a, Enum a) => Integral a where #

Integral numbers, supporting integer division.

The Haskell Report defines no laws for Integral. However, Integral instances are customarily expected to define a Euclidean domain and have the following properties for the 'div'/'mod' and 'quot'/'rem' pairs, given suitable Euclidean functions f and g:

x = y * quot x y + rem x y with rem x y = fromInteger 0 or g (rem x y) < g y
x = y * div x y + mod x y with mod x y = fromInteger 0 or f (mod x y) < f y

An example of a suitable Euclidean function, for Integer's instance, is abs.

Minimal complete definition

quotRem, toInteger

Methods

quot :: a -> a -> a infixl 7 #

integer division truncated toward zero

rem :: a -> a -> a infixl 7 #

integer remainder, satisfying

(x `quot` y)*y + (x `rem` y) == x

div :: a -> a -> a infixl 7 #

integer division truncated toward negative infinity

mod :: a -> a -> a infixl 7 #

integer modulus, satisfying

(x `div` y)*y + (x `mod` y) == x

quotRem :: a -> a -> (a, a) #

simultaneous quot and rem

divMod :: a -> a -> (a, a) #

simultaneous div and mod

toInteger :: a -> Integer #

conversion to Integer

Instances

Integral Int	Since: base-2.0.1
Instance details Defined in GHC.Real Methods quot :: Int -> Int -> Int # rem :: Int -> Int -> Int # div :: Int -> Int -> Int # mod :: Int -> Int -> Int # quotRem :: Int -> Int -> (Int, Int) # divMod :: Int -> Int -> (Int, Int) # toInteger :: Int -> Integer #
Integral Int8	Since: base-2.1
Instance details Defined in GHC.Int Methods quot :: Int8 -> Int8 -> Int8 # rem :: Int8 -> Int8 -> Int8 # div :: Int8 -> Int8 -> Int8 # mod :: Int8 -> Int8 -> Int8 # quotRem :: Int8 -> Int8 -> (Int8, Int8) # divMod :: Int8 -> Int8 -> (Int8, Int8) # toInteger :: Int8 -> Integer #
Integral Int16	Since: base-2.1
Instance details Defined in GHC.Int Methods quot :: Int16 -> Int16 -> Int16 # rem :: Int16 -> Int16 -> Int16 # div :: Int16 -> Int16 -> Int16 # mod :: Int16 -> Int16 -> Int16 # quotRem :: Int16 -> Int16 -> (Int16, Int16) # divMod :: Int16 -> Int16 -> (Int16, Int16) # toInteger :: Int16 -> Integer #
Integral Int32	Since: base-2.1
Instance details Defined in GHC.Int Methods quot :: Int32 -> Int32 -> Int32 # rem :: Int32 -> Int32 -> Int32 # div :: Int32 -> Int32 -> Int32 # mod :: Int32 -> Int32 -> Int32 # quotRem :: Int32 -> Int32 -> (Int32, Int32) # divMod :: Int32 -> Int32 -> (Int32, Int32) # toInteger :: Int32 -> Integer #
Integral Int64	Since: base-2.1
Instance details Defined in GHC.Int Methods quot :: Int64 -> Int64 -> Int64 # rem :: Int64 -> Int64 -> Int64 # div :: Int64 -> Int64 -> Int64 # mod :: Int64 -> Int64 -> Int64 # quotRem :: Int64 -> Int64 -> (Int64, Int64) # divMod :: Int64 -> Int64 -> (Int64, Int64) # toInteger :: Int64 -> Integer #
Integral Integer	Since: base-2.0.1
Instance details Defined in GHC.Real Methods quot :: Integer -> Integer -> Integer # rem :: Integer -> Integer -> Integer # div :: Integer -> Integer -> Integer # mod :: Integer -> Integer -> Integer # quotRem :: Integer -> Integer -> (Integer, Integer) # divMod :: Integer -> Integer -> (Integer, Integer) # toInteger :: Integer -> Integer #
Integral Natural	Since: base-4.8.0.0
Instance details Defined in GHC.Real Methods quot :: Natural -> Natural -> Natural # rem :: Natural -> Natural -> Natural # div :: Natural -> Natural -> Natural # mod :: Natural -> Natural -> Natural # quotRem :: Natural -> Natural -> (Natural, Natural) # divMod :: Natural -> Natural -> (Natural, Natural) # toInteger :: Natural -> Integer #
Integral Word	Since: base-2.1
Instance details Defined in GHC.Real Methods quot :: Word -> Word -> Word # rem :: Word -> Word -> Word # div :: Word -> Word -> Word # mod :: Word -> Word -> Word # quotRem :: Word -> Word -> (Word, Word) # divMod :: Word -> Word -> (Word, Word) # toInteger :: Word -> Integer #
Integral Word8	Since: base-2.1
Instance details Defined in GHC.Word Methods quot :: Word8 -> Word8 -> Word8 # rem :: Word8 -> Word8 -> Word8 # div :: Word8 -> Word8 -> Word8 # mod :: Word8 -> Word8 -> Word8 # quotRem :: Word8 -> Word8 -> (Word8, Word8) # divMod :: Word8 -> Word8 -> (Word8, Word8) # toInteger :: Word8 -> Integer #
Integral Word16	Since: base-2.1
Instance details Defined in GHC.Word Methods quot :: Word16 -> Word16 -> Word16 # rem :: Word16 -> Word16 -> Word16 # div :: Word16 -> Word16 -> Word16 # mod :: Word16 -> Word16 -> Word16 # quotRem :: Word16 -> Word16 -> (Word16, Word16) # divMod :: Word16 -> Word16 -> (Word16, Word16) # toInteger :: Word16 -> Integer #
Integral Word32	Since: base-2.1
Instance details Defined in GHC.Word Methods quot :: Word32 -> Word32 -> Word32 # rem :: Word32 -> Word32 -> Word32 # div :: Word32 -> Word32 -> Word32 # mod :: Word32 -> Word32 -> Word32 # quotRem :: Word32 -> Word32 -> (Word32, Word32) # divMod :: Word32 -> Word32 -> (Word32, Word32) # toInteger :: Word32 -> Integer #
Integral Word64	Since: base-2.1
Instance details Defined in GHC.Word Methods quot :: Word64 -> Word64 -> Word64 # rem :: Word64 -> Word64 -> Word64 # div :: Word64 -> Word64 -> Word64 # mod :: Word64 -> Word64 -> Word64 # quotRem :: Word64 -> Word64 -> (Word64, Word64) # divMod :: Word64 -> Word64 -> (Word64, Word64) # toInteger :: Word64 -> Integer #
Integral CChar
Instance details Defined in Foreign.C.Types Methods quot :: CChar -> CChar -> CChar # rem :: CChar -> CChar -> CChar # div :: CChar -> CChar -> CChar # mod :: CChar -> CChar -> CChar # quotRem :: CChar -> CChar -> (CChar, CChar) # divMod :: CChar -> CChar -> (CChar, CChar) # toInteger :: CChar -> Integer #
Integral CSChar
Instance details Defined in Foreign.C.Types Methods quot :: CSChar -> CSChar -> CSChar # rem :: CSChar -> CSChar -> CSChar # div :: CSChar -> CSChar -> CSChar # mod :: CSChar -> CSChar -> CSChar # quotRem :: CSChar -> CSChar -> (CSChar, CSChar) # divMod :: CSChar -> CSChar -> (CSChar, CSChar) # toInteger :: CSChar -> Integer #
Integral CUChar
Instance details Defined in Foreign.C.Types Methods quot :: CUChar -> CUChar -> CUChar # rem :: CUChar -> CUChar -> CUChar # div :: CUChar -> CUChar -> CUChar # mod :: CUChar -> CUChar -> CUChar # quotRem :: CUChar -> CUChar -> (CUChar, CUChar) # divMod :: CUChar -> CUChar -> (CUChar, CUChar) # toInteger :: CUChar -> Integer #
Integral CShort
Instance details Defined in Foreign.C.Types Methods quot :: CShort -> CShort -> CShort # rem :: CShort -> CShort -> CShort # div :: CShort -> CShort -> CShort # mod :: CShort -> CShort -> CShort # quotRem :: CShort -> CShort -> (CShort, CShort) # divMod :: CShort -> CShort -> (CShort, CShort) # toInteger :: CShort -> Integer #
Integral CUShort
Instance details Defined in Foreign.C.Types Methods quot :: CUShort -> CUShort -> CUShort # rem :: CUShort -> CUShort -> CUShort # div :: CUShort -> CUShort -> CUShort # mod :: CUShort -> CUShort -> CUShort # quotRem :: CUShort -> CUShort -> (CUShort, CUShort) # divMod :: CUShort -> CUShort -> (CUShort, CUShort) # toInteger :: CUShort -> Integer #
Integral CInt
Instance details Defined in Foreign.C.Types Methods quot :: CInt -> CInt -> CInt # rem :: CInt -> CInt -> CInt # div :: CInt -> CInt -> CInt # mod :: CInt -> CInt -> CInt # quotRem :: CInt -> CInt -> (CInt, CInt) # divMod :: CInt -> CInt -> (CInt, CInt) # toInteger :: CInt -> Integer #
Integral CUInt
Instance details Defined in Foreign.C.Types Methods quot :: CUInt -> CUInt -> CUInt # rem :: CUInt -> CUInt -> CUInt # div :: CUInt -> CUInt -> CUInt # mod :: CUInt -> CUInt -> CUInt # quotRem :: CUInt -> CUInt -> (CUInt, CUInt) # divMod :: CUInt -> CUInt -> (CUInt, CUInt) # toInteger :: CUInt -> Integer #
Integral CLong
Instance details Defined in Foreign.C.Types Methods quot :: CLong -> CLong -> CLong # rem :: CLong -> CLong -> CLong # div :: CLong -> CLong -> CLong # mod :: CLong -> CLong -> CLong # quotRem :: CLong -> CLong -> (CLong, CLong) # divMod :: CLong -> CLong -> (CLong, CLong) # toInteger :: CLong -> Integer #
Integral CULong
Instance details Defined in Foreign.C.Types Methods quot :: CULong -> CULong -> CULong # rem :: CULong -> CULong -> CULong # div :: CULong -> CULong -> CULong # mod :: CULong -> CULong -> CULong # quotRem :: CULong -> CULong -> (CULong, CULong) # divMod :: CULong -> CULong -> (CULong, CULong) # toInteger :: CULong -> Integer #
Integral CLLong
Instance details Defined in Foreign.C.Types Methods quot :: CLLong -> CLLong -> CLLong # rem :: CLLong -> CLLong -> CLLong # div :: CLLong -> CLLong -> CLLong # mod :: CLLong -> CLLong -> CLLong # quotRem :: CLLong -> CLLong -> (CLLong, CLLong) # divMod :: CLLong -> CLLong -> (CLLong, CLLong) # toInteger :: CLLong -> Integer #
Integral CULLong
Instance details Defined in Foreign.C.Types Methods quot :: CULLong -> CULLong -> CULLong # rem :: CULLong -> CULLong -> CULLong # div :: CULLong -> CULLong -> CULLong # mod :: CULLong -> CULLong -> CULLong # quotRem :: CULLong -> CULLong -> (CULLong, CULLong) # divMod :: CULLong -> CULLong -> (CULLong, CULLong) # toInteger :: CULLong -> Integer #
Integral CBool
Instance details Defined in Foreign.C.Types Methods quot :: CBool -> CBool -> CBool # rem :: CBool -> CBool -> CBool # div :: CBool -> CBool -> CBool # mod :: CBool -> CBool -> CBool # quotRem :: CBool -> CBool -> (CBool, CBool) # divMod :: CBool -> CBool -> (CBool, CBool) # toInteger :: CBool -> Integer #
Integral CPtrdiff
Instance details Defined in Foreign.C.Types Methods quot :: CPtrdiff -> CPtrdiff -> CPtrdiff # rem :: CPtrdiff -> CPtrdiff -> CPtrdiff # div :: CPtrdiff -> CPtrdiff -> CPtrdiff # mod :: CPtrdiff -> CPtrdiff -> CPtrdiff # quotRem :: CPtrdiff -> CPtrdiff -> (CPtrdiff, CPtrdiff) # divMod :: CPtrdiff -> CPtrdiff -> (CPtrdiff, CPtrdiff) # toInteger :: CPtrdiff -> Integer #
Integral CSize
Instance details Defined in Foreign.C.Types Methods quot :: CSize -> CSize -> CSize # rem :: CSize -> CSize -> CSize # div :: CSize -> CSize -> CSize # mod :: CSize -> CSize -> CSize # quotRem :: CSize -> CSize -> (CSize, CSize) # divMod :: CSize -> CSize -> (CSize, CSize) # toInteger :: CSize -> Integer #
Integral CWchar
Instance details Defined in Foreign.C.Types Methods quot :: CWchar -> CWchar -> CWchar # rem :: CWchar -> CWchar -> CWchar # div :: CWchar -> CWchar -> CWchar # mod :: CWchar -> CWchar -> CWchar # quotRem :: CWchar -> CWchar -> (CWchar, CWchar) # divMod :: CWchar -> CWchar -> (CWchar, CWchar) # toInteger :: CWchar -> Integer #
Integral CSigAtomic
Instance details Defined in Foreign.C.Types Methods quot :: CSigAtomic -> CSigAtomic -> CSigAtomic # rem :: CSigAtomic -> CSigAtomic -> CSigAtomic # div :: CSigAtomic -> CSigAtomic -> CSigAtomic # mod :: CSigAtomic -> CSigAtomic -> CSigAtomic # quotRem :: CSigAtomic -> CSigAtomic -> (CSigAtomic, CSigAtomic) # divMod :: CSigAtomic -> CSigAtomic -> (CSigAtomic, CSigAtomic) # toInteger :: CSigAtomic -> Integer #
Integral CIntPtr
Instance details Defined in Foreign.C.Types Methods quot :: CIntPtr -> CIntPtr -> CIntPtr # rem :: CIntPtr -> CIntPtr -> CIntPtr # div :: CIntPtr -> CIntPtr -> CIntPtr # mod :: CIntPtr -> CIntPtr -> CIntPtr # quotRem :: CIntPtr -> CIntPtr -> (CIntPtr, CIntPtr) # divMod :: CIntPtr -> CIntPtr -> (CIntPtr, CIntPtr) # toInteger :: CIntPtr -> Integer #
Integral CUIntPtr
Instance details Defined in Foreign.C.Types Methods quot :: CUIntPtr -> CUIntPtr -> CUIntPtr # rem :: CUIntPtr -> CUIntPtr -> CUIntPtr # div :: CUIntPtr -> CUIntPtr -> CUIntPtr # mod :: CUIntPtr -> CUIntPtr -> CUIntPtr # quotRem :: CUIntPtr -> CUIntPtr -> (CUIntPtr, CUIntPtr) # divMod :: CUIntPtr -> CUIntPtr -> (CUIntPtr, CUIntPtr) # toInteger :: CUIntPtr -> Integer #
Integral CIntMax
Instance details Defined in Foreign.C.Types Methods quot :: CIntMax -> CIntMax -> CIntMax # rem :: CIntMax -> CIntMax -> CIntMax # div :: CIntMax -> CIntMax -> CIntMax # mod :: CIntMax -> CIntMax -> CIntMax # quotRem :: CIntMax -> CIntMax -> (CIntMax, CIntMax) # divMod :: CIntMax -> CIntMax -> (CIntMax, CIntMax) # toInteger :: CIntMax -> Integer #
Integral CUIntMax
Instance details Defined in Foreign.C.Types Methods quot :: CUIntMax -> CUIntMax -> CUIntMax # rem :: CUIntMax -> CUIntMax -> CUIntMax # div :: CUIntMax -> CUIntMax -> CUIntMax # mod :: CUIntMax -> CUIntMax -> CUIntMax # quotRem :: CUIntMax -> CUIntMax -> (CUIntMax, CUIntMax) # divMod :: CUIntMax -> CUIntMax -> (CUIntMax, CUIntMax) # toInteger :: CUIntMax -> Integer #
Integral WordPtr
Instance details Defined in Foreign.Ptr Methods quot :: WordPtr -> WordPtr -> WordPtr # rem :: WordPtr -> WordPtr -> WordPtr # div :: WordPtr -> WordPtr -> WordPtr # mod :: WordPtr -> WordPtr -> WordPtr # quotRem :: WordPtr -> WordPtr -> (WordPtr, WordPtr) # divMod :: WordPtr -> WordPtr -> (WordPtr, WordPtr) # toInteger :: WordPtr -> Integer #
Integral IntPtr
Instance details Defined in Foreign.Ptr Methods quot :: IntPtr -> IntPtr -> IntPtr # rem :: IntPtr -> IntPtr -> IntPtr # div :: IntPtr -> IntPtr -> IntPtr # mod :: IntPtr -> IntPtr -> IntPtr # quotRem :: IntPtr -> IntPtr -> (IntPtr, IntPtr) # divMod :: IntPtr -> IntPtr -> (IntPtr, IntPtr) # toInteger :: IntPtr -> Integer #
Integral a => Integral (Identity a)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Identity Methods quot :: Identity a -> Identity a -> Identity a # rem :: Identity a -> Identity a -> Identity a # div :: Identity a -> Identity a -> Identity a # mod :: Identity a -> Identity a -> Identity a # quotRem :: Identity a -> Identity a -> (Identity a, Identity a) # divMod :: Identity a -> Identity a -> (Identity a, Identity a) # toInteger :: Identity a -> Integer #
Integral a => Integral (Const a b)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Const Methods quot :: Const a b -> Const a b -> Const a b # rem :: Const a b -> Const a b -> Const a b # div :: Const a b -> Const a b -> Const a b # mod :: Const a b -> Const a b -> Const a b # quotRem :: Const a b -> Const a b -> (Const a b, Const a b) # divMod :: Const a b -> Const a b -> (Const a b, Const a b) # toInteger :: Const a b -> Integer #

class Applicative m => Monad (m :: Type -> Type) where #

The Monad class defines the basic operations over a monad, a concept from a branch of mathematics known as category theory. From the perspective of a Haskell programmer, however, it is best to think of a monad as an abstract datatype of actions. Haskell's do expressions provide a convenient syntax for writing monadic expressions.

Instances of Monad should satisfy the following laws:

```
return a >>= k  =  k a
```
```
m >>= return  =  m
```

m >>= (\x -> k x >>= h)  =  (m >>= k) >>= h

Furthermore, the Monad and Applicative operations should relate as follows:

```
pure = return
```
```
(<*>) = ap
```

The above laws imply:

```
fmap f xs  =  xs >>= return . f
```
```
(>>) = (*>)
```

and that pure and (<*>) satisfy the applicative functor laws.

The instances of Monad for lists, Maybe and IO defined in the Prelude satisfy these laws.

Minimal complete definition

(>>=)

Methods

(>>=) :: m a -> (a -> m b) -> m b infixl 1 #

Sequentially compose two actions, passing any value produced by the first as an argument to the second.

(>>) :: m a -> m b -> m b infixl 1 #

Sequentially compose two actions, discarding any value produced by the first, like sequencing operators (such as the semicolon) in imperative languages.

return :: a -> m a #

Inject a value into the monadic type.

fail :: String -> m a #

Fail with a message. This operation is not part of the mathematical definition of a monad, but is invoked on pattern-match failure in a do expression.

As part of the MonadFail proposal (MFP), this function is moved to its own class MonadFail (see Control.Monad.Fail for more details). The definition here will be removed in a future release.

Instances

Monad []	Since: base-2.1
Instance details Defined in GHC.Base Methods (>>=) :: [a] -> (a -> [b]) -> [b] # (>>) :: [a] -> [b] -> [b] # return :: a -> [a] # fail :: String -> [a] #
Monad Maybe	Since: base-2.1
Instance details Defined in GHC.Base Methods (>>=) :: Maybe a -> (a -> Maybe b) -> Maybe b # (>>) :: Maybe a -> Maybe b -> Maybe b # return :: a -> Maybe a # fail :: String -> Maybe a #
Monad IO	Since: base-2.1
Instance details Defined in GHC.Base Methods (>>=) :: IO a -> (a -> IO b) -> IO b # (>>) :: IO a -> IO b -> IO b # return :: a -> IO a # fail :: String -> IO a #
Monad Par1	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods (>>=) :: Par1 a -> (a -> Par1 b) -> Par1 b # (>>) :: Par1 a -> Par1 b -> Par1 b # return :: a -> Par1 a # fail :: String -> Par1 a #
Monad Complex	Since: base-4.9.0.0
Instance details Defined in Data.Complex Methods (>>=) :: Complex a -> (a -> Complex b) -> Complex b # (>>) :: Complex a -> Complex b -> Complex b # return :: a -> Complex a # fail :: String -> Complex a #
Monad Min	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods (>>=) :: Min a -> (a -> Min b) -> Min b # (>>) :: Min a -> Min b -> Min b # return :: a -> Min a # fail :: String -> Min a #
Monad Max	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods (>>=) :: Max a -> (a -> Max b) -> Max b # (>>) :: Max a -> Max b -> Max b # return :: a -> Max a # fail :: String -> Max a #
Monad First	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods (>>=) :: First a -> (a -> First b) -> First b # (>>) :: First a -> First b -> First b # return :: a -> First a # fail :: String -> First a #
Monad Last	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods (>>=) :: Last a -> (a -> Last b) -> Last b # (>>) :: Last a -> Last b -> Last b # return :: a -> Last a # fail :: String -> Last a #
Monad Option	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods (>>=) :: Option a -> (a -> Option b) -> Option b # (>>) :: Option a -> Option b -> Option b # return :: a -> Option a # fail :: String -> Option a #
Monad Identity	Since: base-4.8.0.0
Instance details Defined in Data.Functor.Identity Methods (>>=) :: Identity a -> (a -> Identity b) -> Identity b # (>>) :: Identity a -> Identity b -> Identity b # return :: a -> Identity a # fail :: String -> Identity a #
Monad STM	Since: base-4.3.0.0
Instance details Defined in GHC.Conc.Sync Methods (>>=) :: STM a -> (a -> STM b) -> STM b # (>>) :: STM a -> STM b -> STM b # return :: a -> STM a # fail :: String -> STM a #
Monad First	Since: base-4.8.0.0
Instance details Defined in Data.Monoid Methods (>>=) :: First a -> (a -> First b) -> First b # (>>) :: First a -> First b -> First b # return :: a -> First a # fail :: String -> First a #
Monad Last	Since: base-4.8.0.0
Instance details Defined in Data.Monoid Methods (>>=) :: Last a -> (a -> Last b) -> Last b # (>>) :: Last a -> Last b -> Last b # return :: a -> Last a # fail :: String -> Last a #
Monad Dual	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods (>>=) :: Dual a -> (a -> Dual b) -> Dual b # (>>) :: Dual a -> Dual b -> Dual b # return :: a -> Dual a # fail :: String -> Dual a #
Monad Sum	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods (>>=) :: Sum a -> (a -> Sum b) -> Sum b # (>>) :: Sum a -> Sum b -> Sum b # return :: a -> Sum a # fail :: String -> Sum a #
Monad Product	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods (>>=) :: Product a -> (a -> Product b) -> Product b # (>>) :: Product a -> Product b -> Product b # return :: a -> Product a # fail :: String -> Product a #
Monad Down	Since: base-4.11.0.0
Instance details Defined in Data.Ord Methods (>>=) :: Down a -> (a -> Down b) -> Down b # (>>) :: Down a -> Down b -> Down b # return :: a -> Down a # fail :: String -> Down a #
Monad ReadP	Since: base-2.1
Instance details Defined in Text.ParserCombinators.ReadP Methods (>>=) :: ReadP a -> (a -> ReadP b) -> ReadP b # (>>) :: ReadP a -> ReadP b -> ReadP b # return :: a -> ReadP a # fail :: String -> ReadP a #
Monad NonEmpty	Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods (>>=) :: NonEmpty a -> (a -> NonEmpty b) -> NonEmpty b # (>>) :: NonEmpty a -> NonEmpty b -> NonEmpty b # return :: a -> NonEmpty a # fail :: String -> NonEmpty a #
Monad SmallArray
Instance details Defined in Data.Primitive.SmallArray Methods (>>=) :: SmallArray a -> (a -> SmallArray b) -> SmallArray b # (>>) :: SmallArray a -> SmallArray b -> SmallArray b # return :: a -> SmallArray a # fail :: String -> SmallArray a #
Monad Array
Instance details Defined in Data.Primitive.Array Methods (>>=) :: Array a -> (a -> Array b) -> Array b # (>>) :: Array a -> Array b -> Array b # return :: a -> Array a # fail :: String -> Array a #
Monad Id
Instance details Defined in Data.Vector.Fusion.Util Methods (>>=) :: Id a -> (a -> Id b) -> Id b # (>>) :: Id a -> Id b -> Id b # return :: a -> Id a # fail :: String -> Id a #
Monad Box
Instance details Defined in Data.Vector.Fusion.Util Methods (>>=) :: Box a -> (a -> Box b) -> Box b # (>>) :: Box a -> Box b -> Box b # return :: a -> Box a # fail :: String -> Box a #
Monad P	Since: base-2.1
Instance details Defined in Text.ParserCombinators.ReadP Methods (>>=) :: P a -> (a -> P b) -> P b # (>>) :: P a -> P b -> P b # return :: a -> P a # fail :: String -> P a #
Monad (Either e)	Since: base-4.4.0.0
Instance details Defined in Data.Either Methods (>>=) :: Either e a -> (a -> Either e b) -> Either e b # (>>) :: Either e a -> Either e b -> Either e b # return :: a -> Either e a # fail :: String -> Either e a #
Monad (U1 :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods (>>=) :: U1 a -> (a -> U1 b) -> U1 b # (>>) :: U1 a -> U1 b -> U1 b # return :: a -> U1 a # fail :: String -> U1 a #
Monoid a => Monad ((,) a)	Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods (>>=) :: (a, a0) -> (a0 -> (a, b)) -> (a, b) # (>>) :: (a, a0) -> (a, b) -> (a, b) # return :: a0 -> (a, a0) # fail :: String -> (a, a0) #
Monad (ST s)	Since: base-2.1
Instance details Defined in GHC.ST Methods (>>=) :: ST s a -> (a -> ST s b) -> ST s b # (>>) :: ST s a -> ST s b -> ST s b # return :: a -> ST s a # fail :: String -> ST s a #
Monad m => Monad (WrappedMonad m)	Since: base-4.7.0.0
Instance details Defined in Control.Applicative Methods (>>=) :: WrappedMonad m a -> (a -> WrappedMonad m b) -> WrappedMonad m b # (>>) :: WrappedMonad m a -> WrappedMonad m b -> WrappedMonad m b # return :: a -> WrappedMonad m a # fail :: String -> WrappedMonad m a #
Monad (Proxy :: Type -> Type)	Since: base-4.7.0.0
Instance details Defined in Data.Proxy Methods (>>=) :: Proxy a -> (a -> Proxy b) -> Proxy b # (>>) :: Proxy a -> Proxy b -> Proxy b # return :: a -> Proxy a # fail :: String -> Proxy a #
Monad m => Monad (MaybeT m)
Instance details Defined in Control.Monad.Trans.Maybe Methods (>>=) :: MaybeT m a -> (a -> MaybeT m b) -> MaybeT m b # (>>) :: MaybeT m a -> MaybeT m b -> MaybeT m b # return :: a -> MaybeT m a # fail :: String -> MaybeT m a #
Monad m => Monad (ListT m)
Instance details Defined in Control.Monad.Trans.List Methods (>>=) :: ListT m a -> (a -> ListT m b) -> ListT m b # (>>) :: ListT m a -> ListT m b -> ListT m b # return :: a -> ListT m a # fail :: String -> ListT m a #
Monad f => Monad (Rec1 f)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods (>>=) :: Rec1 f a -> (a -> Rec1 f b) -> Rec1 f b # (>>) :: Rec1 f a -> Rec1 f b -> Rec1 f b # return :: a -> Rec1 f a # fail :: String -> Rec1 f a #
Monad f => Monad (Ap f)	Since: base-4.12.0.0
Instance details Defined in Data.Monoid Methods (>>=) :: Ap f a -> (a -> Ap f b) -> Ap f b # (>>) :: Ap f a -> Ap f b -> Ap f b # return :: a -> Ap f a # fail :: String -> Ap f a #
Monad f => Monad (Alt f)	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods (>>=) :: Alt f a -> (a -> Alt f b) -> Alt f b # (>>) :: Alt f a -> Alt f b -> Alt f b # return :: a -> Alt f a # fail :: String -> Alt f a #
(Monoid w, Monad m) => Monad (WriterT w m)
Instance details Defined in Control.Monad.Trans.Writer.Strict Methods (>>=) :: WriterT w m a -> (a -> WriterT w m b) -> WriterT w m b # (>>) :: WriterT w m a -> WriterT w m b -> WriterT w m b # return :: a -> WriterT w m a # fail :: String -> WriterT w m a #
(Monoid w, Functor m, Monad m) => Monad (AccumT w m)
Instance details Defined in Control.Monad.Trans.Accum Methods (>>=) :: AccumT w m a -> (a -> AccumT w m b) -> AccumT w m b # (>>) :: AccumT w m a -> AccumT w m b -> AccumT w m b # return :: a -> AccumT w m a # fail :: String -> AccumT w m a #
(Monoid w, Monad m) => Monad (WriterT w m)
Instance details Defined in Control.Monad.Trans.Writer.Lazy Methods (>>=) :: WriterT w m a -> (a -> WriterT w m b) -> WriterT w m b # (>>) :: WriterT w m a -> WriterT w m b -> WriterT w m b # return :: a -> WriterT w m a # fail :: String -> WriterT w m a #
Monad m => Monad (StateT s m)
Instance details Defined in Control.Monad.Trans.State.Strict Methods (>>=) :: StateT s m a -> (a -> StateT s m b) -> StateT s m b # (>>) :: StateT s m a -> StateT s m b -> StateT s m b # return :: a -> StateT s m a # fail :: String -> StateT s m a #
Monad m => Monad (StateT s m)
Instance details Defined in Control.Monad.Trans.State.Lazy Methods (>>=) :: StateT s m a -> (a -> StateT s m b) -> StateT s m b # (>>) :: StateT s m a -> StateT s m b -> StateT s m b # return :: a -> StateT s m a # fail :: String -> StateT s m a #
Monad m => Monad (SelectT r m)
Instance details Defined in Control.Monad.Trans.Select Methods (>>=) :: SelectT r m a -> (a -> SelectT r m b) -> SelectT r m b # (>>) :: SelectT r m a -> SelectT r m b -> SelectT r m b # return :: a -> SelectT r m a # fail :: String -> SelectT r m a #
Monad m => Monad (IdentityT m)
Instance details Defined in Control.Monad.Trans.Identity Methods (>>=) :: IdentityT m a -> (a -> IdentityT m b) -> IdentityT m b # (>>) :: IdentityT m a -> IdentityT m b -> IdentityT m b # return :: a -> IdentityT m a # fail :: String -> IdentityT m a #
Monad m => Monad (ExceptT e m)
Instance details Defined in Control.Monad.Trans.Except Methods (>>=) :: ExceptT e m a -> (a -> ExceptT e m b) -> ExceptT e m b # (>>) :: ExceptT e m a -> ExceptT e m b -> ExceptT e m b # return :: a -> ExceptT e m a # fail :: String -> ExceptT e m a #
(Monad m, Error e) => Monad (ErrorT e m)
Instance details Defined in Control.Monad.Trans.Error Methods (>>=) :: ErrorT e m a -> (a -> ErrorT e m b) -> ErrorT e m b # (>>) :: ErrorT e m a -> ErrorT e m b -> ErrorT e m b # return :: a -> ErrorT e m a # fail :: String -> ErrorT e m a #
Monad ((->) r :: Type -> Type)	Since: base-2.1
Instance details Defined in GHC.Base Methods (>>=) :: (r -> a) -> (a -> r -> b) -> r -> b # (>>) :: (r -> a) -> (r -> b) -> r -> b # return :: a -> r -> a # fail :: String -> r -> a #
(Monad f, Monad g) => Monad (f :*: g)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods (>>=) :: (f :: g) a -> (a -> (f :: g) b) -> (f :: g) b # (>>) :: (f :: g) a -> (f :: g) b -> (f :: g) b # return :: a -> (f :: g) a # fail :: String -> (f :: g) a #
(Monad f, Monad g) => Monad (Product f g)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Product Methods (>>=) :: Product f g a -> (a -> Product f g b) -> Product f g b # (>>) :: Product f g a -> Product f g b -> Product f g b # return :: a -> Product f g a # fail :: String -> Product f g a #
Monad m => Monad (ReaderT r m)
Instance details Defined in Control.Monad.Trans.Reader Methods (>>=) :: ReaderT r m a -> (a -> ReaderT r m b) -> ReaderT r m b # (>>) :: ReaderT r m a -> ReaderT r m b -> ReaderT r m b # return :: a -> ReaderT r m a # fail :: String -> ReaderT r m a #
Monad (ContT r m)
Instance details Defined in Control.Monad.Trans.Cont Methods (>>=) :: ContT r m a -> (a -> ContT r m b) -> ContT r m b # (>>) :: ContT r m a -> ContT r m b -> ContT r m b # return :: a -> ContT r m a # fail :: String -> ContT r m a #
Monad f => Monad (M1 i c f)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods (>>=) :: M1 i c f a -> (a -> M1 i c f b) -> M1 i c f b # (>>) :: M1 i c f a -> M1 i c f b -> M1 i c f b # return :: a -> M1 i c f a # fail :: String -> M1 i c f a #
(Monoid w, Monad m) => Monad (RWST r w s m)
Instance details Defined in Control.Monad.Trans.RWS.Strict Methods (>>=) :: RWST r w s m a -> (a -> RWST r w s m b) -> RWST r w s m b # (>>) :: RWST r w s m a -> RWST r w s m b -> RWST r w s m b # return :: a -> RWST r w s m a # fail :: String -> RWST r w s m a #
(Monoid w, Monad m) => Monad (RWST r w s m)
Instance details Defined in Control.Monad.Trans.RWS.Lazy Methods (>>=) :: RWST r w s m a -> (a -> RWST r w s m b) -> RWST r w s m b # (>>) :: RWST r w s m a -> RWST r w s m b -> RWST r w s m b # return :: a -> RWST r w s m a # fail :: String -> RWST r w s m a #

class Functor (f :: Type -> Type) where #

The Functor class is used for types that can be mapped over. Instances of Functor should satisfy the following laws:

fmap id  ==  id
fmap (f . g)  ==  fmap f . fmap g

The instances of Functor for lists, Maybe and IO satisfy these laws.

Minimal complete definition

fmap

Methods

fmap :: (a -> b) -> f a -> f b #

(<$) :: a -> f b -> f a infixl 4 #

Replace all locations in the input with the same value. The default definition is fmap . const, but this may be overridden with a more efficient version.

Instances

Functor []	Since: base-2.1
Instance details Defined in GHC.Base Methods fmap :: (a -> b) -> [a] -> [b] # (<$) :: a -> [b] -> [a] #
Functor Maybe	Since: base-2.1
Instance details Defined in GHC.Base Methods fmap :: (a -> b) -> Maybe a -> Maybe b # (<$) :: a -> Maybe b -> Maybe a #
Functor IO	Since: base-2.1
Instance details Defined in GHC.Base Methods fmap :: (a -> b) -> IO a -> IO b # (<$) :: a -> IO b -> IO a #
Functor Par1	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods fmap :: (a -> b) -> Par1 a -> Par1 b # (<$) :: a -> Par1 b -> Par1 a #
Functor Complex	Since: base-4.9.0.0
Instance details Defined in Data.Complex Methods fmap :: (a -> b) -> Complex a -> Complex b # (<$) :: a -> Complex b -> Complex a #
Functor Min	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods fmap :: (a -> b) -> Min a -> Min b # (<$) :: a -> Min b -> Min a #
Functor Max	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods fmap :: (a -> b) -> Max a -> Max b # (<$) :: a -> Max b -> Max a #
Functor First	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods fmap :: (a -> b) -> First a -> First b # (<$) :: a -> First b -> First a #
Functor Last	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods fmap :: (a -> b) -> Last a -> Last b # (<$) :: a -> Last b -> Last a #
Functor Option	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods fmap :: (a -> b) -> Option a -> Option b # (<$) :: a -> Option b -> Option a #
Functor ZipList	Since: base-2.1
Instance details Defined in Control.Applicative Methods fmap :: (a -> b) -> ZipList a -> ZipList b # (<$) :: a -> ZipList b -> ZipList a #
Functor Identity	Since: base-4.8.0.0
Instance details Defined in Data.Functor.Identity Methods fmap :: (a -> b) -> Identity a -> Identity b # (<$) :: a -> Identity b -> Identity a #
Functor STM	Since: base-4.3.0.0
Instance details Defined in GHC.Conc.Sync Methods fmap :: (a -> b) -> STM a -> STM b # (<$) :: a -> STM b -> STM a #
Functor First	Since: base-4.8.0.0
Instance details Defined in Data.Monoid Methods fmap :: (a -> b) -> First a -> First b # (<$) :: a -> First b -> First a #
Functor Last	Since: base-4.8.0.0
Instance details Defined in Data.Monoid Methods fmap :: (a -> b) -> Last a -> Last b # (<$) :: a -> Last b -> Last a #
Functor Dual	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods fmap :: (a -> b) -> Dual a -> Dual b # (<$) :: a -> Dual b -> Dual a #
Functor Sum	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods fmap :: (a -> b) -> Sum a -> Sum b # (<$) :: a -> Sum b -> Sum a #
Functor Product	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods fmap :: (a -> b) -> Product a -> Product b # (<$) :: a -> Product b -> Product a #
Functor Down	Since: base-4.11.0.0
Instance details Defined in Data.Ord Methods fmap :: (a -> b) -> Down a -> Down b # (<$) :: a -> Down b -> Down a #
Functor ReadP	Since: base-2.1
Instance details Defined in Text.ParserCombinators.ReadP Methods fmap :: (a -> b) -> ReadP a -> ReadP b # (<$) :: a -> ReadP b -> ReadP a #
Functor NonEmpty	Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods fmap :: (a -> b) -> NonEmpty a -> NonEmpty b # (<$) :: a -> NonEmpty b -> NonEmpty a #
Functor SmallArray
Instance details Defined in Data.Primitive.SmallArray Methods fmap :: (a -> b) -> SmallArray a -> SmallArray b # (<$) :: a -> SmallArray b -> SmallArray a #
Functor Array
Instance details Defined in Data.Primitive.Array Methods fmap :: (a -> b) -> Array a -> Array b # (<$) :: a -> Array b -> Array a #
Functor Id
Instance details Defined in Data.Vector.Fusion.Util Methods fmap :: (a -> b) -> Id a -> Id b # (<$) :: a -> Id b -> Id a #
Functor Box
Instance details Defined in Data.Vector.Fusion.Util Methods fmap :: (a -> b) -> Box a -> Box b # (<$) :: a -> Box b -> Box a #
Functor P	Since: base-4.8.0.0
Instance details Defined in Text.ParserCombinators.ReadP Methods fmap :: (a -> b) -> P a -> P b # (<$) :: a -> P b -> P a #
Functor (Either a)	Since: base-3.0
Instance details Defined in Data.Either Methods fmap :: (a0 -> b) -> Either a a0 -> Either a b # (<$) :: a0 -> Either a b -> Either a a0 #
Functor (V1 :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods fmap :: (a -> b) -> V1 a -> V1 b # (<$) :: a -> V1 b -> V1 a #
Functor (U1 :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods fmap :: (a -> b) -> U1 a -> U1 b # (<$) :: a -> U1 b -> U1 a #
Functor ((,) a)	Since: base-2.1
Instance details Defined in GHC.Base Methods fmap :: (a0 -> b) -> (a, a0) -> (a, b) # (<$) :: a0 -> (a, b) -> (a, a0) #
Functor (ST s)	Since: base-2.1
Instance details Defined in GHC.ST Methods fmap :: (a -> b) -> ST s a -> ST s b # (<$) :: a -> ST s b -> ST s a #
Functor (Array i)	Since: base-2.1
Instance details Defined in GHC.Arr Methods fmap :: (a -> b) -> Array i a -> Array i b # (<$) :: a -> Array i b -> Array i a #
Functor (Arg a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods fmap :: (a0 -> b) -> Arg a a0 -> Arg a b # (<$) :: a0 -> Arg a b -> Arg a a0 #
Monad m => Functor (WrappedMonad m)	Since: base-2.1
Instance details Defined in Control.Applicative Methods fmap :: (a -> b) -> WrappedMonad m a -> WrappedMonad m b # (<$) :: a -> WrappedMonad m b -> WrappedMonad m a #
Functor (Proxy :: Type -> Type)	Since: base-4.7.0.0
Instance details Defined in Data.Proxy Methods fmap :: (a -> b) -> Proxy a -> Proxy b # (<$) :: a -> Proxy b -> Proxy a #
Functor m => Functor (MaybeT m)
Instance details Defined in Control.Monad.Trans.Maybe Methods fmap :: (a -> b) -> MaybeT m a -> MaybeT m b # (<$) :: a -> MaybeT m b -> MaybeT m a #
Functor m => Functor (ListT m)
Instance details Defined in Control.Monad.Trans.List Methods fmap :: (a -> b) -> ListT m a -> ListT m b # (<$) :: a -> ListT m b -> ListT m a #
Functor f => Functor (Rec1 f)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods fmap :: (a -> b) -> Rec1 f a -> Rec1 f b # (<$) :: a -> Rec1 f b -> Rec1 f a #
Functor (URec Char :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods fmap :: (a -> b) -> URec Char a -> URec Char b # (<$) :: a -> URec Char b -> URec Char a #
Functor (URec Double :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods fmap :: (a -> b) -> URec Double a -> URec Double b # (<$) :: a -> URec Double b -> URec Double a #
Functor (URec Float :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods fmap :: (a -> b) -> URec Float a -> URec Float b # (<$) :: a -> URec Float b -> URec Float a #
Functor (URec Int :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods fmap :: (a -> b) -> URec Int a -> URec Int b # (<$) :: a -> URec Int b -> URec Int a #
Functor (URec Word :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods fmap :: (a -> b) -> URec Word a -> URec Word b # (<$) :: a -> URec Word b -> URec Word a #
Functor (URec (Ptr ()) :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods fmap :: (a -> b) -> URec (Ptr ()) a -> URec (Ptr ()) b # (<$) :: a -> URec (Ptr ()) b -> URec (Ptr ()) a #
Arrow a => Functor (WrappedArrow a b)	Since: base-2.1
Instance details Defined in Control.Applicative Methods fmap :: (a0 -> b0) -> WrappedArrow a b a0 -> WrappedArrow a b b0 # (<$) :: a0 -> WrappedArrow a b b0 -> WrappedArrow a b a0 #
Functor (Const m :: Type -> Type)	Since: base-2.1
Instance details Defined in Data.Functor.Const Methods fmap :: (a -> b) -> Const m a -> Const m b # (<$) :: a -> Const m b -> Const m a #
Functor f => Functor (Ap f)	Since: base-4.12.0.0
Instance details Defined in Data.Monoid Methods fmap :: (a -> b) -> Ap f a -> Ap f b # (<$) :: a -> Ap f b -> Ap f a #
Functor f => Functor (Alt f)	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods fmap :: (a -> b) -> Alt f a -> Alt f b # (<$) :: a -> Alt f b -> Alt f a #
Functor m => Functor (WriterT w m)
Instance details Defined in Control.Monad.Trans.Writer.Strict Methods fmap :: (a -> b) -> WriterT w m a -> WriterT w m b # (<$) :: a -> WriterT w m b -> WriterT w m a #
Functor m => Functor (AccumT w m)
Instance details Defined in Control.Monad.Trans.Accum Methods fmap :: (a -> b) -> AccumT w m a -> AccumT w m b # (<$) :: a -> AccumT w m b -> AccumT w m a #
Functor m => Functor (WriterT w m)
Instance details Defined in Control.Monad.Trans.Writer.Lazy Methods fmap :: (a -> b) -> WriterT w m a -> WriterT w m b # (<$) :: a -> WriterT w m b -> WriterT w m a #
Functor m => Functor (StateT s m)
Instance details Defined in Control.Monad.Trans.State.Strict Methods fmap :: (a -> b) -> StateT s m a -> StateT s m b # (<$) :: a -> StateT s m b -> StateT s m a #
Functor m => Functor (StateT s m)
Instance details Defined in Control.Monad.Trans.State.Lazy Methods fmap :: (a -> b) -> StateT s m a -> StateT s m b # (<$) :: a -> StateT s m b -> StateT s m a #
Functor m => Functor (SelectT r m)
Instance details Defined in Control.Monad.Trans.Select Methods fmap :: (a -> b) -> SelectT r m a -> SelectT r m b # (<$) :: a -> SelectT r m b -> SelectT r m a #
Functor m => Functor (IdentityT m)
Instance details Defined in Control.Monad.Trans.Identity Methods fmap :: (a -> b) -> IdentityT m a -> IdentityT m b # (<$) :: a -> IdentityT m b -> IdentityT m a #
Functor m => Functor (ExceptT e m)
Instance details Defined in Control.Monad.Trans.Except Methods fmap :: (a -> b) -> ExceptT e m a -> ExceptT e m b # (<$) :: a -> ExceptT e m b -> ExceptT e m a #
Functor m => Functor (ErrorT e m)
Instance details Defined in Control.Monad.Trans.Error Methods fmap :: (a -> b) -> ErrorT e m a -> ErrorT e m b # (<$) :: a -> ErrorT e m b -> ErrorT e m a #
Monad m => Functor (Bundle m v)
Instance details Defined in Data.Vector.Fusion.Bundle.Monadic Methods fmap :: (a -> b) -> Bundle m v a -> Bundle m v b # (<$) :: a -> Bundle m v b -> Bundle m v a #
KnownVariant v => Functor (Dimensional v d) Source #	A `Functor` instance for `Dimensional`. Note that this instance is dubious, because it allows you to break the dimensional abstraction. See `dmap` for more information. Note that, while this instance overlaps with that given for `Dimensionless`, it is confluent with that instance. Note that this is an orphan instance.
Instance details Defined in Numeric.Units.Dimensional.Functor Methods fmap :: (a -> b) -> Dimensional v d a -> Dimensional v d b # (<$) :: a -> Dimensional v d b -> Dimensional v d a #
Functor (SQuantity s DOne) Source #
Instance details Defined in Numeric.Units.Dimensional.Internal Methods fmap :: (a -> b) -> SQuantity s DOne a -> SQuantity s DOne b # (<$) :: a -> SQuantity s DOne b -> SQuantity s DOne a #
Functor ((->) r :: Type -> Type)	Since: base-2.1
Instance details Defined in GHC.Base Methods fmap :: (a -> b) -> (r -> a) -> r -> b # (<$) :: a -> (r -> b) -> r -> a #
Functor (K1 i c :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods fmap :: (a -> b) -> K1 i c a -> K1 i c b # (<$) :: a -> K1 i c b -> K1 i c a #
(Functor f, Functor g) => Functor (f :+: g)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods fmap :: (a -> b) -> (f :+: g) a -> (f :+: g) b # (<$) :: a -> (f :+: g) b -> (f :+: g) a #
(Functor f, Functor g) => Functor (f :*: g)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods fmap :: (a -> b) -> (f :: g) a -> (f :: g) b # (<$) :: a -> (f :: g) b -> (f :: g) a #
(Functor f, Functor g) => Functor (Product f g)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Product Methods fmap :: (a -> b) -> Product f g a -> Product f g b # (<$) :: a -> Product f g b -> Product f g a #
(Functor f, Functor g) => Functor (Sum f g)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Sum Methods fmap :: (a -> b) -> Sum f g a -> Sum f g b # (<$) :: a -> Sum f g b -> Sum f g a #
Functor m => Functor (ReaderT r m)
Instance details Defined in Control.Monad.Trans.Reader Methods fmap :: (a -> b) -> ReaderT r m a -> ReaderT r m b # (<$) :: a -> ReaderT r m b -> ReaderT r m a #
Functor (ContT r m)
Instance details Defined in Control.Monad.Trans.Cont Methods fmap :: (a -> b) -> ContT r m a -> ContT r m b # (<$) :: a -> ContT r m b -> ContT r m a #
Functor f => Functor (M1 i c f)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods fmap :: (a -> b) -> M1 i c f a -> M1 i c f b # (<$) :: a -> M1 i c f b -> M1 i c f a #
(Functor f, Functor g) => Functor (f :.: g)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods fmap :: (a -> b) -> (f :.: g) a -> (f :.: g) b # (<$) :: a -> (f :.: g) b -> (f :.: g) a #
(Functor f, Functor g) => Functor (Compose f g)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Compose Methods fmap :: (a -> b) -> Compose f g a -> Compose f g b # (<$) :: a -> Compose f g b -> Compose f g a #
Functor m => Functor (RWST r w s m)
Instance details Defined in Control.Monad.Trans.RWS.Strict Methods fmap :: (a -> b) -> RWST r w s m a -> RWST r w s m b # (<$) :: a -> RWST r w s m b -> RWST r w s m a #
Functor m => Functor (RWST r w s m)
Instance details Defined in Control.Monad.Trans.RWS.Lazy Methods fmap :: (a -> b) -> RWST r w s m a -> RWST r w s m b # (<$) :: a -> RWST r w s m b -> RWST r w s m a #

class Num a where #

Basic numeric class.

The Haskell Report defines no laws for Num. However, '(+)' and '(*)' are customarily expected to define a ring and have the following properties:

Associativity of (+): (x + y) + z = x + (y + z)
Commutativity of (+): x + y = y + x
fromInteger 0 is the additive identity: x + fromInteger 0 = x
negate gives the additive inverse: x + negate x = fromInteger 0
Associativity of (*): (x * y) * z = x * (y * z)
fromInteger 1 is the multiplicative identity: x * fromInteger 1 = x and fromInteger 1 * x = x
Distributivity of (*) with respect to (+): a * (b + c) = (a * b) + (a * c) and (b + c) * a = (b * a) + (c * a)

Note that it isn't customarily expected that a type instance of both Num and Ord implement an ordered ring. Indeed, in base only Integer and Rational do.

Minimal complete definition

(+), (*), abs, signum, fromInteger, (negate | (-))

Methods

fromInteger :: Integer -> a #

Conversion from an Integer. An integer literal represents the application of the function fromInteger to the appropriate value of type Integer, so such literals have type (Num a) => a.

Instances

Num Int	Since: base-2.1
Instance details Defined in GHC.Num Methods (+) :: Int -> Int -> Int # (-) :: Int -> Int -> Int # (*) :: Int -> Int -> Int # negate :: Int -> Int # abs :: Int -> Int # signum :: Int -> Int # fromInteger :: Integer -> Int #
Num Int8	Since: base-2.1
Instance details Defined in GHC.Int Methods (+) :: Int8 -> Int8 -> Int8 # (-) :: Int8 -> Int8 -> Int8 # (*) :: Int8 -> Int8 -> Int8 # negate :: Int8 -> Int8 # abs :: Int8 -> Int8 # signum :: Int8 -> Int8 # fromInteger :: Integer -> Int8 #
Num Int16	Since: base-2.1
Instance details Defined in GHC.Int Methods (+) :: Int16 -> Int16 -> Int16 # (-) :: Int16 -> Int16 -> Int16 # (*) :: Int16 -> Int16 -> Int16 # negate :: Int16 -> Int16 # abs :: Int16 -> Int16 # signum :: Int16 -> Int16 # fromInteger :: Integer -> Int16 #
Num Int32	Since: base-2.1
Instance details Defined in GHC.Int Methods (+) :: Int32 -> Int32 -> Int32 # (-) :: Int32 -> Int32 -> Int32 # (*) :: Int32 -> Int32 -> Int32 # negate :: Int32 -> Int32 # abs :: Int32 -> Int32 # signum :: Int32 -> Int32 # fromInteger :: Integer -> Int32 #
Num Int64	Since: base-2.1
Instance details Defined in GHC.Int Methods (+) :: Int64 -> Int64 -> Int64 # (-) :: Int64 -> Int64 -> Int64 # (*) :: Int64 -> Int64 -> Int64 # negate :: Int64 -> Int64 # abs :: Int64 -> Int64 # signum :: Int64 -> Int64 # fromInteger :: Integer -> Int64 #
Num Integer	Since: base-2.1
Instance details Defined in GHC.Num Methods (+) :: Integer -> Integer -> Integer # (-) :: Integer -> Integer -> Integer # (*) :: Integer -> Integer -> Integer # negate :: Integer -> Integer # abs :: Integer -> Integer # signum :: Integer -> Integer # fromInteger :: Integer -> Integer #
Num Natural	Note that `Natural`'s `Num` instance isn't a ring: no element but 0 has an additive inverse. It is a semiring though. Since: base-4.8.0.0
Instance details Defined in GHC.Num Methods (+) :: Natural -> Natural -> Natural # (-) :: Natural -> Natural -> Natural # (*) :: Natural -> Natural -> Natural # negate :: Natural -> Natural # abs :: Natural -> Natural # signum :: Natural -> Natural # fromInteger :: Integer -> Natural #
Num Word	Since: base-2.1
Instance details Defined in GHC.Num Methods (+) :: Word -> Word -> Word # (-) :: Word -> Word -> Word # (*) :: Word -> Word -> Word # negate :: Word -> Word # abs :: Word -> Word # signum :: Word -> Word # fromInteger :: Integer -> Word #
Num Word8	Since: base-2.1
Instance details Defined in GHC.Word Methods (+) :: Word8 -> Word8 -> Word8 # (-) :: Word8 -> Word8 -> Word8 # (*) :: Word8 -> Word8 -> Word8 # negate :: Word8 -> Word8 # abs :: Word8 -> Word8 # signum :: Word8 -> Word8 # fromInteger :: Integer -> Word8 #
Num Word16	Since: base-2.1
Instance details Defined in GHC.Word Methods (+) :: Word16 -> Word16 -> Word16 # (-) :: Word16 -> Word16 -> Word16 # (*) :: Word16 -> Word16 -> Word16 # negate :: Word16 -> Word16 # abs :: Word16 -> Word16 # signum :: Word16 -> Word16 # fromInteger :: Integer -> Word16 #
Num Word32	Since: base-2.1
Instance details Defined in GHC.Word Methods (+) :: Word32 -> Word32 -> Word32 # (-) :: Word32 -> Word32 -> Word32 # (*) :: Word32 -> Word32 -> Word32 # negate :: Word32 -> Word32 # abs :: Word32 -> Word32 # signum :: Word32 -> Word32 # fromInteger :: Integer -> Word32 #
Num Word64	Since: base-2.1
Instance details Defined in GHC.Word Methods (+) :: Word64 -> Word64 -> Word64 # (-) :: Word64 -> Word64 -> Word64 # (*) :: Word64 -> Word64 -> Word64 # negate :: Word64 -> Word64 # abs :: Word64 -> Word64 # signum :: Word64 -> Word64 # fromInteger :: Integer -> Word64 #
Num CChar
Instance details Defined in Foreign.C.Types Methods (+) :: CChar -> CChar -> CChar # (-) :: CChar -> CChar -> CChar # (*) :: CChar -> CChar -> CChar # negate :: CChar -> CChar # abs :: CChar -> CChar # signum :: CChar -> CChar # fromInteger :: Integer -> CChar #
Num CSChar
Instance details Defined in Foreign.C.Types Methods (+) :: CSChar -> CSChar -> CSChar # (-) :: CSChar -> CSChar -> CSChar # (*) :: CSChar -> CSChar -> CSChar # negate :: CSChar -> CSChar # abs :: CSChar -> CSChar # signum :: CSChar -> CSChar # fromInteger :: Integer -> CSChar #
Num CUChar
Instance details Defined in Foreign.C.Types Methods (+) :: CUChar -> CUChar -> CUChar # (-) :: CUChar -> CUChar -> CUChar # (*) :: CUChar -> CUChar -> CUChar # negate :: CUChar -> CUChar # abs :: CUChar -> CUChar # signum :: CUChar -> CUChar # fromInteger :: Integer -> CUChar #
Num CShort
Instance details Defined in Foreign.C.Types Methods (+) :: CShort -> CShort -> CShort # (-) :: CShort -> CShort -> CShort # (*) :: CShort -> CShort -> CShort # negate :: CShort -> CShort # abs :: CShort -> CShort # signum :: CShort -> CShort # fromInteger :: Integer -> CShort #
Num CUShort
Instance details Defined in Foreign.C.Types Methods (+) :: CUShort -> CUShort -> CUShort # (-) :: CUShort -> CUShort -> CUShort # (*) :: CUShort -> CUShort -> CUShort # negate :: CUShort -> CUShort # abs :: CUShort -> CUShort # signum :: CUShort -> CUShort # fromInteger :: Integer -> CUShort #
Num CInt
Instance details Defined in Foreign.C.Types Methods (+) :: CInt -> CInt -> CInt # (-) :: CInt -> CInt -> CInt # (*) :: CInt -> CInt -> CInt # negate :: CInt -> CInt # abs :: CInt -> CInt # signum :: CInt -> CInt # fromInteger :: Integer -> CInt #
Num CUInt
Instance details Defined in Foreign.C.Types Methods (+) :: CUInt -> CUInt -> CUInt # (-) :: CUInt -> CUInt -> CUInt # (*) :: CUInt -> CUInt -> CUInt # negate :: CUInt -> CUInt # abs :: CUInt -> CUInt # signum :: CUInt -> CUInt # fromInteger :: Integer -> CUInt #
Num CLong
Instance details Defined in Foreign.C.Types Methods (+) :: CLong -> CLong -> CLong # (-) :: CLong -> CLong -> CLong # (*) :: CLong -> CLong -> CLong # negate :: CLong -> CLong # abs :: CLong -> CLong # signum :: CLong -> CLong # fromInteger :: Integer -> CLong #
Num CULong
Instance details Defined in Foreign.C.Types Methods (+) :: CULong -> CULong -> CULong # (-) :: CULong -> CULong -> CULong # (*) :: CULong -> CULong -> CULong # negate :: CULong -> CULong # abs :: CULong -> CULong # signum :: CULong -> CULong # fromInteger :: Integer -> CULong #
Num CLLong
Instance details Defined in Foreign.C.Types Methods (+) :: CLLong -> CLLong -> CLLong # (-) :: CLLong -> CLLong -> CLLong # (*) :: CLLong -> CLLong -> CLLong # negate :: CLLong -> CLLong # abs :: CLLong -> CLLong # signum :: CLLong -> CLLong # fromInteger :: Integer -> CLLong #
Num CULLong
Instance details Defined in Foreign.C.Types Methods (+) :: CULLong -> CULLong -> CULLong # (-) :: CULLong -> CULLong -> CULLong # (*) :: CULLong -> CULLong -> CULLong # negate :: CULLong -> CULLong # abs :: CULLong -> CULLong # signum :: CULLong -> CULLong # fromInteger :: Integer -> CULLong #
Num CBool
Instance details Defined in Foreign.C.Types Methods (+) :: CBool -> CBool -> CBool # (-) :: CBool -> CBool -> CBool # (*) :: CBool -> CBool -> CBool # negate :: CBool -> CBool # abs :: CBool -> CBool # signum :: CBool -> CBool # fromInteger :: Integer -> CBool #
Num CFloat
Instance details Defined in Foreign.C.Types Methods (+) :: CFloat -> CFloat -> CFloat # (-) :: CFloat -> CFloat -> CFloat # (*) :: CFloat -> CFloat -> CFloat # negate :: CFloat -> CFloat # abs :: CFloat -> CFloat # signum :: CFloat -> CFloat # fromInteger :: Integer -> CFloat #
Num CDouble
Instance details Defined in Foreign.C.Types Methods (+) :: CDouble -> CDouble -> CDouble # (-) :: CDouble -> CDouble -> CDouble # (*) :: CDouble -> CDouble -> CDouble # negate :: CDouble -> CDouble # abs :: CDouble -> CDouble # signum :: CDouble -> CDouble # fromInteger :: Integer -> CDouble #
Num CPtrdiff
Instance details Defined in Foreign.C.Types Methods (+) :: CPtrdiff -> CPtrdiff -> CPtrdiff # (-) :: CPtrdiff -> CPtrdiff -> CPtrdiff # (*) :: CPtrdiff -> CPtrdiff -> CPtrdiff # negate :: CPtrdiff -> CPtrdiff # abs :: CPtrdiff -> CPtrdiff # signum :: CPtrdiff -> CPtrdiff # fromInteger :: Integer -> CPtrdiff #
Num CSize
Instance details Defined in Foreign.C.Types Methods (+) :: CSize -> CSize -> CSize # (-) :: CSize -> CSize -> CSize # (*) :: CSize -> CSize -> CSize # negate :: CSize -> CSize # abs :: CSize -> CSize # signum :: CSize -> CSize # fromInteger :: Integer -> CSize #
Num CWchar
Instance details Defined in Foreign.C.Types Methods (+) :: CWchar -> CWchar -> CWchar # (-) :: CWchar -> CWchar -> CWchar # (*) :: CWchar -> CWchar -> CWchar # negate :: CWchar -> CWchar # abs :: CWchar -> CWchar # signum :: CWchar -> CWchar # fromInteger :: Integer -> CWchar #
Num CSigAtomic
Instance details Defined in Foreign.C.Types Methods (+) :: CSigAtomic -> CSigAtomic -> CSigAtomic # (-) :: CSigAtomic -> CSigAtomic -> CSigAtomic # (*) :: CSigAtomic -> CSigAtomic -> CSigAtomic # negate :: CSigAtomic -> CSigAtomic # abs :: CSigAtomic -> CSigAtomic # signum :: CSigAtomic -> CSigAtomic # fromInteger :: Integer -> CSigAtomic #
Num CClock
Instance details Defined in Foreign.C.Types Methods (+) :: CClock -> CClock -> CClock # (-) :: CClock -> CClock -> CClock # (*) :: CClock -> CClock -> CClock # negate :: CClock -> CClock # abs :: CClock -> CClock # signum :: CClock -> CClock # fromInteger :: Integer -> CClock #
Num CTime
Instance details Defined in Foreign.C.Types Methods (+) :: CTime -> CTime -> CTime # (-) :: CTime -> CTime -> CTime # (*) :: CTime -> CTime -> CTime # negate :: CTime -> CTime # abs :: CTime -> CTime # signum :: CTime -> CTime # fromInteger :: Integer -> CTime #
Num CUSeconds
Instance details Defined in Foreign.C.Types Methods (+) :: CUSeconds -> CUSeconds -> CUSeconds # (-) :: CUSeconds -> CUSeconds -> CUSeconds # (*) :: CUSeconds -> CUSeconds -> CUSeconds # negate :: CUSeconds -> CUSeconds # abs :: CUSeconds -> CUSeconds # signum :: CUSeconds -> CUSeconds # fromInteger :: Integer -> CUSeconds #
Num CSUSeconds
Instance details Defined in Foreign.C.Types Methods (+) :: CSUSeconds -> CSUSeconds -> CSUSeconds # (-) :: CSUSeconds -> CSUSeconds -> CSUSeconds # (*) :: CSUSeconds -> CSUSeconds -> CSUSeconds # negate :: CSUSeconds -> CSUSeconds # abs :: CSUSeconds -> CSUSeconds # signum :: CSUSeconds -> CSUSeconds # fromInteger :: Integer -> CSUSeconds #
Num CIntPtr
Instance details Defined in Foreign.C.Types Methods (+) :: CIntPtr -> CIntPtr -> CIntPtr # (-) :: CIntPtr -> CIntPtr -> CIntPtr # (*) :: CIntPtr -> CIntPtr -> CIntPtr # negate :: CIntPtr -> CIntPtr # abs :: CIntPtr -> CIntPtr # signum :: CIntPtr -> CIntPtr # fromInteger :: Integer -> CIntPtr #
Num CUIntPtr
Instance details Defined in Foreign.C.Types Methods (+) :: CUIntPtr -> CUIntPtr -> CUIntPtr # (-) :: CUIntPtr -> CUIntPtr -> CUIntPtr # (*) :: CUIntPtr -> CUIntPtr -> CUIntPtr # negate :: CUIntPtr -> CUIntPtr # abs :: CUIntPtr -> CUIntPtr # signum :: CUIntPtr -> CUIntPtr # fromInteger :: Integer -> CUIntPtr #
Num CIntMax
Instance details Defined in Foreign.C.Types Methods (+) :: CIntMax -> CIntMax -> CIntMax # (-) :: CIntMax -> CIntMax -> CIntMax # (*) :: CIntMax -> CIntMax -> CIntMax # negate :: CIntMax -> CIntMax # abs :: CIntMax -> CIntMax # signum :: CIntMax -> CIntMax # fromInteger :: Integer -> CIntMax #
Num CUIntMax
Instance details Defined in Foreign.C.Types Methods (+) :: CUIntMax -> CUIntMax -> CUIntMax # (-) :: CUIntMax -> CUIntMax -> CUIntMax # (*) :: CUIntMax -> CUIntMax -> CUIntMax # negate :: CUIntMax -> CUIntMax # abs :: CUIntMax -> CUIntMax # signum :: CUIntMax -> CUIntMax # fromInteger :: Integer -> CUIntMax #
Num WordPtr
Instance details Defined in Foreign.Ptr Methods (+) :: WordPtr -> WordPtr -> WordPtr # (-) :: WordPtr -> WordPtr -> WordPtr # (*) :: WordPtr -> WordPtr -> WordPtr # negate :: WordPtr -> WordPtr # abs :: WordPtr -> WordPtr # signum :: WordPtr -> WordPtr # fromInteger :: Integer -> WordPtr #
Num IntPtr
Instance details Defined in Foreign.Ptr Methods (+) :: IntPtr -> IntPtr -> IntPtr # (-) :: IntPtr -> IntPtr -> IntPtr # (*) :: IntPtr -> IntPtr -> IntPtr # negate :: IntPtr -> IntPtr # abs :: IntPtr -> IntPtr # signum :: IntPtr -> IntPtr # fromInteger :: Integer -> IntPtr #
Num ExactPi
Instance details Defined in Data.ExactPi Methods (+) :: ExactPi -> ExactPi -> ExactPi # (-) :: ExactPi -> ExactPi -> ExactPi # (*) :: ExactPi -> ExactPi -> ExactPi # negate :: ExactPi -> ExactPi # abs :: ExactPi -> ExactPi # signum :: ExactPi -> ExactPi # fromInteger :: Integer -> ExactPi #
KnownMinCtxt Num
Instance details Defined in Data.ExactPi.TypeLevel Methods inj :: Num a => Proxy Num -> ExactPi -> a
Integral a => Num (Ratio a)	Since: base-2.0.1
Instance details Defined in GHC.Real Methods (+) :: Ratio a -> Ratio a -> Ratio a # (-) :: Ratio a -> Ratio a -> Ratio a # (*) :: Ratio a -> Ratio a -> Ratio a # negate :: Ratio a -> Ratio a # abs :: Ratio a -> Ratio a # signum :: Ratio a -> Ratio a # fromInteger :: Integer -> Ratio a #
RealFloat a => Num (Complex a)	Since: base-2.1
Instance details Defined in Data.Complex Methods (+) :: Complex a -> Complex a -> Complex a # (-) :: Complex a -> Complex a -> Complex a # (*) :: Complex a -> Complex a -> Complex a # negate :: Complex a -> Complex a # abs :: Complex a -> Complex a # signum :: Complex a -> Complex a # fromInteger :: Integer -> Complex a #
HasResolution a => Num (Fixed a)	Since: base-2.1
Instance details Defined in Data.Fixed Methods (+) :: Fixed a -> Fixed a -> Fixed a # (-) :: Fixed a -> Fixed a -> Fixed a # (*) :: Fixed a -> Fixed a -> Fixed a # negate :: Fixed a -> Fixed a # abs :: Fixed a -> Fixed a # signum :: Fixed a -> Fixed a # fromInteger :: Integer -> Fixed a #
Num a => Num (Min a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods (+) :: Min a -> Min a -> Min a # (-) :: Min a -> Min a -> Min a # (*) :: Min a -> Min a -> Min a # negate :: Min a -> Min a # abs :: Min a -> Min a # signum :: Min a -> Min a # fromInteger :: Integer -> Min a #
Num a => Num (Max a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods (+) :: Max a -> Max a -> Max a # (-) :: Max a -> Max a -> Max a # (*) :: Max a -> Max a -> Max a # negate :: Max a -> Max a # abs :: Max a -> Max a # signum :: Max a -> Max a # fromInteger :: Integer -> Max a #
Num a => Num (Identity a)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Identity Methods (+) :: Identity a -> Identity a -> Identity a # (-) :: Identity a -> Identity a -> Identity a # (*) :: Identity a -> Identity a -> Identity a # negate :: Identity a -> Identity a # abs :: Identity a -> Identity a # signum :: Identity a -> Identity a # fromInteger :: Integer -> Identity a #
Num a => Num (Sum a)	Since: base-4.7.0.0
Instance details Defined in Data.Semigroup.Internal Methods (+) :: Sum a -> Sum a -> Sum a # (-) :: Sum a -> Sum a -> Sum a # (*) :: Sum a -> Sum a -> Sum a # negate :: Sum a -> Sum a # abs :: Sum a -> Sum a # signum :: Sum a -> Sum a # fromInteger :: Integer -> Sum a #
Num a => Num (Product a)	Since: base-4.7.0.0
Instance details Defined in Data.Semigroup.Internal Methods (+) :: Product a -> Product a -> Product a # (-) :: Product a -> Product a -> Product a # (*) :: Product a -> Product a -> Product a # negate :: Product a -> Product a # abs :: Product a -> Product a # signum :: Product a -> Product a # fromInteger :: Integer -> Product a #
Num a => Num (Down a)	Since: base-4.11.0.0
Instance details Defined in Data.Ord Methods (+) :: Down a -> Down a -> Down a # (-) :: Down a -> Down a -> Down a # (*) :: Down a -> Down a -> Down a # negate :: Down a -> Down a # abs :: Down a -> Down a # signum :: Down a -> Down a # fromInteger :: Integer -> Down a #
Num a => Num (DynQuantity a) Source #
Instance details Defined in Numeric.Units.Dimensional.Dynamic Methods (+) :: DynQuantity a -> DynQuantity a -> DynQuantity a # (-) :: DynQuantity a -> DynQuantity a -> DynQuantity a # (*) :: DynQuantity a -> DynQuantity a -> DynQuantity a # negate :: DynQuantity a -> DynQuantity a # abs :: DynQuantity a -> DynQuantity a # signum :: DynQuantity a -> DynQuantity a # fromInteger :: Integer -> DynQuantity a #
Num a => Num (Const a b)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Const Methods (+) :: Const a b -> Const a b -> Const a b # (-) :: Const a b -> Const a b -> Const a b # (*) :: Const a b -> Const a b -> Const a b # negate :: Const a b -> Const a b # abs :: Const a b -> Const a b # signum :: Const a b -> Const a b # fromInteger :: Integer -> Const a b #
(Applicative f, Num a) => Num (Ap f a)	Since: base-4.12.0.0
Instance details Defined in Data.Monoid Methods (+) :: Ap f a -> Ap f a -> Ap f a # (-) :: Ap f a -> Ap f a -> Ap f a # (*) :: Ap f a -> Ap f a -> Ap f a # negate :: Ap f a -> Ap f a # abs :: Ap f a -> Ap f a # signum :: Ap f a -> Ap f a # fromInteger :: Integer -> Ap f a #
Num (f a) => Num (Alt f a)	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods (+) :: Alt f a -> Alt f a -> Alt f a # (-) :: Alt f a -> Alt f a -> Alt f a # (*) :: Alt f a -> Alt f a -> Alt f a # negate :: Alt f a -> Alt f a # abs :: Alt f a -> Alt f a # signum :: Alt f a -> Alt f a # fromInteger :: Integer -> Alt f a #

class Eq a => Ord a where #

The Ord class is used for totally ordered datatypes.

Instances of Ord can be derived for any user-defined datatype whose constituent types are in Ord. The declared order of the constructors in the data declaration determines the ordering in derived Ord instances. The Ordering datatype allows a single comparison to determine the precise ordering of two objects.

The Haskell Report defines no laws for Ord. However, <= is customarily expected to implement a non-strict partial order and have the following properties:

Transitivity: if x <= y && y <= z = True, then x <= z = True
Reflexivity: x <= x = True
Antisymmetry: if x <= y && y <= x = True, then x == y = True

Note that the following operator interactions are expected to hold:

x >= y = y <= x
x < y = x <= y && x /= y
x > y = y < x
x < y = compare x y == LT
x > y = compare x y == GT
x == y = compare x y == EQ
min x y == if x <= y then x else y = True
max x y == if x >= y then x else y = True

Minimal complete definition: either compare or <=. Using compare can be more efficient for complex types.

Minimal complete definition

compare | (<=)

Methods

compare :: a -> a -> Ordering #

(<) :: a -> a -> Bool infix 4 #

(<=) :: a -> a -> Bool infix 4 #

(>) :: a -> a -> Bool infix 4 #

(>=) :: a -> a -> Bool infix 4 #

max :: a -> a -> a #

min :: a -> a -> a #

Instances

Ord Bool
Instance details Defined in GHC.Classes Methods compare :: Bool -> Bool -> Ordering # (<) :: Bool -> Bool -> Bool # (<=) :: Bool -> Bool -> Bool # (>) :: Bool -> Bool -> Bool # (>=) :: Bool -> Bool -> Bool # max :: Bool -> Bool -> Bool # min :: Bool -> Bool -> Bool #
Ord Char
Instance details Defined in GHC.Classes Methods compare :: Char -> Char -> Ordering # (<) :: Char -> Char -> Bool # (<=) :: Char -> Char -> Bool # (>) :: Char -> Char -> Bool # (>=) :: Char -> Char -> Bool # max :: Char -> Char -> Char # min :: Char -> Char -> Char #
Ord Double	Note that due to the presence of `NaN`, `Double`'s `Ord` instance does not satisfy reflexivity. `>>>` `0/0 <= (0/0 :: Double)`False Also note that, due to the same, `Ord`'s operator interactions are not respected by `Double`'s instance: `>>>` `(0/0 :: Double) > 1`False `>>>` `compare (0/0 :: Double) 1`GT
Instance details Defined in GHC.Classes Methods compare :: Double -> Double -> Ordering # (<) :: Double -> Double -> Bool # (<=) :: Double -> Double -> Bool # (>) :: Double -> Double -> Bool # (>=) :: Double -> Double -> Bool # max :: Double -> Double -> Double # min :: Double -> Double -> Double #
Ord Float	Note that due to the presence of `NaN`, `Float`'s `Ord` instance does not satisfy reflexivity. `>>>` `0/0 <= (0/0 :: Float)`False Also note that, due to the same, `Ord`'s operator interactions are not respected by `Float`'s instance: `>>>` `(0/0 :: Float) > 1`False `>>>` `compare (0/0 :: Float) 1`GT
Instance details Defined in GHC.Classes Methods compare :: Float -> Float -> Ordering # (<) :: Float -> Float -> Bool # (<=) :: Float -> Float -> Bool # (>) :: Float -> Float -> Bool # (>=) :: Float -> Float -> Bool # max :: Float -> Float -> Float # min :: Float -> Float -> Float #
Ord Int
Instance details Defined in GHC.Classes Methods compare :: Int -> Int -> Ordering # (<) :: Int -> Int -> Bool # (<=) :: Int -> Int -> Bool # (>) :: Int -> Int -> Bool # (>=) :: Int -> Int -> Bool # max :: Int -> Int -> Int # min :: Int -> Int -> Int #
Ord Int8	Since: base-2.1
Instance details Defined in GHC.Int Methods compare :: Int8 -> Int8 -> Ordering # (<) :: Int8 -> Int8 -> Bool # (<=) :: Int8 -> Int8 -> Bool # (>) :: Int8 -> Int8 -> Bool # (>=) :: Int8 -> Int8 -> Bool # max :: Int8 -> Int8 -> Int8 # min :: Int8 -> Int8 -> Int8 #
Ord Int16	Since: base-2.1
Instance details Defined in GHC.Int Methods compare :: Int16 -> Int16 -> Ordering # (<) :: Int16 -> Int16 -> Bool # (<=) :: Int16 -> Int16 -> Bool # (>) :: Int16 -> Int16 -> Bool # (>=) :: Int16 -> Int16 -> Bool # max :: Int16 -> Int16 -> Int16 # min :: Int16 -> Int16 -> Int16 #
Ord Int32	Since: base-2.1
Instance details Defined in GHC.Int Methods compare :: Int32 -> Int32 -> Ordering # (<) :: Int32 -> Int32 -> Bool # (<=) :: Int32 -> Int32 -> Bool # (>) :: Int32 -> Int32 -> Bool # (>=) :: Int32 -> Int32 -> Bool # max :: Int32 -> Int32 -> Int32 # min :: Int32 -> Int32 -> Int32 #
Ord Int64	Since: base-2.1
Instance details Defined in GHC.Int Methods compare :: Int64 -> Int64 -> Ordering # (<) :: Int64 -> Int64 -> Bool # (<=) :: Int64 -> Int64 -> Bool # (>) :: Int64 -> Int64 -> Bool # (>=) :: Int64 -> Int64 -> Bool # max :: Int64 -> Int64 -> Int64 # min :: Int64 -> Int64 -> Int64 #
Ord Integer
Instance details Defined in GHC.Integer.Type Methods compare :: Integer -> Integer -> Ordering # (<) :: Integer -> Integer -> Bool # (<=) :: Integer -> Integer -> Bool # (>) :: Integer -> Integer -> Bool # (>=) :: Integer -> Integer -> Bool # max :: Integer -> Integer -> Integer # min :: Integer -> Integer -> Integer #
Ord Natural	Since: base-4.8.0.0
Instance details Defined in GHC.Natural Methods compare :: Natural -> Natural -> Ordering # (<) :: Natural -> Natural -> Bool # (<=) :: Natural -> Natural -> Bool # (>) :: Natural -> Natural -> Bool # (>=) :: Natural -> Natural -> Bool # max :: Natural -> Natural -> Natural # min :: Natural -> Natural -> Natural #
Ord Ordering
Instance details Defined in GHC.Classes Methods compare :: Ordering -> Ordering -> Ordering # (<) :: Ordering -> Ordering -> Bool # (<=) :: Ordering -> Ordering -> Bool # (>) :: Ordering -> Ordering -> Bool # (>=) :: Ordering -> Ordering -> Bool # max :: Ordering -> Ordering -> Ordering # min :: Ordering -> Ordering -> Ordering #
Ord Word
Instance details Defined in GHC.Classes Methods compare :: Word -> Word -> Ordering # (<) :: Word -> Word -> Bool # (<=) :: Word -> Word -> Bool # (>) :: Word -> Word -> Bool # (>=) :: Word -> Word -> Bool # max :: Word -> Word -> Word # min :: Word -> Word -> Word #
Ord Word8	Since: base-2.1
Instance details Defined in GHC.Word Methods compare :: Word8 -> Word8 -> Ordering # (<) :: Word8 -> Word8 -> Bool # (<=) :: Word8 -> Word8 -> Bool # (>) :: Word8 -> Word8 -> Bool # (>=) :: Word8 -> Word8 -> Bool # max :: Word8 -> Word8 -> Word8 # min :: Word8 -> Word8 -> Word8 #
Ord Word16	Since: base-2.1
Instance details Defined in GHC.Word Methods compare :: Word16 -> Word16 -> Ordering # (<) :: Word16 -> Word16 -> Bool # (<=) :: Word16 -> Word16 -> Bool # (>) :: Word16 -> Word16 -> Bool # (>=) :: Word16 -> Word16 -> Bool # max :: Word16 -> Word16 -> Word16 # min :: Word16 -> Word16 -> Word16 #
Ord Word32	Since: base-2.1
Instance details Defined in GHC.Word Methods compare :: Word32 -> Word32 -> Ordering # (<) :: Word32 -> Word32 -> Bool # (<=) :: Word32 -> Word32 -> Bool # (>) :: Word32 -> Word32 -> Bool # (>=) :: Word32 -> Word32 -> Bool # max :: Word32 -> Word32 -> Word32 # min :: Word32 -> Word32 -> Word32 #
Ord Word64	Since: base-2.1
Instance details Defined in GHC.Word Methods compare :: Word64 -> Word64 -> Ordering # (<) :: Word64 -> Word64 -> Bool # (<=) :: Word64 -> Word64 -> Bool # (>) :: Word64 -> Word64 -> Bool # (>=) :: Word64 -> Word64 -> Bool # max :: Word64 -> Word64 -> Word64 # min :: Word64 -> Word64 -> Word64 #
Ord SomeTypeRep
Instance details Defined in Data.Typeable.Internal Methods compare :: SomeTypeRep -> SomeTypeRep -> Ordering # (<) :: SomeTypeRep -> SomeTypeRep -> Bool # (<=) :: SomeTypeRep -> SomeTypeRep -> Bool # (>) :: SomeTypeRep -> SomeTypeRep -> Bool # (>=) :: SomeTypeRep -> SomeTypeRep -> Bool # max :: SomeTypeRep -> SomeTypeRep -> SomeTypeRep # min :: SomeTypeRep -> SomeTypeRep -> SomeTypeRep #
Ord ()
Instance details Defined in GHC.Classes Methods compare :: () -> () -> Ordering # (<) :: () -> () -> Bool # (<=) :: () -> () -> Bool # (>) :: () -> () -> Bool # (>=) :: () -> () -> Bool # max :: () -> () -> () # min :: () -> () -> () #
Ord TyCon
Instance details Defined in GHC.Classes Methods compare :: TyCon -> TyCon -> Ordering # (<) :: TyCon -> TyCon -> Bool # (<=) :: TyCon -> TyCon -> Bool # (>) :: TyCon -> TyCon -> Bool # (>=) :: TyCon -> TyCon -> Bool # max :: TyCon -> TyCon -> TyCon # min :: TyCon -> TyCon -> TyCon #
Ord BigNat
Instance details Defined in GHC.Integer.Type Methods compare :: BigNat -> BigNat -> Ordering # (<) :: BigNat -> BigNat -> Bool # (<=) :: BigNat -> BigNat -> Bool # (>) :: BigNat -> BigNat -> Bool # (>=) :: BigNat -> BigNat -> Bool # max :: BigNat -> BigNat -> BigNat # min :: BigNat -> BigNat -> BigNat #
Ord Void	Since: base-4.8.0.0
Instance details Defined in Data.Void Methods compare :: Void -> Void -> Ordering # (<) :: Void -> Void -> Bool # (<=) :: Void -> Void -> Bool # (>) :: Void -> Void -> Bool # (>=) :: Void -> Void -> Bool # max :: Void -> Void -> Void # min :: Void -> Void -> Void #
Ord Unique
Instance details Defined in Data.Unique Methods compare :: Unique -> Unique -> Ordering # (<) :: Unique -> Unique -> Bool # (<=) :: Unique -> Unique -> Bool # (>) :: Unique -> Unique -> Bool # (>=) :: Unique -> Unique -> Bool # max :: Unique -> Unique -> Unique # min :: Unique -> Unique -> Unique #
Ord Version	Since: base-2.1
Instance details Defined in Data.Version Methods compare :: Version -> Version -> Ordering # (<) :: Version -> Version -> Bool # (<=) :: Version -> Version -> Bool # (>) :: Version -> Version -> Bool # (>=) :: Version -> Version -> Bool # max :: Version -> Version -> Version # min :: Version -> Version -> Version #
Ord ThreadId	Since: base-4.2.0.0
Instance details Defined in GHC.Conc.Sync Methods compare :: ThreadId -> ThreadId -> Ordering # (<) :: ThreadId -> ThreadId -> Bool # (<=) :: ThreadId -> ThreadId -> Bool # (>) :: ThreadId -> ThreadId -> Bool # (>=) :: ThreadId -> ThreadId -> Bool # max :: ThreadId -> ThreadId -> ThreadId # min :: ThreadId -> ThreadId -> ThreadId #
Ord BlockReason	Since: base-4.3.0.0
Instance details Defined in GHC.Conc.Sync Methods compare :: BlockReason -> BlockReason -> Ordering # (<) :: BlockReason -> BlockReason -> Bool # (<=) :: BlockReason -> BlockReason -> Bool # (>) :: BlockReason -> BlockReason -> Bool # (>=) :: BlockReason -> BlockReason -> Bool # max :: BlockReason -> BlockReason -> BlockReason # min :: BlockReason -> BlockReason -> BlockReason #
Ord ThreadStatus	Since: base-4.3.0.0
Instance details Defined in GHC.Conc.Sync Methods compare :: ThreadStatus -> ThreadStatus -> Ordering # (<) :: ThreadStatus -> ThreadStatus -> Bool # (<=) :: ThreadStatus -> ThreadStatus -> Bool # (>) :: ThreadStatus -> ThreadStatus -> Bool # (>=) :: ThreadStatus -> ThreadStatus -> Bool # max :: ThreadStatus -> ThreadStatus -> ThreadStatus # min :: ThreadStatus -> ThreadStatus -> ThreadStatus #
Ord AsyncException	Since: base-4.2.0.0
Instance details Defined in GHC.IO.Exception Methods compare :: AsyncException -> AsyncException -> Ordering # (<) :: AsyncException -> AsyncException -> Bool # (<=) :: AsyncException -> AsyncException -> Bool # (>) :: AsyncException -> AsyncException -> Bool # (>=) :: AsyncException -> AsyncException -> Bool # max :: AsyncException -> AsyncException -> AsyncException # min :: AsyncException -> AsyncException -> AsyncException #
Ord ArrayException	Since: base-4.2.0.0
Instance details Defined in GHC.IO.Exception Methods compare :: ArrayException -> ArrayException -> Ordering # (<) :: ArrayException -> ArrayException -> Bool # (<=) :: ArrayException -> ArrayException -> Bool # (>) :: ArrayException -> ArrayException -> Bool # (>=) :: ArrayException -> ArrayException -> Bool # max :: ArrayException -> ArrayException -> ArrayException # min :: ArrayException -> ArrayException -> ArrayException #
Ord ExitCode
Instance details Defined in GHC.IO.Exception Methods compare :: ExitCode -> ExitCode -> Ordering # (<) :: ExitCode -> ExitCode -> Bool # (<=) :: ExitCode -> ExitCode -> Bool # (>) :: ExitCode -> ExitCode -> Bool # (>=) :: ExitCode -> ExitCode -> Bool # max :: ExitCode -> ExitCode -> ExitCode # min :: ExitCode -> ExitCode -> ExitCode #
Ord All	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods compare :: All -> All -> Ordering # (<) :: All -> All -> Bool # (<=) :: All -> All -> Bool # (>) :: All -> All -> Bool # (>=) :: All -> All -> Bool # max :: All -> All -> All # min :: All -> All -> All #
Ord Any	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods compare :: Any -> Any -> Ordering # (<) :: Any -> Any -> Bool # (<=) :: Any -> Any -> Bool # (>) :: Any -> Any -> Bool # (>=) :: Any -> Any -> Bool # max :: Any -> Any -> Any # min :: Any -> Any -> Any #
Ord Fixity	Since: base-4.6.0.0
Instance details Defined in GHC.Generics Methods compare :: Fixity -> Fixity -> Ordering # (<) :: Fixity -> Fixity -> Bool # (<=) :: Fixity -> Fixity -> Bool # (>) :: Fixity -> Fixity -> Bool # (>=) :: Fixity -> Fixity -> Bool # max :: Fixity -> Fixity -> Fixity # min :: Fixity -> Fixity -> Fixity #
Ord Associativity	Since: base-4.6.0.0
Instance details Defined in GHC.Generics Methods compare :: Associativity -> Associativity -> Ordering # (<) :: Associativity -> Associativity -> Bool # (<=) :: Associativity -> Associativity -> Bool # (>) :: Associativity -> Associativity -> Bool # (>=) :: Associativity -> Associativity -> Bool # max :: Associativity -> Associativity -> Associativity # min :: Associativity -> Associativity -> Associativity #
Ord SourceUnpackedness	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods compare :: SourceUnpackedness -> SourceUnpackedness -> Ordering # (<) :: SourceUnpackedness -> SourceUnpackedness -> Bool # (<=) :: SourceUnpackedness -> SourceUnpackedness -> Bool # (>) :: SourceUnpackedness -> SourceUnpackedness -> Bool # (>=) :: SourceUnpackedness -> SourceUnpackedness -> Bool # max :: SourceUnpackedness -> SourceUnpackedness -> SourceUnpackedness # min :: SourceUnpackedness -> SourceUnpackedness -> SourceUnpackedness #
Ord SourceStrictness	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods compare :: SourceStrictness -> SourceStrictness -> Ordering # (<) :: SourceStrictness -> SourceStrictness -> Bool # (<=) :: SourceStrictness -> SourceStrictness -> Bool # (>) :: SourceStrictness -> SourceStrictness -> Bool # (>=) :: SourceStrictness -> SourceStrictness -> Bool # max :: SourceStrictness -> SourceStrictness -> SourceStrictness # min :: SourceStrictness -> SourceStrictness -> SourceStrictness #
Ord DecidedStrictness	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods compare :: DecidedStrictness -> DecidedStrictness -> Ordering # (<) :: DecidedStrictness -> DecidedStrictness -> Bool # (<=) :: DecidedStrictness -> DecidedStrictness -> Bool # (>) :: DecidedStrictness -> DecidedStrictness -> Bool # (>=) :: DecidedStrictness -> DecidedStrictness -> Bool # max :: DecidedStrictness -> DecidedStrictness -> DecidedStrictness # min :: DecidedStrictness -> DecidedStrictness -> DecidedStrictness #
Ord SomeSymbol	Since: base-4.7.0.0
Instance details Defined in GHC.TypeLits Methods compare :: SomeSymbol -> SomeSymbol -> Ordering # (<) :: SomeSymbol -> SomeSymbol -> Bool # (<=) :: SomeSymbol -> SomeSymbol -> Bool # (>) :: SomeSymbol -> SomeSymbol -> Bool # (>=) :: SomeSymbol -> SomeSymbol -> Bool # max :: SomeSymbol -> SomeSymbol -> SomeSymbol # min :: SomeSymbol -> SomeSymbol -> SomeSymbol #
Ord SomeNat	Since: base-4.7.0.0
Instance details Defined in GHC.TypeNats Methods compare :: SomeNat -> SomeNat -> Ordering # (<) :: SomeNat -> SomeNat -> Bool # (<=) :: SomeNat -> SomeNat -> Bool # (>) :: SomeNat -> SomeNat -> Bool # (>=) :: SomeNat -> SomeNat -> Bool # max :: SomeNat -> SomeNat -> SomeNat # min :: SomeNat -> SomeNat -> SomeNat #
Ord CChar
Instance details Defined in Foreign.C.Types Methods compare :: CChar -> CChar -> Ordering # (<) :: CChar -> CChar -> Bool # (<=) :: CChar -> CChar -> Bool # (>) :: CChar -> CChar -> Bool # (>=) :: CChar -> CChar -> Bool # max :: CChar -> CChar -> CChar # min :: CChar -> CChar -> CChar #
Ord CSChar
Instance details Defined in Foreign.C.Types Methods compare :: CSChar -> CSChar -> Ordering # (<) :: CSChar -> CSChar -> Bool # (<=) :: CSChar -> CSChar -> Bool # (>) :: CSChar -> CSChar -> Bool # (>=) :: CSChar -> CSChar -> Bool # max :: CSChar -> CSChar -> CSChar # min :: CSChar -> CSChar -> CSChar #
Ord CUChar
Instance details Defined in Foreign.C.Types Methods compare :: CUChar -> CUChar -> Ordering # (<) :: CUChar -> CUChar -> Bool # (<=) :: CUChar -> CUChar -> Bool # (>) :: CUChar -> CUChar -> Bool # (>=) :: CUChar -> CUChar -> Bool # max :: CUChar -> CUChar -> CUChar # min :: CUChar -> CUChar -> CUChar #
Ord CShort
Instance details Defined in Foreign.C.Types Methods compare :: CShort -> CShort -> Ordering # (<) :: CShort -> CShort -> Bool # (<=) :: CShort -> CShort -> Bool # (>) :: CShort -> CShort -> Bool # (>=) :: CShort -> CShort -> Bool # max :: CShort -> CShort -> CShort # min :: CShort -> CShort -> CShort #
Ord CUShort
Instance details Defined in Foreign.C.Types Methods compare :: CUShort -> CUShort -> Ordering # (<) :: CUShort -> CUShort -> Bool # (<=) :: CUShort -> CUShort -> Bool # (>) :: CUShort -> CUShort -> Bool # (>=) :: CUShort -> CUShort -> Bool # max :: CUShort -> CUShort -> CUShort # min :: CUShort -> CUShort -> CUShort #
Ord CInt
Instance details Defined in Foreign.C.Types Methods compare :: CInt -> CInt -> Ordering # (<) :: CInt -> CInt -> Bool # (<=) :: CInt -> CInt -> Bool # (>) :: CInt -> CInt -> Bool # (>=) :: CInt -> CInt -> Bool # max :: CInt -> CInt -> CInt # min :: CInt -> CInt -> CInt #
Ord CUInt
Instance details Defined in Foreign.C.Types Methods compare :: CUInt -> CUInt -> Ordering # (<) :: CUInt -> CUInt -> Bool # (<=) :: CUInt -> CUInt -> Bool # (>) :: CUInt -> CUInt -> Bool # (>=) :: CUInt -> CUInt -> Bool # max :: CUInt -> CUInt -> CUInt # min :: CUInt -> CUInt -> CUInt #
Ord CLong
Instance details Defined in Foreign.C.Types Methods compare :: CLong -> CLong -> Ordering # (<) :: CLong -> CLong -> Bool # (<=) :: CLong -> CLong -> Bool # (>) :: CLong -> CLong -> Bool # (>=) :: CLong -> CLong -> Bool # max :: CLong -> CLong -> CLong # min :: CLong -> CLong -> CLong #
Ord CULong
Instance details Defined in Foreign.C.Types Methods compare :: CULong -> CULong -> Ordering # (<) :: CULong -> CULong -> Bool # (<=) :: CULong -> CULong -> Bool # (>) :: CULong -> CULong -> Bool # (>=) :: CULong -> CULong -> Bool # max :: CULong -> CULong -> CULong # min :: CULong -> CULong -> CULong #
Ord CLLong
Instance details Defined in Foreign.C.Types Methods compare :: CLLong -> CLLong -> Ordering # (<) :: CLLong -> CLLong -> Bool # (<=) :: CLLong -> CLLong -> Bool # (>) :: CLLong -> CLLong -> Bool # (>=) :: CLLong -> CLLong -> Bool # max :: CLLong -> CLLong -> CLLong # min :: CLLong -> CLLong -> CLLong #
Ord CULLong
Instance details Defined in Foreign.C.Types Methods compare :: CULLong -> CULLong -> Ordering # (<) :: CULLong -> CULLong -> Bool # (<=) :: CULLong -> CULLong -> Bool # (>) :: CULLong -> CULLong -> Bool # (>=) :: CULLong -> CULLong -> Bool # max :: CULLong -> CULLong -> CULLong # min :: CULLong -> CULLong -> CULLong #
Ord CBool
Instance details Defined in Foreign.C.Types Methods compare :: CBool -> CBool -> Ordering # (<) :: CBool -> CBool -> Bool # (<=) :: CBool -> CBool -> Bool # (>) :: CBool -> CBool -> Bool # (>=) :: CBool -> CBool -> Bool # max :: CBool -> CBool -> CBool # min :: CBool -> CBool -> CBool #
Ord CFloat
Instance details Defined in Foreign.C.Types Methods compare :: CFloat -> CFloat -> Ordering # (<) :: CFloat -> CFloat -> Bool # (<=) :: CFloat -> CFloat -> Bool # (>) :: CFloat -> CFloat -> Bool # (>=) :: CFloat -> CFloat -> Bool # max :: CFloat -> CFloat -> CFloat # min :: CFloat -> CFloat -> CFloat #
Ord CDouble
Instance details Defined in Foreign.C.Types Methods compare :: CDouble -> CDouble -> Ordering # (<) :: CDouble -> CDouble -> Bool # (<=) :: CDouble -> CDouble -> Bool # (>) :: CDouble -> CDouble -> Bool # (>=) :: CDouble -> CDouble -> Bool # max :: CDouble -> CDouble -> CDouble # min :: CDouble -> CDouble -> CDouble #
Ord CPtrdiff
Instance details Defined in Foreign.C.Types Methods compare :: CPtrdiff -> CPtrdiff -> Ordering # (<) :: CPtrdiff -> CPtrdiff -> Bool # (<=) :: CPtrdiff -> CPtrdiff -> Bool # (>) :: CPtrdiff -> CPtrdiff -> Bool # (>=) :: CPtrdiff -> CPtrdiff -> Bool # max :: CPtrdiff -> CPtrdiff -> CPtrdiff # min :: CPtrdiff -> CPtrdiff -> CPtrdiff #
Ord CSize
Instance details Defined in Foreign.C.Types Methods compare :: CSize -> CSize -> Ordering # (<) :: CSize -> CSize -> Bool # (<=) :: CSize -> CSize -> Bool # (>) :: CSize -> CSize -> Bool # (>=) :: CSize -> CSize -> Bool # max :: CSize -> CSize -> CSize # min :: CSize -> CSize -> CSize #
Ord CWchar
Instance details Defined in Foreign.C.Types Methods compare :: CWchar -> CWchar -> Ordering # (<) :: CWchar -> CWchar -> Bool # (<=) :: CWchar -> CWchar -> Bool # (>) :: CWchar -> CWchar -> Bool # (>=) :: CWchar -> CWchar -> Bool # max :: CWchar -> CWchar -> CWchar # min :: CWchar -> CWchar -> CWchar #
Ord CSigAtomic
Instance details Defined in Foreign.C.Types Methods compare :: CSigAtomic -> CSigAtomic -> Ordering # (<) :: CSigAtomic -> CSigAtomic -> Bool # (<=) :: CSigAtomic -> CSigAtomic -> Bool # (>) :: CSigAtomic -> CSigAtomic -> Bool # (>=) :: CSigAtomic -> CSigAtomic -> Bool # max :: CSigAtomic -> CSigAtomic -> CSigAtomic # min :: CSigAtomic -> CSigAtomic -> CSigAtomic #
Ord CClock
Instance details Defined in Foreign.C.Types Methods compare :: CClock -> CClock -> Ordering # (<) :: CClock -> CClock -> Bool # (<=) :: CClock -> CClock -> Bool # (>) :: CClock -> CClock -> Bool # (>=) :: CClock -> CClock -> Bool # max :: CClock -> CClock -> CClock # min :: CClock -> CClock -> CClock #
Ord CTime
Instance details Defined in Foreign.C.Types Methods compare :: CTime -> CTime -> Ordering # (<) :: CTime -> CTime -> Bool # (<=) :: CTime -> CTime -> Bool # (>) :: CTime -> CTime -> Bool # (>=) :: CTime -> CTime -> Bool # max :: CTime -> CTime -> CTime # min :: CTime -> CTime -> CTime #
Ord CUSeconds
Instance details Defined in Foreign.C.Types Methods compare :: CUSeconds -> CUSeconds -> Ordering # (<) :: CUSeconds -> CUSeconds -> Bool # (<=) :: CUSeconds -> CUSeconds -> Bool # (>) :: CUSeconds -> CUSeconds -> Bool # (>=) :: CUSeconds -> CUSeconds -> Bool # max :: CUSeconds -> CUSeconds -> CUSeconds # min :: CUSeconds -> CUSeconds -> CUSeconds #
Ord CSUSeconds
Instance details Defined in Foreign.C.Types Methods compare :: CSUSeconds -> CSUSeconds -> Ordering # (<) :: CSUSeconds -> CSUSeconds -> Bool # (<=) :: CSUSeconds -> CSUSeconds -> Bool # (>) :: CSUSeconds -> CSUSeconds -> Bool # (>=) :: CSUSeconds -> CSUSeconds -> Bool # max :: CSUSeconds -> CSUSeconds -> CSUSeconds # min :: CSUSeconds -> CSUSeconds -> CSUSeconds #
Ord CIntPtr
Instance details Defined in Foreign.C.Types Methods compare :: CIntPtr -> CIntPtr -> Ordering # (<) :: CIntPtr -> CIntPtr -> Bool # (<=) :: CIntPtr -> CIntPtr -> Bool # (>) :: CIntPtr -> CIntPtr -> Bool # (>=) :: CIntPtr -> CIntPtr -> Bool # max :: CIntPtr -> CIntPtr -> CIntPtr # min :: CIntPtr -> CIntPtr -> CIntPtr #
Ord CUIntPtr
Instance details Defined in Foreign.C.Types Methods compare :: CUIntPtr -> CUIntPtr -> Ordering # (<) :: CUIntPtr -> CUIntPtr -> Bool # (<=) :: CUIntPtr -> CUIntPtr -> Bool # (>) :: CUIntPtr -> CUIntPtr -> Bool # (>=) :: CUIntPtr -> CUIntPtr -> Bool # max :: CUIntPtr -> CUIntPtr -> CUIntPtr # min :: CUIntPtr -> CUIntPtr -> CUIntPtr #
Ord CIntMax
Instance details Defined in Foreign.C.Types Methods compare :: CIntMax -> CIntMax -> Ordering # (<) :: CIntMax -> CIntMax -> Bool # (<=) :: CIntMax -> CIntMax -> Bool # (>) :: CIntMax -> CIntMax -> Bool # (>=) :: CIntMax -> CIntMax -> Bool # max :: CIntMax -> CIntMax -> CIntMax # min :: CIntMax -> CIntMax -> CIntMax #
Ord CUIntMax
Instance details Defined in Foreign.C.Types Methods compare :: CUIntMax -> CUIntMax -> Ordering # (<) :: CUIntMax -> CUIntMax -> Bool # (<=) :: CUIntMax -> CUIntMax -> Bool # (>) :: CUIntMax -> CUIntMax -> Bool # (>=) :: CUIntMax -> CUIntMax -> Bool # max :: CUIntMax -> CUIntMax -> CUIntMax # min :: CUIntMax -> CUIntMax -> CUIntMax #
Ord WordPtr
Instance details Defined in Foreign.Ptr Methods compare :: WordPtr -> WordPtr -> Ordering # (<) :: WordPtr -> WordPtr -> Bool # (<=) :: WordPtr -> WordPtr -> Bool # (>) :: WordPtr -> WordPtr -> Bool # (>=) :: WordPtr -> WordPtr -> Bool # max :: WordPtr -> WordPtr -> WordPtr # min :: WordPtr -> WordPtr -> WordPtr #
Ord IntPtr
Instance details Defined in Foreign.Ptr Methods compare :: IntPtr -> IntPtr -> Ordering # (<) :: IntPtr -> IntPtr -> Bool # (<=) :: IntPtr -> IntPtr -> Bool # (>) :: IntPtr -> IntPtr -> Bool # (>=) :: IntPtr -> IntPtr -> Bool # max :: IntPtr -> IntPtr -> IntPtr # min :: IntPtr -> IntPtr -> IntPtr #
Ord Fingerprint	Since: base-4.4.0.0
Instance details Defined in GHC.Fingerprint.Type Methods compare :: Fingerprint -> Fingerprint -> Ordering # (<) :: Fingerprint -> Fingerprint -> Bool # (<=) :: Fingerprint -> Fingerprint -> Bool # (>) :: Fingerprint -> Fingerprint -> Bool # (>=) :: Fingerprint -> Fingerprint -> Bool # max :: Fingerprint -> Fingerprint -> Fingerprint # min :: Fingerprint -> Fingerprint -> Fingerprint #
Ord ByteArray	Non-lexicographic ordering. This compares the lengths of the byte arrays first and uses a lexicographic ordering if the lengths are equal. Subject to change between major versions. Since: primitive-0.6.3.0
Instance details Defined in Data.Primitive.ByteArray Methods compare :: ByteArray -> ByteArray -> Ordering # (<) :: ByteArray -> ByteArray -> Bool # (<=) :: ByteArray -> ByteArray -> Bool # (>) :: ByteArray -> ByteArray -> Bool # (>=) :: ByteArray -> ByteArray -> Bool # max :: ByteArray -> ByteArray -> ByteArray # min :: ByteArray -> ByteArray -> ByteArray #
Ord Addr
Instance details Defined in Data.Primitive.Types Methods compare :: Addr -> Addr -> Ordering # (<) :: Addr -> Addr -> Bool # (<=) :: Addr -> Addr -> Bool # (>) :: Addr -> Addr -> Bool # (>=) :: Addr -> Addr -> Bool # max :: Addr -> Addr -> Addr # min :: Addr -> Addr -> Addr #
Ord DynamicDimension Source #
Instance details Defined in Numeric.Units.Dimensional.Dimensions.TermLevel Methods compare :: DynamicDimension -> DynamicDimension -> Ordering # (<) :: DynamicDimension -> DynamicDimension -> Bool # (<=) :: DynamicDimension -> DynamicDimension -> Bool # (>) :: DynamicDimension -> DynamicDimension -> Bool # (>=) :: DynamicDimension -> DynamicDimension -> Bool # max :: DynamicDimension -> DynamicDimension -> DynamicDimension # min :: DynamicDimension -> DynamicDimension -> DynamicDimension #
Ord Dimension' Source #
Instance details Defined in Numeric.Units.Dimensional.Dimensions.TermLevel Methods compare :: Dimension' -> Dimension' -> Ordering # (<) :: Dimension' -> Dimension' -> Bool # (<=) :: Dimension' -> Dimension' -> Bool # (>) :: Dimension' -> Dimension' -> Bool # (>=) :: Dimension' -> Dimension' -> Bool # max :: Dimension' -> Dimension' -> Dimension' # min :: Dimension' -> Dimension' -> Dimension' #
Ord InterchangeName Source #
Instance details Defined in Numeric.Units.Dimensional.UnitNames.InterchangeNames Methods compare :: InterchangeName -> InterchangeName -> Ordering # (<) :: InterchangeName -> InterchangeName -> Bool # (<=) :: InterchangeName -> InterchangeName -> Bool # (>) :: InterchangeName -> InterchangeName -> Bool # (>=) :: InterchangeName -> InterchangeName -> Bool # max :: InterchangeName -> InterchangeName -> InterchangeName # min :: InterchangeName -> InterchangeName -> InterchangeName #
Ord InterchangeNameAuthority Source #
Instance details Defined in Numeric.Units.Dimensional.UnitNames.InterchangeNames Methods compare :: InterchangeNameAuthority -> InterchangeNameAuthority -> Ordering # (<) :: InterchangeNameAuthority -> InterchangeNameAuthority -> Bool # (<=) :: InterchangeNameAuthority -> InterchangeNameAuthority -> Bool # (>) :: InterchangeNameAuthority -> InterchangeNameAuthority -> Bool # (>=) :: InterchangeNameAuthority -> InterchangeNameAuthority -> Bool # max :: InterchangeNameAuthority -> InterchangeNameAuthority -> InterchangeNameAuthority # min :: InterchangeNameAuthority -> InterchangeNameAuthority -> InterchangeNameAuthority #
Ord Metricality Source #
Instance details Defined in Numeric.Units.Dimensional.Variants Methods compare :: Metricality -> Metricality -> Ordering # (<) :: Metricality -> Metricality -> Bool # (<=) :: Metricality -> Metricality -> Bool # (>) :: Metricality -> Metricality -> Bool # (>=) :: Metricality -> Metricality -> Bool # max :: Metricality -> Metricality -> Metricality # min :: Metricality -> Metricality -> Metricality #
Ord Prefix Source #
Instance details Defined in Numeric.Units.Dimensional.UnitNames.Internal Methods compare :: Prefix -> Prefix -> Ordering # (<) :: Prefix -> Prefix -> Bool # (<=) :: Prefix -> Prefix -> Bool # (>) :: Prefix -> Prefix -> Bool # (>=) :: Prefix -> Prefix -> Bool # max :: Prefix -> Prefix -> Prefix # min :: Prefix -> Prefix -> Prefix #
Ord a => Ord [a]
Instance details Defined in GHC.Classes Methods compare :: [a] -> [a] -> Ordering # (<) :: [a] -> [a] -> Bool # (<=) :: [a] -> [a] -> Bool # (>) :: [a] -> [a] -> Bool # (>=) :: [a] -> [a] -> Bool # max :: [a] -> [a] -> [a] # min :: [a] -> [a] -> [a] #
Ord a => Ord (Maybe a)	Since: base-2.1
Instance details Defined in GHC.Maybe Methods compare :: Maybe a -> Maybe a -> Ordering # (<) :: Maybe a -> Maybe a -> Bool # (<=) :: Maybe a -> Maybe a -> Bool # (>) :: Maybe a -> Maybe a -> Bool # (>=) :: Maybe a -> Maybe a -> Bool # max :: Maybe a -> Maybe a -> Maybe a # min :: Maybe a -> Maybe a -> Maybe a #
Integral a => Ord (Ratio a)	Since: base-2.0.1
Instance details Defined in GHC.Real Methods compare :: Ratio a -> Ratio a -> Ordering # (<) :: Ratio a -> Ratio a -> Bool # (<=) :: Ratio a -> Ratio a -> Bool # (>) :: Ratio a -> Ratio a -> Bool # (>=) :: Ratio a -> Ratio a -> Bool # max :: Ratio a -> Ratio a -> Ratio a # min :: Ratio a -> Ratio a -> Ratio a #
Ord (Ptr a)	Since: base-2.1
Instance details Defined in GHC.Ptr Methods compare :: Ptr a -> Ptr a -> Ordering # (<) :: Ptr a -> Ptr a -> Bool # (<=) :: Ptr a -> Ptr a -> Bool # (>) :: Ptr a -> Ptr a -> Bool # (>=) :: Ptr a -> Ptr a -> Bool # max :: Ptr a -> Ptr a -> Ptr a # min :: Ptr a -> Ptr a -> Ptr a #
Ord (FunPtr a)
Instance details Defined in GHC.Ptr Methods compare :: FunPtr a -> FunPtr a -> Ordering # (<) :: FunPtr a -> FunPtr a -> Bool # (<=) :: FunPtr a -> FunPtr a -> Bool # (>) :: FunPtr a -> FunPtr a -> Bool # (>=) :: FunPtr a -> FunPtr a -> Bool # max :: FunPtr a -> FunPtr a -> FunPtr a # min :: FunPtr a -> FunPtr a -> FunPtr a #
Ord p => Ord (Par1 p)	Since: base-4.7.0.0
Instance details Defined in GHC.Generics Methods compare :: Par1 p -> Par1 p -> Ordering # (<) :: Par1 p -> Par1 p -> Bool # (<=) :: Par1 p -> Par1 p -> Bool # (>) :: Par1 p -> Par1 p -> Bool # (>=) :: Par1 p -> Par1 p -> Bool # max :: Par1 p -> Par1 p -> Par1 p # min :: Par1 p -> Par1 p -> Par1 p #
Ord (ForeignPtr a)	Since: base-2.1
Instance details Defined in GHC.ForeignPtr Methods compare :: ForeignPtr a -> ForeignPtr a -> Ordering # (<) :: ForeignPtr a -> ForeignPtr a -> Bool # (<=) :: ForeignPtr a -> ForeignPtr a -> Bool # (>) :: ForeignPtr a -> ForeignPtr a -> Bool # (>=) :: ForeignPtr a -> ForeignPtr a -> Bool # max :: ForeignPtr a -> ForeignPtr a -> ForeignPtr a # min :: ForeignPtr a -> ForeignPtr a -> ForeignPtr a #
Ord (Fixed a)	Since: base-2.1
Instance details Defined in Data.Fixed Methods compare :: Fixed a -> Fixed a -> Ordering # (<) :: Fixed a -> Fixed a -> Bool # (<=) :: Fixed a -> Fixed a -> Bool # (>) :: Fixed a -> Fixed a -> Bool # (>=) :: Fixed a -> Fixed a -> Bool # max :: Fixed a -> Fixed a -> Fixed a # min :: Fixed a -> Fixed a -> Fixed a #
Ord a => Ord (Min a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods compare :: Min a -> Min a -> Ordering # (<) :: Min a -> Min a -> Bool # (<=) :: Min a -> Min a -> Bool # (>) :: Min a -> Min a -> Bool # (>=) :: Min a -> Min a -> Bool # max :: Min a -> Min a -> Min a # min :: Min a -> Min a -> Min a #
Ord a => Ord (Max a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods compare :: Max a -> Max a -> Ordering # (<) :: Max a -> Max a -> Bool # (<=) :: Max a -> Max a -> Bool # (>) :: Max a -> Max a -> Bool # (>=) :: Max a -> Max a -> Bool # max :: Max a -> Max a -> Max a # min :: Max a -> Max a -> Max a #
Ord a => Ord (First a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods compare :: First a -> First a -> Ordering # (<) :: First a -> First a -> Bool # (<=) :: First a -> First a -> Bool # (>) :: First a -> First a -> Bool # (>=) :: First a -> First a -> Bool # max :: First a -> First a -> First a # min :: First a -> First a -> First a #
Ord a => Ord (Last a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods compare :: Last a -> Last a -> Ordering # (<) :: Last a -> Last a -> Bool # (<=) :: Last a -> Last a -> Bool # (>) :: Last a -> Last a -> Bool # (>=) :: Last a -> Last a -> Bool # max :: Last a -> Last a -> Last a # min :: Last a -> Last a -> Last a #
Ord m => Ord (WrappedMonoid m)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods compare :: WrappedMonoid m -> WrappedMonoid m -> Ordering # (<) :: WrappedMonoid m -> WrappedMonoid m -> Bool # (<=) :: WrappedMonoid m -> WrappedMonoid m -> Bool # (>) :: WrappedMonoid m -> WrappedMonoid m -> Bool # (>=) :: WrappedMonoid m -> WrappedMonoid m -> Bool # max :: WrappedMonoid m -> WrappedMonoid m -> WrappedMonoid m # min :: WrappedMonoid m -> WrappedMonoid m -> WrappedMonoid m #
Ord a => Ord (Option a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods compare :: Option a -> Option a -> Ordering # (<) :: Option a -> Option a -> Bool # (<=) :: Option a -> Option a -> Bool # (>) :: Option a -> Option a -> Bool # (>=) :: Option a -> Option a -> Bool # max :: Option a -> Option a -> Option a # min :: Option a -> Option a -> Option a #
Ord a => Ord (ZipList a)	Since: base-4.7.0.0
Instance details Defined in Control.Applicative Methods compare :: ZipList a -> ZipList a -> Ordering # (<) :: ZipList a -> ZipList a -> Bool # (<=) :: ZipList a -> ZipList a -> Bool # (>) :: ZipList a -> ZipList a -> Bool # (>=) :: ZipList a -> ZipList a -> Bool # max :: ZipList a -> ZipList a -> ZipList a # min :: ZipList a -> ZipList a -> ZipList a #
Ord a => Ord (Identity a)	Since: base-4.8.0.0
Instance details Defined in Data.Functor.Identity Methods compare :: Identity a -> Identity a -> Ordering # (<) :: Identity a -> Identity a -> Bool # (<=) :: Identity a -> Identity a -> Bool # (>) :: Identity a -> Identity a -> Bool # (>=) :: Identity a -> Identity a -> Bool # max :: Identity a -> Identity a -> Identity a # min :: Identity a -> Identity a -> Identity a #
Ord a => Ord (First a)	Since: base-2.1
Instance details Defined in Data.Monoid Methods compare :: First a -> First a -> Ordering # (<) :: First a -> First a -> Bool # (<=) :: First a -> First a -> Bool # (>) :: First a -> First a -> Bool # (>=) :: First a -> First a -> Bool # max :: First a -> First a -> First a # min :: First a -> First a -> First a #
Ord a => Ord (Last a)	Since: base-2.1
Instance details Defined in Data.Monoid Methods compare :: Last a -> Last a -> Ordering # (<) :: Last a -> Last a -> Bool # (<=) :: Last a -> Last a -> Bool # (>) :: Last a -> Last a -> Bool # (>=) :: Last a -> Last a -> Bool # max :: Last a -> Last a -> Last a # min :: Last a -> Last a -> Last a #
Ord a => Ord (Dual a)	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods compare :: Dual a -> Dual a -> Ordering # (<) :: Dual a -> Dual a -> Bool # (<=) :: Dual a -> Dual a -> Bool # (>) :: Dual a -> Dual a -> Bool # (>=) :: Dual a -> Dual a -> Bool # max :: Dual a -> Dual a -> Dual a # min :: Dual a -> Dual a -> Dual a #
Ord a => Ord (Sum a)	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods compare :: Sum a -> Sum a -> Ordering # (<) :: Sum a -> Sum a -> Bool # (<=) :: Sum a -> Sum a -> Bool # (>) :: Sum a -> Sum a -> Bool # (>=) :: Sum a -> Sum a -> Bool # max :: Sum a -> Sum a -> Sum a # min :: Sum a -> Sum a -> Sum a #
Ord a => Ord (Product a)	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods compare :: Product a -> Product a -> Ordering # (<) :: Product a -> Product a -> Bool # (<=) :: Product a -> Product a -> Bool # (>) :: Product a -> Product a -> Bool # (>=) :: Product a -> Product a -> Bool # max :: Product a -> Product a -> Product a # min :: Product a -> Product a -> Product a #
Ord a => Ord (Down a)	Since: base-4.6.0.0
Instance details Defined in Data.Ord Methods compare :: Down a -> Down a -> Ordering # (<) :: Down a -> Down a -> Bool # (<=) :: Down a -> Down a -> Bool # (>) :: Down a -> Down a -> Bool # (>=) :: Down a -> Down a -> Bool # max :: Down a -> Down a -> Down a # min :: Down a -> Down a -> Down a #
Ord a => Ord (NonEmpty a)	Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods compare :: NonEmpty a -> NonEmpty a -> Ordering # (<) :: NonEmpty a -> NonEmpty a -> Bool # (<=) :: NonEmpty a -> NonEmpty a -> Bool # (>) :: NonEmpty a -> NonEmpty a -> Bool # (>=) :: NonEmpty a -> NonEmpty a -> Bool # max :: NonEmpty a -> NonEmpty a -> NonEmpty a # min :: NonEmpty a -> NonEmpty a -> NonEmpty a #
(Ord a, PrimUnlifted a) => Ord (UnliftedArray a)	Lexicographic ordering. Subject to change between major versions. Since: primitive-0.6.4.0
Instance details Defined in Data.Primitive.UnliftedArray Methods compare :: UnliftedArray a -> UnliftedArray a -> Ordering # (<) :: UnliftedArray a -> UnliftedArray a -> Bool # (<=) :: UnliftedArray a -> UnliftedArray a -> Bool # (>) :: UnliftedArray a -> UnliftedArray a -> Bool # (>=) :: UnliftedArray a -> UnliftedArray a -> Bool # max :: UnliftedArray a -> UnliftedArray a -> UnliftedArray a # min :: UnliftedArray a -> UnliftedArray a -> UnliftedArray a #
(Ord a, Prim a) => Ord (PrimArray a)	Lexicographic ordering. Subject to change between major versions. Since: primitive-0.6.4.0
Instance details Defined in Data.Primitive.PrimArray Methods compare :: PrimArray a -> PrimArray a -> Ordering # (<) :: PrimArray a -> PrimArray a -> Bool # (<=) :: PrimArray a -> PrimArray a -> Bool # (>) :: PrimArray a -> PrimArray a -> Bool # (>=) :: PrimArray a -> PrimArray a -> Bool # max :: PrimArray a -> PrimArray a -> PrimArray a # min :: PrimArray a -> PrimArray a -> PrimArray a #
Ord a => Ord (SmallArray a)	Lexicographic ordering. Subject to change between major versions.
Instance details Defined in Data.Primitive.SmallArray Methods compare :: SmallArray a -> SmallArray a -> Ordering # (<) :: SmallArray a -> SmallArray a -> Bool # (<=) :: SmallArray a -> SmallArray a -> Bool # (>) :: SmallArray a -> SmallArray a -> Bool # (>=) :: SmallArray a -> SmallArray a -> Bool # max :: SmallArray a -> SmallArray a -> SmallArray a # min :: SmallArray a -> SmallArray a -> SmallArray a #
Ord a => Ord (Array a)	Lexicographic ordering. Subject to change between major versions.
Instance details Defined in Data.Primitive.Array Methods compare :: Array a -> Array a -> Ordering # (<) :: Array a -> Array a -> Bool # (<=) :: Array a -> Array a -> Bool # (>) :: Array a -> Array a -> Bool # (>=) :: Array a -> Array a -> Bool # max :: Array a -> Array a -> Array a # min :: Array a -> Array a -> Array a #
(Prim a, Ord a) => Ord (Vector a)
Instance details Defined in Data.Vector.Primitive Methods compare :: Vector a -> Vector a -> Ordering # (<) :: Vector a -> Vector a -> Bool # (<=) :: Vector a -> Vector a -> Bool # (>) :: Vector a -> Vector a -> Bool # (>=) :: Vector a -> Vector a -> Bool # max :: Vector a -> Vector a -> Vector a # min :: Vector a -> Vector a -> Vector a #
Ord (NameAtom m) Source #
Instance details Defined in Numeric.Units.Dimensional.UnitNames.Internal Methods compare :: NameAtom m -> NameAtom m -> Ordering # (<) :: NameAtom m -> NameAtom m -> Bool # (<=) :: NameAtom m -> NameAtom m -> Bool # (>) :: NameAtom m -> NameAtom m -> Bool # (>=) :: NameAtom m -> NameAtom m -> Bool # max :: NameAtom m -> NameAtom m -> NameAtom m # min :: NameAtom m -> NameAtom m -> NameAtom m #
(Ord a, Ord b) => Ord (Either a b)	Since: base-2.1
Instance details Defined in Data.Either Methods compare :: Either a b -> Either a b -> Ordering # (<) :: Either a b -> Either a b -> Bool # (<=) :: Either a b -> Either a b -> Bool # (>) :: Either a b -> Either a b -> Bool # (>=) :: Either a b -> Either a b -> Bool # max :: Either a b -> Either a b -> Either a b # min :: Either a b -> Either a b -> Either a b #
Ord (V1 p)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods compare :: V1 p -> V1 p -> Ordering # (<) :: V1 p -> V1 p -> Bool # (<=) :: V1 p -> V1 p -> Bool # (>) :: V1 p -> V1 p -> Bool # (>=) :: V1 p -> V1 p -> Bool # max :: V1 p -> V1 p -> V1 p # min :: V1 p -> V1 p -> V1 p #
Ord (U1 p)	Since: base-4.7.0.0
Instance details Defined in GHC.Generics Methods compare :: U1 p -> U1 p -> Ordering # (<) :: U1 p -> U1 p -> Bool # (<=) :: U1 p -> U1 p -> Bool # (>) :: U1 p -> U1 p -> Bool # (>=) :: U1 p -> U1 p -> Bool # max :: U1 p -> U1 p -> U1 p # min :: U1 p -> U1 p -> U1 p #
Ord (TypeRep a)	Since: base-4.4.0.0
Instance details Defined in Data.Typeable.Internal Methods compare :: TypeRep a -> TypeRep a -> Ordering # (<) :: TypeRep a -> TypeRep a -> Bool # (<=) :: TypeRep a -> TypeRep a -> Bool # (>) :: TypeRep a -> TypeRep a -> Bool # (>=) :: TypeRep a -> TypeRep a -> Bool # max :: TypeRep a -> TypeRep a -> TypeRep a # min :: TypeRep a -> TypeRep a -> TypeRep a #
(Ord a, Ord b) => Ord (a, b)
Instance details Defined in GHC.Classes Methods compare :: (a, b) -> (a, b) -> Ordering # (<) :: (a, b) -> (a, b) -> Bool # (<=) :: (a, b) -> (a, b) -> Bool # (>) :: (a, b) -> (a, b) -> Bool # (>=) :: (a, b) -> (a, b) -> Bool # max :: (a, b) -> (a, b) -> (a, b) # min :: (a, b) -> (a, b) -> (a, b) #
(Ix i, Ord e) => Ord (Array i e)	Since: base-2.1
Instance details Defined in GHC.Arr Methods compare :: Array i e -> Array i e -> Ordering # (<) :: Array i e -> Array i e -> Bool # (<=) :: Array i e -> Array i e -> Bool # (>) :: Array i e -> Array i e -> Bool # (>=) :: Array i e -> Array i e -> Bool # max :: Array i e -> Array i e -> Array i e # min :: Array i e -> Array i e -> Array i e #
Ord a => Ord (Arg a b)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods compare :: Arg a b -> Arg a b -> Ordering # (<) :: Arg a b -> Arg a b -> Bool # (<=) :: Arg a b -> Arg a b -> Bool # (>) :: Arg a b -> Arg a b -> Bool # (>=) :: Arg a b -> Arg a b -> Bool # max :: Arg a b -> Arg a b -> Arg a b # min :: Arg a b -> Arg a b -> Arg a b #
Ord (Proxy s)	Since: base-4.7.0.0
Instance details Defined in Data.Proxy Methods compare :: Proxy s -> Proxy s -> Ordering # (<) :: Proxy s -> Proxy s -> Bool # (<=) :: Proxy s -> Proxy s -> Bool # (>) :: Proxy s -> Proxy s -> Bool # (>=) :: Proxy s -> Proxy s -> Bool # max :: Proxy s -> Proxy s -> Proxy s # min :: Proxy s -> Proxy s -> Proxy s #
(Ord1 m, Ord a) => Ord (MaybeT m a)
Instance details Defined in Control.Monad.Trans.Maybe Methods compare :: MaybeT m a -> MaybeT m a -> Ordering # (<) :: MaybeT m a -> MaybeT m a -> Bool # (<=) :: MaybeT m a -> MaybeT m a -> Bool # (>) :: MaybeT m a -> MaybeT m a -> Bool # (>=) :: MaybeT m a -> MaybeT m a -> Bool # max :: MaybeT m a -> MaybeT m a -> MaybeT m a # min :: MaybeT m a -> MaybeT m a -> MaybeT m a #
(Ord1 m, Ord a) => Ord (ListT m a)
Instance details Defined in Control.Monad.Trans.List Methods compare :: ListT m a -> ListT m a -> Ordering # (<) :: ListT m a -> ListT m a -> Bool # (<=) :: ListT m a -> ListT m a -> Bool # (>) :: ListT m a -> ListT m a -> Bool # (>=) :: ListT m a -> ListT m a -> Bool # max :: ListT m a -> ListT m a -> ListT m a # min :: ListT m a -> ListT m a -> ListT m a #
Ord (f p) => Ord (Rec1 f p)	Since: base-4.7.0.0
Instance details Defined in GHC.Generics Methods compare :: Rec1 f p -> Rec1 f p -> Ordering # (<) :: Rec1 f p -> Rec1 f p -> Bool # (<=) :: Rec1 f p -> Rec1 f p -> Bool # (>) :: Rec1 f p -> Rec1 f p -> Bool # (>=) :: Rec1 f p -> Rec1 f p -> Bool # max :: Rec1 f p -> Rec1 f p -> Rec1 f p # min :: Rec1 f p -> Rec1 f p -> Rec1 f p #
Ord (URec (Ptr ()) p)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods compare :: URec (Ptr ()) p -> URec (Ptr ()) p -> Ordering # (<) :: URec (Ptr ()) p -> URec (Ptr ()) p -> Bool # (<=) :: URec (Ptr ()) p -> URec (Ptr ()) p -> Bool # (>) :: URec (Ptr ()) p -> URec (Ptr ()) p -> Bool # (>=) :: URec (Ptr ()) p -> URec (Ptr ()) p -> Bool # max :: URec (Ptr ()) p -> URec (Ptr ()) p -> URec (Ptr ()) p # min :: URec (Ptr ()) p -> URec (Ptr ()) p -> URec (Ptr ()) p #
Ord (URec Char p)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods compare :: URec Char p -> URec Char p -> Ordering # (<) :: URec Char p -> URec Char p -> Bool # (<=) :: URec Char p -> URec Char p -> Bool # (>) :: URec Char p -> URec Char p -> Bool # (>=) :: URec Char p -> URec Char p -> Bool # max :: URec Char p -> URec Char p -> URec Char p # min :: URec Char p -> URec Char p -> URec Char p #
Ord (URec Double p)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods compare :: URec Double p -> URec Double p -> Ordering # (<) :: URec Double p -> URec Double p -> Bool # (<=) :: URec Double p -> URec Double p -> Bool # (>) :: URec Double p -> URec Double p -> Bool # (>=) :: URec Double p -> URec Double p -> Bool # max :: URec Double p -> URec Double p -> URec Double p # min :: URec Double p -> URec Double p -> URec Double p #
Ord (URec Float p)
Instance details Defined in GHC.Generics Methods compare :: URec Float p -> URec Float p -> Ordering # (<) :: URec Float p -> URec Float p -> Bool # (<=) :: URec Float p -> URec Float p -> Bool # (>) :: URec Float p -> URec Float p -> Bool # (>=) :: URec Float p -> URec Float p -> Bool # max :: URec Float p -> URec Float p -> URec Float p # min :: URec Float p -> URec Float p -> URec Float p #
Ord (URec Int p)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods compare :: URec Int p -> URec Int p -> Ordering # (<) :: URec Int p -> URec Int p -> Bool # (<=) :: URec Int p -> URec Int p -> Bool # (>) :: URec Int p -> URec Int p -> Bool # (>=) :: URec Int p -> URec Int p -> Bool # max :: URec Int p -> URec Int p -> URec Int p # min :: URec Int p -> URec Int p -> URec Int p #
Ord (URec Word p)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods compare :: URec Word p -> URec Word p -> Ordering # (<) :: URec Word p -> URec Word p -> Bool # (<=) :: URec Word p -> URec Word p -> Bool # (>) :: URec Word p -> URec Word p -> Bool # (>=) :: URec Word p -> URec Word p -> Bool # max :: URec Word p -> URec Word p -> URec Word p # min :: URec Word p -> URec Word p -> URec Word p #
(Ord a, Ord b, Ord c) => Ord (a, b, c)
Instance details Defined in GHC.Classes Methods compare :: (a, b, c) -> (a, b, c) -> Ordering # (<) :: (a, b, c) -> (a, b, c) -> Bool # (<=) :: (a, b, c) -> (a, b, c) -> Bool # (>) :: (a, b, c) -> (a, b, c) -> Bool # (>=) :: (a, b, c) -> (a, b, c) -> Bool # max :: (a, b, c) -> (a, b, c) -> (a, b, c) # min :: (a, b, c) -> (a, b, c) -> (a, b, c) #
Ord a => Ord (Const a b)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Const Methods compare :: Const a b -> Const a b -> Ordering # (<) :: Const a b -> Const a b -> Bool # (<=) :: Const a b -> Const a b -> Bool # (>) :: Const a b -> Const a b -> Bool # (>=) :: Const a b -> Const a b -> Bool # max :: Const a b -> Const a b -> Const a b # min :: Const a b -> Const a b -> Const a b #
Ord (f a) => Ord (Ap f a)	Since: base-4.12.0.0
Instance details Defined in Data.Monoid Methods compare :: Ap f a -> Ap f a -> Ordering # (<) :: Ap f a -> Ap f a -> Bool # (<=) :: Ap f a -> Ap f a -> Bool # (>) :: Ap f a -> Ap f a -> Bool # (>=) :: Ap f a -> Ap f a -> Bool # max :: Ap f a -> Ap f a -> Ap f a # min :: Ap f a -> Ap f a -> Ap f a #
Ord (f a) => Ord (Alt f a)	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods compare :: Alt f a -> Alt f a -> Ordering # (<) :: Alt f a -> Alt f a -> Bool # (<=) :: Alt f a -> Alt f a -> Bool # (>) :: Alt f a -> Alt f a -> Bool # (>=) :: Alt f a -> Alt f a -> Bool # max :: Alt f a -> Alt f a -> Alt f a # min :: Alt f a -> Alt f a -> Alt f a #
Ord (Coercion a b)	Since: base-4.7.0.0
Instance details Defined in Data.Type.Coercion Methods compare :: Coercion a b -> Coercion a b -> Ordering # (<) :: Coercion a b -> Coercion a b -> Bool # (<=) :: Coercion a b -> Coercion a b -> Bool # (>) :: Coercion a b -> Coercion a b -> Bool # (>=) :: Coercion a b -> Coercion a b -> Bool # max :: Coercion a b -> Coercion a b -> Coercion a b # min :: Coercion a b -> Coercion a b -> Coercion a b #
Ord (a :~: b)	Since: base-4.7.0.0
Instance details Defined in Data.Type.Equality Methods compare :: (a :~: b) -> (a :~: b) -> Ordering # (<) :: (a :~: b) -> (a :~: b) -> Bool # (<=) :: (a :~: b) -> (a :~: b) -> Bool # (>) :: (a :~: b) -> (a :~: b) -> Bool # (>=) :: (a :~: b) -> (a :~: b) -> Bool # max :: (a :~: b) -> (a :~: b) -> a :~: b # min :: (a :~: b) -> (a :~: b) -> a :~: b #
(Ord w, Ord1 m, Ord a) => Ord (WriterT w m a)
Instance details Defined in Control.Monad.Trans.Writer.Strict Methods compare :: WriterT w m a -> WriterT w m a -> Ordering # (<) :: WriterT w m a -> WriterT w m a -> Bool # (<=) :: WriterT w m a -> WriterT w m a -> Bool # (>) :: WriterT w m a -> WriterT w m a -> Bool # (>=) :: WriterT w m a -> WriterT w m a -> Bool # max :: WriterT w m a -> WriterT w m a -> WriterT w m a # min :: WriterT w m a -> WriterT w m a -> WriterT w m a #
(Ord w, Ord1 m, Ord a) => Ord (WriterT w m a)
Instance details Defined in Control.Monad.Trans.Writer.Lazy Methods compare :: WriterT w m a -> WriterT w m a -> Ordering # (<) :: WriterT w m a -> WriterT w m a -> Bool # (<=) :: WriterT w m a -> WriterT w m a -> Bool # (>) :: WriterT w m a -> WriterT w m a -> Bool # (>=) :: WriterT w m a -> WriterT w m a -> Bool # max :: WriterT w m a -> WriterT w m a -> WriterT w m a # min :: WriterT w m a -> WriterT w m a -> WriterT w m a #
(Ord1 f, Ord a) => Ord (IdentityT f a)
Instance details Defined in Control.Monad.Trans.Identity Methods compare :: IdentityT f a -> IdentityT f a -> Ordering # (<) :: IdentityT f a -> IdentityT f a -> Bool # (<=) :: IdentityT f a -> IdentityT f a -> Bool # (>) :: IdentityT f a -> IdentityT f a -> Bool # (>=) :: IdentityT f a -> IdentityT f a -> Bool # max :: IdentityT f a -> IdentityT f a -> IdentityT f a # min :: IdentityT f a -> IdentityT f a -> IdentityT f a #
(Ord e, Ord1 m, Ord a) => Ord (ExceptT e m a)
Instance details Defined in Control.Monad.Trans.Except Methods compare :: ExceptT e m a -> ExceptT e m a -> Ordering # (<) :: ExceptT e m a -> ExceptT e m a -> Bool # (<=) :: ExceptT e m a -> ExceptT e m a -> Bool # (>) :: ExceptT e m a -> ExceptT e m a -> Bool # (>=) :: ExceptT e m a -> ExceptT e m a -> Bool # max :: ExceptT e m a -> ExceptT e m a -> ExceptT e m a # min :: ExceptT e m a -> ExceptT e m a -> ExceptT e m a #
(Ord e, Ord1 m, Ord a) => Ord (ErrorT e m a)
Instance details Defined in Control.Monad.Trans.Error Methods compare :: ErrorT e m a -> ErrorT e m a -> Ordering # (<) :: ErrorT e m a -> ErrorT e m a -> Bool # (<=) :: ErrorT e m a -> ErrorT e m a -> Bool # (>) :: ErrorT e m a -> ErrorT e m a -> Bool # (>=) :: ErrorT e m a -> ErrorT e m a -> Bool # max :: ErrorT e m a -> ErrorT e m a -> ErrorT e m a # min :: ErrorT e m a -> ErrorT e m a -> ErrorT e m a #
Ord a => Ord (Dimensional (DQuantity s) d a) Source #
Instance details Defined in Numeric.Units.Dimensional.Internal Methods compare :: Dimensional (DQuantity s) d a -> Dimensional (DQuantity s) d a -> Ordering # (<) :: Dimensional (DQuantity s) d a -> Dimensional (DQuantity s) d a -> Bool # (<=) :: Dimensional (DQuantity s) d a -> Dimensional (DQuantity s) d a -> Bool # (>) :: Dimensional (DQuantity s) d a -> Dimensional (DQuantity s) d a -> Bool # (>=) :: Dimensional (DQuantity s) d a -> Dimensional (DQuantity s) d a -> Bool # max :: Dimensional (DQuantity s) d a -> Dimensional (DQuantity s) d a -> Dimensional (DQuantity s) d a # min :: Dimensional (DQuantity s) d a -> Dimensional (DQuantity s) d a -> Dimensional (DQuantity s) d a #
Ord c => Ord (K1 i c p)	Since: base-4.7.0.0
Instance details Defined in GHC.Generics Methods compare :: K1 i c p -> K1 i c p -> Ordering # (<) :: K1 i c p -> K1 i c p -> Bool # (<=) :: K1 i c p -> K1 i c p -> Bool # (>) :: K1 i c p -> K1 i c p -> Bool # (>=) :: K1 i c p -> K1 i c p -> Bool # max :: K1 i c p -> K1 i c p -> K1 i c p # min :: K1 i c p -> K1 i c p -> K1 i c p #
(Ord (f p), Ord (g p)) => Ord ((f :+: g) p)	Since: base-4.7.0.0
Instance details Defined in GHC.Generics Methods compare :: (f :+: g) p -> (f :+: g) p -> Ordering # (<) :: (f :+: g) p -> (f :+: g) p -> Bool # (<=) :: (f :+: g) p -> (f :+: g) p -> Bool # (>) :: (f :+: g) p -> (f :+: g) p -> Bool # (>=) :: (f :+: g) p -> (f :+: g) p -> Bool # max :: (f :+: g) p -> (f :+: g) p -> (f :+: g) p # min :: (f :+: g) p -> (f :+: g) p -> (f :+: g) p #
(Ord (f p), Ord (g p)) => Ord ((f :*: g) p)	Since: base-4.7.0.0
Instance details Defined in GHC.Generics Methods compare :: (f :: g) p -> (f :: g) p -> Ordering # (<) :: (f :: g) p -> (f :: g) p -> Bool # (<=) :: (f :: g) p -> (f :: g) p -> Bool # (>) :: (f :: g) p -> (f :: g) p -> Bool # (>=) :: (f :: g) p -> (f :: g) p -> Bool # max :: (f :: g) p -> (f :: g) p -> (f :: g) p # min :: (f :: g) p -> (f :: g) p -> (f :: g) p #
(Ord a, Ord b, Ord c, Ord d) => Ord (a, b, c, d)
Instance details Defined in GHC.Classes Methods compare :: (a, b, c, d) -> (a, b, c, d) -> Ordering # (<) :: (a, b, c, d) -> (a, b, c, d) -> Bool # (<=) :: (a, b, c, d) -> (a, b, c, d) -> Bool # (>) :: (a, b, c, d) -> (a, b, c, d) -> Bool # (>=) :: (a, b, c, d) -> (a, b, c, d) -> Bool # max :: (a, b, c, d) -> (a, b, c, d) -> (a, b, c, d) # min :: (a, b, c, d) -> (a, b, c, d) -> (a, b, c, d) #
(Ord1 f, Ord1 g, Ord a) => Ord (Product f g a)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Product Methods compare :: Product f g a -> Product f g a -> Ordering # (<) :: Product f g a -> Product f g a -> Bool # (<=) :: Product f g a -> Product f g a -> Bool # (>) :: Product f g a -> Product f g a -> Bool # (>=) :: Product f g a -> Product f g a -> Bool # max :: Product f g a -> Product f g a -> Product f g a # min :: Product f g a -> Product f g a -> Product f g a #
(Ord1 f, Ord1 g, Ord a) => Ord (Sum f g a)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Sum Methods compare :: Sum f g a -> Sum f g a -> Ordering # (<) :: Sum f g a -> Sum f g a -> Bool # (<=) :: Sum f g a -> Sum f g a -> Bool # (>) :: Sum f g a -> Sum f g a -> Bool # (>=) :: Sum f g a -> Sum f g a -> Bool # max :: Sum f g a -> Sum f g a -> Sum f g a # min :: Sum f g a -> Sum f g a -> Sum f g a #
Ord (a :~~: b)	Since: base-4.10.0.0
Instance details Defined in Data.Type.Equality Methods compare :: (a :~~: b) -> (a :~~: b) -> Ordering # (<) :: (a :~~: b) -> (a :~~: b) -> Bool # (<=) :: (a :~~: b) -> (a :~~: b) -> Bool # (>) :: (a :~~: b) -> (a :~~: b) -> Bool # (>=) :: (a :~~: b) -> (a :~~: b) -> Bool # max :: (a :~~: b) -> (a :~~: b) -> a :~~: b # min :: (a :~~: b) -> (a :~~: b) -> a :~~: b #
Ord (f p) => Ord (M1 i c f p)	Since: base-4.7.0.0
Instance details Defined in GHC.Generics Methods compare :: M1 i c f p -> M1 i c f p -> Ordering # (<) :: M1 i c f p -> M1 i c f p -> Bool # (<=) :: M1 i c f p -> M1 i c f p -> Bool # (>) :: M1 i c f p -> M1 i c f p -> Bool # (>=) :: M1 i c f p -> M1 i c f p -> Bool # max :: M1 i c f p -> M1 i c f p -> M1 i c f p # min :: M1 i c f p -> M1 i c f p -> M1 i c f p #
Ord (f (g p)) => Ord ((f :.: g) p)	Since: base-4.7.0.0
Instance details Defined in GHC.Generics Methods compare :: (f :.: g) p -> (f :.: g) p -> Ordering # (<) :: (f :.: g) p -> (f :.: g) p -> Bool # (<=) :: (f :.: g) p -> (f :.: g) p -> Bool # (>) :: (f :.: g) p -> (f :.: g) p -> Bool # (>=) :: (f :.: g) p -> (f :.: g) p -> Bool # max :: (f :.: g) p -> (f :.: g) p -> (f :.: g) p # min :: (f :.: g) p -> (f :.: g) p -> (f :.: g) p #
(Ord a, Ord b, Ord c, Ord d, Ord e) => Ord (a, b, c, d, e)
Instance details Defined in GHC.Classes Methods compare :: (a, b, c, d, e) -> (a, b, c, d, e) -> Ordering # (<) :: (a, b, c, d, e) -> (a, b, c, d, e) -> Bool # (<=) :: (a, b, c, d, e) -> (a, b, c, d, e) -> Bool # (>) :: (a, b, c, d, e) -> (a, b, c, d, e) -> Bool # (>=) :: (a, b, c, d, e) -> (a, b, c, d, e) -> Bool # max :: (a, b, c, d, e) -> (a, b, c, d, e) -> (a, b, c, d, e) # min :: (a, b, c, d, e) -> (a, b, c, d, e) -> (a, b, c, d, e) #
(Ord1 f, Ord1 g, Ord a) => Ord (Compose f g a)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Compose Methods compare :: Compose f g a -> Compose f g a -> Ordering # (<) :: Compose f g a -> Compose f g a -> Bool # (<=) :: Compose f g a -> Compose f g a -> Bool # (>) :: Compose f g a -> Compose f g a -> Bool # (>=) :: Compose f g a -> Compose f g a -> Bool # max :: Compose f g a -> Compose f g a -> Compose f g a # min :: Compose f g a -> Compose f g a -> Compose f g a #
(Ord a, Ord b, Ord c, Ord d, Ord e, Ord f) => Ord (a, b, c, d, e, f)
Instance details Defined in GHC.Classes Methods compare :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> Ordering # (<) :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> Bool # (<=) :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> Bool # (>) :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> Bool # (>=) :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> Bool # max :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> (a, b, c, d, e, f) # min :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> (a, b, c, d, e, f) #
(Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g) => Ord (a, b, c, d, e, f, g)
Instance details Defined in GHC.Classes Methods compare :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) -> Ordering # (<) :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) -> Bool # (<=) :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) -> Bool # (>) :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) -> Bool # (>=) :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) -> Bool # max :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) # min :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) #
(Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h) => Ord (a, b, c, d, e, f, g, h)
Instance details Defined in GHC.Classes Methods compare :: (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) -> Ordering # (<) :: (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) -> Bool # (<=) :: (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) -> Bool # (>) :: (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) -> Bool # (>=) :: (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) -> Bool # max :: (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) # min :: (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) #
(Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i) => Ord (a, b, c, d, e, f, g, h, i)
Instance details Defined in GHC.Classes Methods compare :: (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) -> Ordering # (<) :: (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) -> Bool # (<=) :: (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) -> Bool # (>) :: (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) -> Bool # (>=) :: (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) -> Bool # max :: (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) # min :: (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) #
(Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i, Ord j) => Ord (a, b, c, d, e, f, g, h, i, j)
Instance details Defined in GHC.Classes Methods compare :: (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) -> Ordering # (<) :: (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) -> Bool # (<=) :: (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) -> Bool # (>) :: (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) -> Bool # (>=) :: (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) -> Bool # max :: (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) # min :: (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) #
(Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i, Ord j, Ord k) => Ord (a, b, c, d, e, f, g, h, i, j, k)
Instance details Defined in GHC.Classes Methods compare :: (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k) -> Ordering # (<) :: (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k) -> Bool # (<=) :: (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k) -> Bool # (>) :: (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k) -> Bool # (>=) :: (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k) -> Bool # max :: (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k) # min :: (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k) #
(Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i, Ord j, Ord k, Ord l) => Ord (a, b, c, d, e, f, g, h, i, j, k, l)
Instance details Defined in GHC.Classes Methods compare :: (a, b, c, d, e, f, g, h, i, j, k, l) -> (a, b, c, d, e, f, g, h, i, j, k, l) -> Ordering # (<) :: (a, b, c, d, e, f, g, h, i, j, k, l) -> (a, b, c, d, e, f, g, h, i, j, k, l) -> Bool # (<=) :: (a, b, c, d, e, f, g, h, i, j, k, l) -> (a, b, c, d, e, f, g, h, i, j, k, l) -> Bool # (>) :: (a, b, c, d, e, f, g, h, i, j, k, l) -> (a, b, c, d, e, f, g, h, i, j, k, l) -> Bool # (>=) :: (a, b, c, d, e, f, g, h, i, j, k, l) -> (a, b, c, d, e, f, g, h, i, j, k, l) -> Bool # max :: (a, b, c, d, e, f, g, h, i, j, k, l) -> (a, b, c, d, e, f, g, h, i, j, k, l) -> (a, b, c, d, e, f, g, h, i, j, k, l) # min :: (a, b, c, d, e, f, g, h, i, j, k, l) -> (a, b, c, d, e, f, g, h, i, j, k, l) -> (a, b, c, d, e, f, g, h, i, j, k, l) #
(Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i, Ord j, Ord k, Ord l, Ord m) => Ord (a, b, c, d, e, f, g, h, i, j, k, l, m)
Instance details Defined in GHC.Classes Methods compare :: (a, b, c, d, e, f, g, h, i, j, k, l, m) -> (a, b, c, d, e, f, g, h, i, j, k, l, m) -> Ordering # (<) :: (a, b, c, d, e, f, g, h, i, j, k, l, m) -> (a, b, c, d, e, f, g, h, i, j, k, l, m) -> Bool # (<=) :: (a, b, c, d, e, f, g, h, i, j, k, l, m) -> (a, b, c, d, e, f, g, h, i, j, k, l, m) -> Bool # (>) :: (a, b, c, d, e, f, g, h, i, j, k, l, m) -> (a, b, c, d, e, f, g, h, i, j, k, l, m) -> Bool # (>=) :: (a, b, c, d, e, f, g, h, i, j, k, l, m) -> (a, b, c, d, e, f, g, h, i, j, k, l, m) -> Bool # max :: (a, b, c, d, e, f, g, h, i, j, k, l, m) -> (a, b, c, d, e, f, g, h, i, j, k, l, m) -> (a, b, c, d, e, f, g, h, i, j, k, l, m) # min :: (a, b, c, d, e, f, g, h, i, j, k, l, m) -> (a, b, c, d, e, f, g, h, i, j, k, l, m) -> (a, b, c, d, e, f, g, h, i, j, k, l, m) #
(Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i, Ord j, Ord k, Ord l, Ord m, Ord n) => Ord (a, b, c, d, e, f, g, h, i, j, k, l, m, n)
Instance details Defined in GHC.Classes Methods compare :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> Ordering # (<) :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> Bool # (<=) :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> Bool # (>) :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> Bool # (>=) :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> Bool # max :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n) # min :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n) #
(Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i, Ord j, Ord k, Ord l, Ord m, Ord n, Ord o) => Ord (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o)
Instance details Defined in GHC.Classes Methods compare :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> Ordering # (<) :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> Bool # (<=) :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> Bool # (>) :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> Bool # (>=) :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> Bool # max :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) # min :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) #

class Read a where #

Parsing of Strings, producing values.

Derived instances of Read make the following assumptions, which derived instances of Show obey:

If the constructor is defined to be an infix operator, then the derived Read instance will parse only infix applications of the constructor (not the prefix form).
Associativity is not used to reduce the occurrence of parentheses, although precedence may be.
If the constructor is defined using record syntax, the derived Read will parse only the record-syntax form, and furthermore, the fields must be given in the same order as the original declaration.
The derived Read instance allows arbitrary Haskell whitespace between tokens of the input string. Extra parentheses are also allowed.

For example, given the declarations

infixr 5 :^:
data Tree a =  Leaf a  |  Tree a :^: Tree a

the derived instance of Read in Haskell 2010 is equivalent to

instance (Read a) => Read (Tree a) where

        readsPrec d r =  readParen (d > app_prec)
                         (\r -> [(Leaf m,t) |
                                 ("Leaf",s) <- lex r,
                                 (m,t) <- readsPrec (app_prec+1) s]) r

                      ++ readParen (d > up_prec)
                         (\r -> [(u:^:v,w) |
                                 (u,s) <- readsPrec (up_prec+1) r,
                                 (":^:",t) <- lex s,
                                 (v,w) <- readsPrec (up_prec+1) t]) r

          where app_prec = 10
                up_prec = 5

Note that right-associativity of :^: is unused.

The derived instance in GHC is equivalent to

instance (Read a) => Read (Tree a) where

        readPrec = parens $ (prec app_prec $ do
                                 Ident "Leaf" <- lexP
                                 m <- step readPrec
                                 return (Leaf m))

                     +++ (prec up_prec $ do
                                 u <- step readPrec
                                 Symbol ":^:" <- lexP
                                 v <- step readPrec
                                 return (u :^: v))

          where app_prec = 10
                up_prec = 5

        readListPrec = readListPrecDefault

Why do both readsPrec and readPrec exist, and why does GHC opt to implement readPrec in derived Read instances instead of readsPrec? The reason is that readsPrec is based on the ReadS type, and although ReadS is mentioned in the Haskell 2010 Report, it is not a very efficient parser data structure.

readPrec, on the other hand, is based on a much more efficient ReadPrec datatype (a.k.a "new-style parsers"), but its definition relies on the use of the RankNTypes language extension. Therefore, readPrec (and its cousin, readListPrec) are marked as GHC-only. Nevertheless, it is recommended to use readPrec instead of readsPrec whenever possible for the efficiency improvements it brings.

As mentioned above, derived Read instances in GHC will implement readPrec instead of readsPrec. The default implementations of readsPrec (and its cousin, readList) will simply use readPrec under the hood. If you are writing a Read instance by hand, it is recommended to write it like so:

instance Read T where
  readPrec     = ...
  readListPrec = readListPrecDefault

Minimal complete definition

readsPrec | readPrec

Methods

readsPrec #

Arguments

:: Int	the operator precedence of the enclosing context (a number from `0` to `11`). Function application has precedence `10`.
-> ReadS a

attempts to parse a value from the front of the string, returning a list of (parsed value, remaining string) pairs. If there is no successful parse, the returned list is empty.

Derived instances of Read and Show satisfy the following:

(x,"") is an element of (readsPrec d (showsPrec d x "")).

That is, readsPrec parses the string produced by showsPrec, and delivers the value that showsPrec started with.

readList :: ReadS [a] #

The method readList is provided to allow the programmer to give a specialised way of parsing lists of values. For example, this is used by the predefined Read instance of the Char type, where values of type String should be are expected to use double quotes, rather than square brackets.

Instances

Read Bool	Since: base-2.1
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS Bool # readList :: ReadS [Bool] # readPrec :: ReadPrec Bool # readListPrec :: ReadPrec [Bool] #
Read Char	Since: base-2.1
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS Char # readList :: ReadS [Char] # readPrec :: ReadPrec Char # readListPrec :: ReadPrec [Char] #
Read Double	Since: base-2.1
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS Double # readList :: ReadS [Double] # readPrec :: ReadPrec Double # readListPrec :: ReadPrec [Double] #
Read Float	Since: base-2.1
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS Float # readList :: ReadS [Float] # readPrec :: ReadPrec Float # readListPrec :: ReadPrec [Float] #
Read Int	Since: base-2.1
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS Int # readList :: ReadS [Int] # readPrec :: ReadPrec Int # readListPrec :: ReadPrec [Int] #
Read Int8	Since: base-2.1
Instance details Defined in GHC.Int Methods readsPrec :: Int -> ReadS Int8 # readList :: ReadS [Int8] # readPrec :: ReadPrec Int8 # readListPrec :: ReadPrec [Int8] #
Read Int16	Since: base-2.1
Instance details Defined in GHC.Int Methods readsPrec :: Int -> ReadS Int16 # readList :: ReadS [Int16] # readPrec :: ReadPrec Int16 # readListPrec :: ReadPrec [Int16] #
Read Int32	Since: base-2.1
Instance details Defined in GHC.Int Methods readsPrec :: Int -> ReadS Int32 # readList :: ReadS [Int32] # readPrec :: ReadPrec Int32 # readListPrec :: ReadPrec [Int32] #
Read Int64	Since: base-2.1
Instance details Defined in GHC.Int Methods readsPrec :: Int -> ReadS Int64 # readList :: ReadS [Int64] # readPrec :: ReadPrec Int64 # readListPrec :: ReadPrec [Int64] #
Read Integer	Since: base-2.1
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS Integer # readList :: ReadS [Integer] # readPrec :: ReadPrec Integer # readListPrec :: ReadPrec [Integer] #
Read Natural	Since: base-4.8.0.0
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS Natural # readList :: ReadS [Natural] # readPrec :: ReadPrec Natural # readListPrec :: ReadPrec [Natural] #
Read Ordering	Since: base-2.1
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS Ordering # readList :: ReadS [Ordering] # readPrec :: ReadPrec Ordering # readListPrec :: ReadPrec [Ordering] #
Read Word	Since: base-4.5.0.0
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS Word # readList :: ReadS [Word] # readPrec :: ReadPrec Word # readListPrec :: ReadPrec [Word] #
Read Word8	Since: base-2.1
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS Word8 # readList :: ReadS [Word8] # readPrec :: ReadPrec Word8 # readListPrec :: ReadPrec [Word8] #
Read Word16	Since: base-2.1
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS Word16 # readList :: ReadS [Word16] # readPrec :: ReadPrec Word16 # readListPrec :: ReadPrec [Word16] #
Read Word32	Since: base-2.1
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS Word32 # readList :: ReadS [Word32] # readPrec :: ReadPrec Word32 # readListPrec :: ReadPrec [Word32] #
Read Word64	Since: base-2.1
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS Word64 # readList :: ReadS [Word64] # readPrec :: ReadPrec Word64 # readListPrec :: ReadPrec [Word64] #
Read ()	Since: base-2.1
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS () # readList :: ReadS [()] # readPrec :: ReadPrec () # readListPrec :: ReadPrec [()] #
Read Void	Reading a `Void` value is always a parse error, considering `Void` as a data type with no constructors. Since: base-4.8.0.0
Instance details Defined in Data.Void Methods readsPrec :: Int -> ReadS Void # readList :: ReadS [Void] # readPrec :: ReadPrec Void # readListPrec :: ReadPrec [Void] #
Read Version	Since: base-2.1
Instance details Defined in Data.Version Methods readsPrec :: Int -> ReadS Version # readList :: ReadS [Version] # readPrec :: ReadPrec Version # readListPrec :: ReadPrec [Version] #
Read ExitCode
Instance details Defined in GHC.IO.Exception Methods readsPrec :: Int -> ReadS ExitCode # readList :: ReadS [ExitCode] # readPrec :: ReadPrec ExitCode # readListPrec :: ReadPrec [ExitCode] #
Read All	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods readsPrec :: Int -> ReadS All # readList :: ReadS [All] # readPrec :: ReadPrec All # readListPrec :: ReadPrec [All] #
Read Any	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods readsPrec :: Int -> ReadS Any # readList :: ReadS [Any] # readPrec :: ReadPrec Any # readListPrec :: ReadPrec [Any] #
Read Fixity	Since: base-4.6.0.0
Instance details Defined in GHC.Generics Methods readsPrec :: Int -> ReadS Fixity # readList :: ReadS [Fixity] # readPrec :: ReadPrec Fixity # readListPrec :: ReadPrec [Fixity] #
Read Associativity	Since: base-4.6.0.0
Instance details Defined in GHC.Generics Methods readsPrec :: Int -> ReadS Associativity # readList :: ReadS [Associativity] # readPrec :: ReadPrec Associativity # readListPrec :: ReadPrec [Associativity] #
Read SourceUnpackedness	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods readsPrec :: Int -> ReadS SourceUnpackedness # readList :: ReadS [SourceUnpackedness] # readPrec :: ReadPrec SourceUnpackedness # readListPrec :: ReadPrec [SourceUnpackedness] #
Read SourceStrictness	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods readsPrec :: Int -> ReadS SourceStrictness # readList :: ReadS [SourceStrictness] # readPrec :: ReadPrec SourceStrictness # readListPrec :: ReadPrec [SourceStrictness] #
Read DecidedStrictness	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods readsPrec :: Int -> ReadS DecidedStrictness # readList :: ReadS [DecidedStrictness] # readPrec :: ReadPrec DecidedStrictness # readListPrec :: ReadPrec [DecidedStrictness] #
Read SomeSymbol	Since: base-4.7.0.0
Instance details Defined in GHC.TypeLits Methods readsPrec :: Int -> ReadS SomeSymbol # readList :: ReadS [SomeSymbol] # readPrec :: ReadPrec SomeSymbol # readListPrec :: ReadPrec [SomeSymbol] #
Read SomeNat	Since: base-4.7.0.0
Instance details Defined in GHC.TypeNats Methods readsPrec :: Int -> ReadS SomeNat # readList :: ReadS [SomeNat] # readPrec :: ReadPrec SomeNat # readListPrec :: ReadPrec [SomeNat] #
Read CChar
Instance details Defined in Foreign.C.Types Methods readsPrec :: Int -> ReadS CChar # readList :: ReadS [CChar] # readPrec :: ReadPrec CChar # readListPrec :: ReadPrec [CChar] #
Read CSChar
Instance details Defined in Foreign.C.Types Methods readsPrec :: Int -> ReadS CSChar # readList :: ReadS [CSChar] # readPrec :: ReadPrec CSChar # readListPrec :: ReadPrec [CSChar] #
Read CUChar
Instance details Defined in Foreign.C.Types Methods readsPrec :: Int -> ReadS CUChar # readList :: ReadS [CUChar] # readPrec :: ReadPrec CUChar # readListPrec :: ReadPrec [CUChar] #
Read CShort
Instance details Defined in Foreign.C.Types Methods readsPrec :: Int -> ReadS CShort # readList :: ReadS [CShort] # readPrec :: ReadPrec CShort # readListPrec :: ReadPrec [CShort] #
Read CUShort
Instance details Defined in Foreign.C.Types Methods readsPrec :: Int -> ReadS CUShort # readList :: ReadS [CUShort] # readPrec :: ReadPrec CUShort # readListPrec :: ReadPrec [CUShort] #
Read CInt
Instance details Defined in Foreign.C.Types Methods readsPrec :: Int -> ReadS CInt # readList :: ReadS [CInt] # readPrec :: ReadPrec CInt # readListPrec :: ReadPrec [CInt] #
Read CUInt
Instance details Defined in Foreign.C.Types Methods readsPrec :: Int -> ReadS CUInt # readList :: ReadS [CUInt] # readPrec :: ReadPrec CUInt # readListPrec :: ReadPrec [CUInt] #
Read CLong
Instance details Defined in Foreign.C.Types Methods readsPrec :: Int -> ReadS CLong # readList :: ReadS [CLong] # readPrec :: ReadPrec CLong # readListPrec :: ReadPrec [CLong] #
Read CULong
Instance details Defined in Foreign.C.Types Methods readsPrec :: Int -> ReadS CULong # readList :: ReadS [CULong] # readPrec :: ReadPrec CULong # readListPrec :: ReadPrec [CULong] #
Read CLLong
Instance details Defined in Foreign.C.Types Methods readsPrec :: Int -> ReadS CLLong # readList :: ReadS [CLLong] # readPrec :: ReadPrec CLLong # readListPrec :: ReadPrec [CLLong] #
Read CULLong
Instance details Defined in Foreign.C.Types Methods readsPrec :: Int -> ReadS CULLong # readList :: ReadS [CULLong] # readPrec :: ReadPrec CULLong # readListPrec :: ReadPrec [CULLong] #
Read CBool
Instance details Defined in Foreign.C.Types Methods readsPrec :: Int -> ReadS CBool # readList :: ReadS [CBool] # readPrec :: ReadPrec CBool # readListPrec :: ReadPrec [CBool] #
Read CFloat
Instance details Defined in Foreign.C.Types Methods readsPrec :: Int -> ReadS CFloat # readList :: ReadS [CFloat] # readPrec :: ReadPrec CFloat # readListPrec :: ReadPrec [CFloat] #
Read CDouble
Instance details Defined in Foreign.C.Types Methods readsPrec :: Int -> ReadS CDouble # readList :: ReadS [CDouble] # readPrec :: ReadPrec CDouble # readListPrec :: ReadPrec [CDouble] #
Read CPtrdiff
Instance details Defined in Foreign.C.Types Methods readsPrec :: Int -> ReadS CPtrdiff # readList :: ReadS [CPtrdiff] # readPrec :: ReadPrec CPtrdiff # readListPrec :: ReadPrec [CPtrdiff] #
Read CSize
Instance details Defined in Foreign.C.Types Methods readsPrec :: Int -> ReadS CSize # readList :: ReadS [CSize] # readPrec :: ReadPrec CSize # readListPrec :: ReadPrec [CSize] #
Read CWchar
Instance details Defined in Foreign.C.Types Methods readsPrec :: Int -> ReadS CWchar # readList :: ReadS [CWchar] # readPrec :: ReadPrec CWchar # readListPrec :: ReadPrec [CWchar] #
Read CSigAtomic
Instance details Defined in Foreign.C.Types Methods readsPrec :: Int -> ReadS CSigAtomic # readList :: ReadS [CSigAtomic] # readPrec :: ReadPrec CSigAtomic # readListPrec :: ReadPrec [CSigAtomic] #
Read CClock
Instance details Defined in Foreign.C.Types Methods readsPrec :: Int -> ReadS CClock # readList :: ReadS [CClock] # readPrec :: ReadPrec CClock # readListPrec :: ReadPrec [CClock] #
Read CTime
Instance details Defined in Foreign.C.Types Methods readsPrec :: Int -> ReadS CTime # readList :: ReadS [CTime] # readPrec :: ReadPrec CTime # readListPrec :: ReadPrec [CTime] #
Read CUSeconds
Instance details Defined in Foreign.C.Types Methods readsPrec :: Int -> ReadS CUSeconds # readList :: ReadS [CUSeconds] # readPrec :: ReadPrec CUSeconds # readListPrec :: ReadPrec [CUSeconds] #
Read CSUSeconds
Instance details Defined in Foreign.C.Types Methods readsPrec :: Int -> ReadS CSUSeconds # readList :: ReadS [CSUSeconds] # readPrec :: ReadPrec CSUSeconds # readListPrec :: ReadPrec [CSUSeconds] #
Read CIntPtr
Instance details Defined in Foreign.C.Types Methods readsPrec :: Int -> ReadS CIntPtr # readList :: ReadS [CIntPtr] # readPrec :: ReadPrec CIntPtr # readListPrec :: ReadPrec [CIntPtr] #
Read CUIntPtr
Instance details Defined in Foreign.C.Types Methods readsPrec :: Int -> ReadS CUIntPtr # readList :: ReadS [CUIntPtr] # readPrec :: ReadPrec CUIntPtr # readListPrec :: ReadPrec [CUIntPtr] #
Read CIntMax
Instance details Defined in Foreign.C.Types Methods readsPrec :: Int -> ReadS CIntMax # readList :: ReadS [CIntMax] # readPrec :: ReadPrec CIntMax # readListPrec :: ReadPrec [CIntMax] #
Read CUIntMax
Instance details Defined in Foreign.C.Types Methods readsPrec :: Int -> ReadS CUIntMax # readList :: ReadS [CUIntMax] # readPrec :: ReadPrec CUIntMax # readListPrec :: ReadPrec [CUIntMax] #
Read WordPtr
Instance details Defined in Foreign.Ptr Methods readsPrec :: Int -> ReadS WordPtr # readList :: ReadS [WordPtr] # readPrec :: ReadPrec WordPtr # readListPrec :: ReadPrec [WordPtr] #
Read IntPtr
Instance details Defined in Foreign.Ptr Methods readsPrec :: Int -> ReadS IntPtr # readList :: ReadS [IntPtr] # readPrec :: ReadPrec IntPtr # readListPrec :: ReadPrec [IntPtr] #
Read Lexeme	Since: base-2.1
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS Lexeme # readList :: ReadS [Lexeme] # readPrec :: ReadPrec Lexeme # readListPrec :: ReadPrec [Lexeme] #
Read GeneralCategory	Since: base-2.1
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS GeneralCategory # readList :: ReadS [GeneralCategory] # readPrec :: ReadPrec GeneralCategory # readListPrec :: ReadPrec [GeneralCategory] #
Read a => Read [a]	Since: base-2.1
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS [a] # readList :: ReadS [[a]] # readPrec :: ReadPrec [a] # readListPrec :: ReadPrec [[a]] #
Read a => Read (Maybe a)	Since: base-2.1
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS (Maybe a) # readList :: ReadS [Maybe a] # readPrec :: ReadPrec (Maybe a) # readListPrec :: ReadPrec [Maybe a] #
(Integral a, Read a) => Read (Ratio a)	Since: base-2.1
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS (Ratio a) # readList :: ReadS [Ratio a] # readPrec :: ReadPrec (Ratio a) # readListPrec :: ReadPrec [Ratio a] #
Read p => Read (Par1 p)	Since: base-4.7.0.0
Instance details Defined in GHC.Generics Methods readsPrec :: Int -> ReadS (Par1 p) # readList :: ReadS [Par1 p] # readPrec :: ReadPrec (Par1 p) # readListPrec :: ReadPrec [Par1 p] #
Read a => Read (Complex a)	Since: base-2.1
Instance details Defined in Data.Complex Methods readsPrec :: Int -> ReadS (Complex a) # readList :: ReadS [Complex a] # readPrec :: ReadPrec (Complex a) # readListPrec :: ReadPrec [Complex a] #
HasResolution a => Read (Fixed a)	Since: base-4.3.0.0
Instance details Defined in Data.Fixed Methods readsPrec :: Int -> ReadS (Fixed a) # readList :: ReadS [Fixed a] # readPrec :: ReadPrec (Fixed a) # readListPrec :: ReadPrec [Fixed a] #
Read a => Read (Min a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods readsPrec :: Int -> ReadS (Min a) # readList :: ReadS [Min a] # readPrec :: ReadPrec (Min a) # readListPrec :: ReadPrec [Min a] #
Read a => Read (Max a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods readsPrec :: Int -> ReadS (Max a) # readList :: ReadS [Max a] # readPrec :: ReadPrec (Max a) # readListPrec :: ReadPrec [Max a] #
Read a => Read (First a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods readsPrec :: Int -> ReadS (First a) # readList :: ReadS [First a] # readPrec :: ReadPrec (First a) # readListPrec :: ReadPrec [First a] #
Read a => Read (Last a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods readsPrec :: Int -> ReadS (Last a) # readList :: ReadS [Last a] # readPrec :: ReadPrec (Last a) # readListPrec :: ReadPrec [Last a] #
Read m => Read (WrappedMonoid m)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods readsPrec :: Int -> ReadS (WrappedMonoid m) # readList :: ReadS [WrappedMonoid m] # readPrec :: ReadPrec (WrappedMonoid m) # readListPrec :: ReadPrec [WrappedMonoid m] #
Read a => Read (Option a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods readsPrec :: Int -> ReadS (Option a) # readList :: ReadS [Option a] # readPrec :: ReadPrec (Option a) # readListPrec :: ReadPrec [Option a] #
Read a => Read (ZipList a)	Since: base-4.7.0.0
Instance details Defined in Control.Applicative Methods readsPrec :: Int -> ReadS (ZipList a) # readList :: ReadS [ZipList a] # readPrec :: ReadPrec (ZipList a) # readListPrec :: ReadPrec [ZipList a] #
Read a => Read (Identity a)	This instance would be equivalent to the derived instances of the `Identity` newtype if the `runIdentity` field were removed Since: base-4.8.0.0
Instance details Defined in Data.Functor.Identity Methods readsPrec :: Int -> ReadS (Identity a) # readList :: ReadS [Identity a] # readPrec :: ReadPrec (Identity a) # readListPrec :: ReadPrec [Identity a] #
Read a => Read (First a)	Since: base-2.1
Instance details Defined in Data.Monoid Methods readsPrec :: Int -> ReadS (First a) # readList :: ReadS [First a] # readPrec :: ReadPrec (First a) # readListPrec :: ReadPrec [First a] #
Read a => Read (Last a)	Since: base-2.1
Instance details Defined in Data.Monoid Methods readsPrec :: Int -> ReadS (Last a) # readList :: ReadS [Last a] # readPrec :: ReadPrec (Last a) # readListPrec :: ReadPrec [Last a] #
Read a => Read (Dual a)	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods readsPrec :: Int -> ReadS (Dual a) # readList :: ReadS [Dual a] # readPrec :: ReadPrec (Dual a) # readListPrec :: ReadPrec [Dual a] #
Read a => Read (Sum a)	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods readsPrec :: Int -> ReadS (Sum a) # readList :: ReadS [Sum a] # readPrec :: ReadPrec (Sum a) # readListPrec :: ReadPrec [Sum a] #
Read a => Read (Product a)	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods readsPrec :: Int -> ReadS (Product a) # readList :: ReadS [Product a] # readPrec :: ReadPrec (Product a) # readListPrec :: ReadPrec [Product a] #
Read a => Read (Down a)	Since: base-4.7.0.0
Instance details Defined in Data.Ord Methods readsPrec :: Int -> ReadS (Down a) # readList :: ReadS [Down a] # readPrec :: ReadPrec (Down a) # readListPrec :: ReadPrec [Down a] #
Read a => Read (NonEmpty a)	Since: base-4.11.0.0
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS (NonEmpty a) # readList :: ReadS [NonEmpty a] # readPrec :: ReadPrec (NonEmpty a) # readListPrec :: ReadPrec [NonEmpty a] #
Read a => Read (SmallArray a)
Instance details Defined in Data.Primitive.SmallArray Methods readsPrec :: Int -> ReadS (SmallArray a) # readList :: ReadS [SmallArray a] # readPrec :: ReadPrec (SmallArray a) # readListPrec :: ReadPrec [SmallArray a] #
Read a => Read (Array a)
Instance details Defined in Data.Primitive.Array Methods readsPrec :: Int -> ReadS (Array a) # readList :: ReadS [Array a] # readPrec :: ReadPrec (Array a) # readListPrec :: ReadPrec [Array a] #
(Read a, Prim a) => Read (Vector a)
Instance details Defined in Data.Vector.Primitive Methods readsPrec :: Int -> ReadS (Vector a) # readList :: ReadS [Vector a] # readPrec :: ReadPrec (Vector a) # readListPrec :: ReadPrec [Vector a] #
(Read a, Read b) => Read (Either a b)	Since: base-3.0
Instance details Defined in Data.Either Methods readsPrec :: Int -> ReadS (Either a b) # readList :: ReadS [Either a b] # readPrec :: ReadPrec (Either a b) # readListPrec :: ReadPrec [Either a b] #
Read (V1 p)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods readsPrec :: Int -> ReadS (V1 p) # readList :: ReadS [V1 p] # readPrec :: ReadPrec (V1 p) # readListPrec :: ReadPrec [V1 p] #
Read (U1 p)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods readsPrec :: Int -> ReadS (U1 p) # readList :: ReadS [U1 p] # readPrec :: ReadPrec (U1 p) # readListPrec :: ReadPrec [U1 p] #
(Read a, Read b) => Read (a, b)	Since: base-2.1
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS (a, b) # readList :: ReadS [(a, b)] # readPrec :: ReadPrec (a, b) # readListPrec :: ReadPrec [(a, b)] #
(Ix a, Read a, Read b) => Read (Array a b)	Since: base-2.1
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS (Array a b) # readList :: ReadS [Array a b] # readPrec :: ReadPrec (Array a b) # readListPrec :: ReadPrec [Array a b] #
(Read a, Read b) => Read (Arg a b)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods readsPrec :: Int -> ReadS (Arg a b) # readList :: ReadS [Arg a b] # readPrec :: ReadPrec (Arg a b) # readListPrec :: ReadPrec [Arg a b] #
Read (Proxy t)	Since: base-4.7.0.0
Instance details Defined in Data.Proxy Methods readsPrec :: Int -> ReadS (Proxy t) # readList :: ReadS [Proxy t] # readPrec :: ReadPrec (Proxy t) # readListPrec :: ReadPrec [Proxy t] #
(Read1 m, Read a) => Read (MaybeT m a)
Instance details Defined in Control.Monad.Trans.Maybe Methods readsPrec :: Int -> ReadS (MaybeT m a) # readList :: ReadS [MaybeT m a] # readPrec :: ReadPrec (MaybeT m a) # readListPrec :: ReadPrec [MaybeT m a] #
(Read1 m, Read a) => Read (ListT m a)
Instance details Defined in Control.Monad.Trans.List Methods readsPrec :: Int -> ReadS (ListT m a) # readList :: ReadS [ListT m a] # readPrec :: ReadPrec (ListT m a) # readListPrec :: ReadPrec [ListT m a] #
Read (f p) => Read (Rec1 f p)	Since: base-4.7.0.0
Instance details Defined in GHC.Generics Methods readsPrec :: Int -> ReadS (Rec1 f p) # readList :: ReadS [Rec1 f p] # readPrec :: ReadPrec (Rec1 f p) # readListPrec :: ReadPrec [Rec1 f p] #
(Read a, Read b, Read c) => Read (a, b, c)	Since: base-2.1
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS (a, b, c) # readList :: ReadS [(a, b, c)] # readPrec :: ReadPrec (a, b, c) # readListPrec :: ReadPrec [(a, b, c)] #
Read a => Read (Const a b)	This instance would be equivalent to the derived instances of the `Const` newtype if the `runConst` field were removed Since: base-4.8.0.0
Instance details Defined in Data.Functor.Const Methods readsPrec :: Int -> ReadS (Const a b) # readList :: ReadS [Const a b] # readPrec :: ReadPrec (Const a b) # readListPrec :: ReadPrec [Const a b] #
Read (f a) => Read (Ap f a)	Since: base-4.12.0.0
Instance details Defined in Data.Monoid Methods readsPrec :: Int -> ReadS (Ap f a) # readList :: ReadS [Ap f a] # readPrec :: ReadPrec (Ap f a) # readListPrec :: ReadPrec [Ap f a] #
Read (f a) => Read (Alt f a)	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods readsPrec :: Int -> ReadS (Alt f a) # readList :: ReadS [Alt f a] # readPrec :: ReadPrec (Alt f a) # readListPrec :: ReadPrec [Alt f a] #
Coercible a b => Read (Coercion a b)	Since: base-4.7.0.0
Instance details Defined in Data.Type.Coercion Methods readsPrec :: Int -> ReadS (Coercion a b) # readList :: ReadS [Coercion a b] # readPrec :: ReadPrec (Coercion a b) # readListPrec :: ReadPrec [Coercion a b] #
a ~ b => Read (a :~: b)	Since: base-4.7.0.0
Instance details Defined in Data.Type.Equality Methods readsPrec :: Int -> ReadS (a :~: b) # readList :: ReadS [a :~: b] # readPrec :: ReadPrec (a :~: b) # readListPrec :: ReadPrec [a :~: b] #
(Read w, Read1 m, Read a) => Read (WriterT w m a)
Instance details Defined in Control.Monad.Trans.Writer.Strict Methods readsPrec :: Int -> ReadS (WriterT w m a) # readList :: ReadS [WriterT w m a] # readPrec :: ReadPrec (WriterT w m a) # readListPrec :: ReadPrec [WriterT w m a] #
(Read w, Read1 m, Read a) => Read (WriterT w m a)
Instance details Defined in Control.Monad.Trans.Writer.Lazy Methods readsPrec :: Int -> ReadS (WriterT w m a) # readList :: ReadS [WriterT w m a] # readPrec :: ReadPrec (WriterT w m a) # readListPrec :: ReadPrec [WriterT w m a] #
(Read1 f, Read a) => Read (IdentityT f a)
Instance details Defined in Control.Monad.Trans.Identity Methods readsPrec :: Int -> ReadS (IdentityT f a) # readList :: ReadS [IdentityT f a] # readPrec :: ReadPrec (IdentityT f a) # readListPrec :: ReadPrec [IdentityT f a] #
(Read e, Read1 m, Read a) => Read (ExceptT e m a)
Instance details Defined in Control.Monad.Trans.Except Methods readsPrec :: Int -> ReadS (ExceptT e m a) # readList :: ReadS [ExceptT e m a] # readPrec :: ReadPrec (ExceptT e m a) # readListPrec :: ReadPrec [ExceptT e m a] #
(Read e, Read1 m, Read a) => Read (ErrorT e m a)
Instance details Defined in Control.Monad.Trans.Error Methods readsPrec :: Int -> ReadS (ErrorT e m a) # readList :: ReadS [ErrorT e m a] # readPrec :: ReadPrec (ErrorT e m a) # readListPrec :: ReadPrec [ErrorT e m a] #
Read c => Read (K1 i c p)	Since: base-4.7.0.0
Instance details Defined in GHC.Generics Methods readsPrec :: Int -> ReadS (K1 i c p) # readList :: ReadS [K1 i c p] # readPrec :: ReadPrec (K1 i c p) # readListPrec :: ReadPrec [K1 i c p] #
(Read (f p), Read (g p)) => Read ((f :+: g) p)	Since: base-4.7.0.0
Instance details Defined in GHC.Generics Methods readsPrec :: Int -> ReadS ((f :+: g) p) # readList :: ReadS [(f :+: g) p] # readPrec :: ReadPrec ((f :+: g) p) # readListPrec :: ReadPrec [(f :+: g) p] #
(Read (f p), Read (g p)) => Read ((f :*: g) p)	Since: base-4.7.0.0
Instance details Defined in GHC.Generics Methods readsPrec :: Int -> ReadS ((f :: g) p) # readList :: ReadS [(f :: g) p] # readPrec :: ReadPrec ((f :: g) p) # readListPrec :: ReadPrec [(f :: g) p] #
(Read a, Read b, Read c, Read d) => Read (a, b, c, d)	Since: base-2.1
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS (a, b, c, d) # readList :: ReadS [(a, b, c, d)] # readPrec :: ReadPrec (a, b, c, d) # readListPrec :: ReadPrec [(a, b, c, d)] #
(Read1 f, Read1 g, Read a) => Read (Product f g a)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Product Methods readsPrec :: Int -> ReadS (Product f g a) # readList :: ReadS [Product f g a] # readPrec :: ReadPrec (Product f g a) # readListPrec :: ReadPrec [Product f g a] #
(Read1 f, Read1 g, Read a) => Read (Sum f g a)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Sum Methods readsPrec :: Int -> ReadS (Sum f g a) # readList :: ReadS [Sum f g a] # readPrec :: ReadPrec (Sum f g a) # readListPrec :: ReadPrec [Sum f g a] #
a ~~ b => Read (a :~~: b)	Since: base-4.10.0.0
Instance details Defined in Data.Type.Equality Methods readsPrec :: Int -> ReadS (a :~~: b) # readList :: ReadS [a :~~: b] # readPrec :: ReadPrec (a :~~: b) # readListPrec :: ReadPrec [a :~~: b] #
Read (f p) => Read (M1 i c f p)	Since: base-4.7.0.0
Instance details Defined in GHC.Generics Methods readsPrec :: Int -> ReadS (M1 i c f p) # readList :: ReadS [M1 i c f p] # readPrec :: ReadPrec (M1 i c f p) # readListPrec :: ReadPrec [M1 i c f p] #
Read (f (g p)) => Read ((f :.: g) p)	Since: base-4.7.0.0
Instance details Defined in GHC.Generics Methods readsPrec :: Int -> ReadS ((f :.: g) p) # readList :: ReadS [(f :.: g) p] # readPrec :: ReadPrec ((f :.: g) p) # readListPrec :: ReadPrec [(f :.: g) p] #
(Read a, Read b, Read c, Read d, Read e) => Read (a, b, c, d, e)	Since: base-2.1
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS (a, b, c, d, e) # readList :: ReadS [(a, b, c, d, e)] # readPrec :: ReadPrec (a, b, c, d, e) # readListPrec :: ReadPrec [(a, b, c, d, e)] #
(Read1 f, Read1 g, Read a) => Read (Compose f g a)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Compose Methods readsPrec :: Int -> ReadS (Compose f g a) # readList :: ReadS [Compose f g a] # readPrec :: ReadPrec (Compose f g a) # readListPrec :: ReadPrec [Compose f g a] #
(Read a, Read b, Read c, Read d, Read e, Read f) => Read (a, b, c, d, e, f)	Since: base-2.1
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS (a, b, c, d, e, f) # readList :: ReadS [(a, b, c, d, e, f)] # readPrec :: ReadPrec (a, b, c, d, e, f) # readListPrec :: ReadPrec [(a, b, c, d, e, f)] #
(Read a, Read b, Read c, Read d, Read e, Read f, Read g) => Read (a, b, c, d, e, f, g)	Since: base-2.1
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS (a, b, c, d, e, f, g) # readList :: ReadS [(a, b, c, d, e, f, g)] # readPrec :: ReadPrec (a, b, c, d, e, f, g) # readListPrec :: ReadPrec [(a, b, c, d, e, f, g)] #
(Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h) => Read (a, b, c, d, e, f, g, h)	Since: base-2.1
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS (a, b, c, d, e, f, g, h) # readList :: ReadS [(a, b, c, d, e, f, g, h)] # readPrec :: ReadPrec (a, b, c, d, e, f, g, h) # readListPrec :: ReadPrec [(a, b, c, d, e, f, g, h)] #
(Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i) => Read (a, b, c, d, e, f, g, h, i)	Since: base-2.1
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS (a, b, c, d, e, f, g, h, i) # readList :: ReadS [(a, b, c, d, e, f, g, h, i)] # readPrec :: ReadPrec (a, b, c, d, e, f, g, h, i) # readListPrec :: ReadPrec [(a, b, c, d, e, f, g, h, i)] #
(Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i, Read j) => Read (a, b, c, d, e, f, g, h, i, j)	Since: base-2.1
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS (a, b, c, d, e, f, g, h, i, j) # readList :: ReadS [(a, b, c, d, e, f, g, h, i, j)] # readPrec :: ReadPrec (a, b, c, d, e, f, g, h, i, j) # readListPrec :: ReadPrec [(a, b, c, d, e, f, g, h, i, j)] #
(Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i, Read j, Read k) => Read (a, b, c, d, e, f, g, h, i, j, k)	Since: base-2.1
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS (a, b, c, d, e, f, g, h, i, j, k) # readList :: ReadS [(a, b, c, d, e, f, g, h, i, j, k)] # readPrec :: ReadPrec (a, b, c, d, e, f, g, h, i, j, k) # readListPrec :: ReadPrec [(a, b, c, d, e, f, g, h, i, j, k)] #
(Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i, Read j, Read k, Read l) => Read (a, b, c, d, e, f, g, h, i, j, k, l)	Since: base-2.1
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS (a, b, c, d, e, f, g, h, i, j, k, l) # readList :: ReadS [(a, b, c, d, e, f, g, h, i, j, k, l)] # readPrec :: ReadPrec (a, b, c, d, e, f, g, h, i, j, k, l) # readListPrec :: ReadPrec [(a, b, c, d, e, f, g, h, i, j, k, l)] #
(Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i, Read j, Read k, Read l, Read m) => Read (a, b, c, d, e, f, g, h, i, j, k, l, m)	Since: base-2.1
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS (a, b, c, d, e, f, g, h, i, j, k, l, m) # readList :: ReadS [(a, b, c, d, e, f, g, h, i, j, k, l, m)] # readPrec :: ReadPrec (a, b, c, d, e, f, g, h, i, j, k, l, m) # readListPrec :: ReadPrec [(a, b, c, d, e, f, g, h, i, j, k, l, m)] #
(Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i, Read j, Read k, Read l, Read m, Read n) => Read (a, b, c, d, e, f, g, h, i, j, k, l, m, n)	Since: base-2.1
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS (a, b, c, d, e, f, g, h, i, j, k, l, m, n) # readList :: ReadS [(a, b, c, d, e, f, g, h, i, j, k, l, m, n)] # readPrec :: ReadPrec (a, b, c, d, e, f, g, h, i, j, k, l, m, n) # readListPrec :: ReadPrec [(a, b, c, d, e, f, g, h, i, j, k, l, m, n)] #
(Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i, Read j, Read k, Read l, Read m, Read n, Read o) => Read (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o)	Since: base-2.1
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) # readList :: ReadS [(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o)] # readPrec :: ReadPrec (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) # readListPrec :: ReadPrec [(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o)] #

class (Num a, Ord a) => Real a where #

Methods

toRational :: a -> Rational #

the rational equivalent of its real argument with full precision

Instances

Real Int	Since: base-2.0.1
Instance details Defined in GHC.Real Methods toRational :: Int -> Rational #
Real Int8	Since: base-2.1
Instance details Defined in GHC.Int Methods toRational :: Int8 -> Rational #
Real Int16	Since: base-2.1
Instance details Defined in GHC.Int Methods toRational :: Int16 -> Rational #
Real Int32	Since: base-2.1
Instance details Defined in GHC.Int Methods toRational :: Int32 -> Rational #
Real Int64	Since: base-2.1
Instance details Defined in GHC.Int Methods toRational :: Int64 -> Rational #
Real Integer	Since: base-2.0.1
Instance details Defined in GHC.Real Methods toRational :: Integer -> Rational #
Real Natural	Since: base-4.8.0.0
Instance details Defined in GHC.Real Methods toRational :: Natural -> Rational #
Real Word	Since: base-2.1
Instance details Defined in GHC.Real Methods toRational :: Word -> Rational #
Real Word8	Since: base-2.1
Instance details Defined in GHC.Word Methods toRational :: Word8 -> Rational #
Real Word16	Since: base-2.1
Instance details Defined in GHC.Word Methods toRational :: Word16 -> Rational #
Real Word32	Since: base-2.1
Instance details Defined in GHC.Word Methods toRational :: Word32 -> Rational #
Real Word64	Since: base-2.1
Instance details Defined in GHC.Word Methods toRational :: Word64 -> Rational #
Real CChar
Instance details Defined in Foreign.C.Types Methods toRational :: CChar -> Rational #
Real CSChar
Instance details Defined in Foreign.C.Types Methods toRational :: CSChar -> Rational #
Real CUChar
Instance details Defined in Foreign.C.Types Methods toRational :: CUChar -> Rational #
Real CShort
Instance details Defined in Foreign.C.Types Methods toRational :: CShort -> Rational #
Real CUShort
Instance details Defined in Foreign.C.Types Methods toRational :: CUShort -> Rational #
Real CInt
Instance details Defined in Foreign.C.Types Methods toRational :: CInt -> Rational #
Real CUInt
Instance details Defined in Foreign.C.Types Methods toRational :: CUInt -> Rational #
Real CLong
Instance details Defined in Foreign.C.Types Methods toRational :: CLong -> Rational #
Real CULong
Instance details Defined in Foreign.C.Types Methods toRational :: CULong -> Rational #
Real CLLong
Instance details Defined in Foreign.C.Types Methods toRational :: CLLong -> Rational #
Real CULLong
Instance details Defined in Foreign.C.Types Methods toRational :: CULLong -> Rational #
Real CBool
Instance details Defined in Foreign.C.Types Methods toRational :: CBool -> Rational #
Real CFloat
Instance details Defined in Foreign.C.Types Methods toRational :: CFloat -> Rational #
Real CDouble
Instance details Defined in Foreign.C.Types Methods toRational :: CDouble -> Rational #
Real CPtrdiff
Instance details Defined in Foreign.C.Types Methods toRational :: CPtrdiff -> Rational #
Real CSize
Instance details Defined in Foreign.C.Types Methods toRational :: CSize -> Rational #
Real CWchar
Instance details Defined in Foreign.C.Types Methods toRational :: CWchar -> Rational #
Real CSigAtomic
Instance details Defined in Foreign.C.Types Methods toRational :: CSigAtomic -> Rational #
Real CClock
Instance details Defined in Foreign.C.Types Methods toRational :: CClock -> Rational #
Real CTime
Instance details Defined in Foreign.C.Types Methods toRational :: CTime -> Rational #
Real CUSeconds
Instance details Defined in Foreign.C.Types Methods toRational :: CUSeconds -> Rational #
Real CSUSeconds
Instance details Defined in Foreign.C.Types Methods toRational :: CSUSeconds -> Rational #
Real CIntPtr
Instance details Defined in Foreign.C.Types Methods toRational :: CIntPtr -> Rational #
Real CUIntPtr
Instance details Defined in Foreign.C.Types Methods toRational :: CUIntPtr -> Rational #
Real CIntMax
Instance details Defined in Foreign.C.Types Methods toRational :: CIntMax -> Rational #
Real CUIntMax
Instance details Defined in Foreign.C.Types Methods toRational :: CUIntMax -> Rational #
Real WordPtr
Instance details Defined in Foreign.Ptr Methods toRational :: WordPtr -> Rational #
Real IntPtr
Instance details Defined in Foreign.Ptr Methods toRational :: IntPtr -> Rational #
Integral a => Real (Ratio a)	Since: base-2.0.1
Instance details Defined in GHC.Real Methods toRational :: Ratio a -> Rational #
HasResolution a => Real (Fixed a)	Since: base-2.1
Instance details Defined in Data.Fixed Methods toRational :: Fixed a -> Rational #
Real a => Real (Identity a)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Identity Methods toRational :: Identity a -> Rational #
Real a => Real (Const a b)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Const Methods toRational :: Const a b -> Rational #

class (RealFrac a, Floating a) => RealFloat a where #

Efficient, machine-independent access to the components of a floating-point number.

Minimal complete definition

floatRadix, floatDigits, floatRange, decodeFloat, encodeFloat, isNaN, isInfinite, isDenormalized, isNegativeZero, isIEEE

Methods

floatRadix :: a -> Integer #

a constant function, returning the radix of the representation (often 2)

floatDigits :: a -> Int #

a constant function, returning the number of digits of floatRadix in the significand

floatRange :: a -> (Int, Int) #

a constant function, returning the lowest and highest values the exponent may assume

decodeFloat :: a -> (Integer, Int) #

The function decodeFloat applied to a real floating-point number returns the significand expressed as an Integer and an appropriately scaled exponent (an Int). If decodeFloat x yields (m,n), then x is equal in value to m*b^^n, where b is the floating-point radix, and furthermore, either m and n are both zero or else b^(d-1) <= abs m < b^d, where d is the value of floatDigits x. In particular, decodeFloat 0 = (0,0). If the type contains a negative zero, also decodeFloat (-0.0) = (0,0). The result of decodeFloat x is unspecified if either of isNaN x or isInfinite x is True.

encodeFloat :: Integer -> Int -> a #

encodeFloat performs the inverse of decodeFloat in the sense that for finite x with the exception of -0.0, uncurry encodeFloat (decodeFloat x) = x. encodeFloat m n is one of the two closest representable floating-point numbers to m*b^^n (or ±Infinity if overflow occurs); usually the closer, but if m contains too many bits, the result may be rounded in the wrong direction.

exponent :: a -> Int #

exponent corresponds to the second component of decodeFloat. exponent 0 = 0 and for finite nonzero x, exponent x = snd (decodeFloat x) + floatDigits x. If x is a finite floating-point number, it is equal in value to significand x * b ^^ exponent x, where b is the floating-point radix. The behaviour is unspecified on infinite or NaN values.

significand :: a -> a #

The first component of decodeFloat, scaled to lie in the open interval (-1,1), either 0.0 or of absolute value >= 1/b, where b is the floating-point radix. The behaviour is unspecified on infinite or NaN values.

scaleFloat :: Int -> a -> a #

multiplies a floating-point number by an integer power of the radix

isNaN :: a -> Bool #

True if the argument is an IEEE "not-a-number" (NaN) value

isInfinite :: a -> Bool #

True if the argument is an IEEE infinity or negative infinity

isDenormalized :: a -> Bool #

True if the argument is too small to be represented in normalized format

isNegativeZero :: a -> Bool #

True if the argument is an IEEE negative zero

isIEEE :: a -> Bool #

True if the argument is an IEEE floating point number

Instances

RealFloat Double	Since: base-2.1
Instance details Defined in GHC.Float Methods floatRadix :: Double -> Integer # floatDigits :: Double -> Int # floatRange :: Double -> (Int, Int) # decodeFloat :: Double -> (Integer, Int) # encodeFloat :: Integer -> Int -> Double # exponent :: Double -> Int # significand :: Double -> Double # scaleFloat :: Int -> Double -> Double # isNaN :: Double -> Bool # isInfinite :: Double -> Bool # isDenormalized :: Double -> Bool # isNegativeZero :: Double -> Bool # isIEEE :: Double -> Bool # atan2 :: Double -> Double -> Double #
RealFloat Float	Since: base-2.1
Instance details Defined in GHC.Float Methods floatRadix :: Float -> Integer # floatDigits :: Float -> Int # floatRange :: Float -> (Int, Int) # decodeFloat :: Float -> (Integer, Int) # encodeFloat :: Integer -> Int -> Float # exponent :: Float -> Int # significand :: Float -> Float # scaleFloat :: Int -> Float -> Float # isNaN :: Float -> Bool # isInfinite :: Float -> Bool # isDenormalized :: Float -> Bool # isNegativeZero :: Float -> Bool # isIEEE :: Float -> Bool # atan2 :: Float -> Float -> Float #
RealFloat CFloat
Instance details Defined in Foreign.C.Types Methods floatRadix :: CFloat -> Integer # floatDigits :: CFloat -> Int # floatRange :: CFloat -> (Int, Int) # decodeFloat :: CFloat -> (Integer, Int) # encodeFloat :: Integer -> Int -> CFloat # exponent :: CFloat -> Int # significand :: CFloat -> CFloat # scaleFloat :: Int -> CFloat -> CFloat # isNaN :: CFloat -> Bool # isInfinite :: CFloat -> Bool # isDenormalized :: CFloat -> Bool # isNegativeZero :: CFloat -> Bool # isIEEE :: CFloat -> Bool # atan2 :: CFloat -> CFloat -> CFloat #
RealFloat CDouble
Instance details Defined in Foreign.C.Types Methods floatRadix :: CDouble -> Integer # floatDigits :: CDouble -> Int # floatRange :: CDouble -> (Int, Int) # decodeFloat :: CDouble -> (Integer, Int) # encodeFloat :: Integer -> Int -> CDouble # exponent :: CDouble -> Int # significand :: CDouble -> CDouble # scaleFloat :: Int -> CDouble -> CDouble # isNaN :: CDouble -> Bool # isInfinite :: CDouble -> Bool # isDenormalized :: CDouble -> Bool # isNegativeZero :: CDouble -> Bool # isIEEE :: CDouble -> Bool # atan2 :: CDouble -> CDouble -> CDouble #
RealFloat a => RealFloat (Identity a)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Identity Methods floatRadix :: Identity a -> Integer # floatDigits :: Identity a -> Int # floatRange :: Identity a -> (Int, Int) # decodeFloat :: Identity a -> (Integer, Int) # encodeFloat :: Integer -> Int -> Identity a # exponent :: Identity a -> Int # significand :: Identity a -> Identity a # scaleFloat :: Int -> Identity a -> Identity a # isNaN :: Identity a -> Bool # isInfinite :: Identity a -> Bool # isDenormalized :: Identity a -> Bool # isNegativeZero :: Identity a -> Bool # isIEEE :: Identity a -> Bool # atan2 :: Identity a -> Identity a -> Identity a #
RealFloat a => RealFloat (Const a b)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Const Methods floatRadix :: Const a b -> Integer # floatDigits :: Const a b -> Int # floatRange :: Const a b -> (Int, Int) # decodeFloat :: Const a b -> (Integer, Int) # encodeFloat :: Integer -> Int -> Const a b # exponent :: Const a b -> Int # significand :: Const a b -> Const a b # scaleFloat :: Int -> Const a b -> Const a b # isNaN :: Const a b -> Bool # isInfinite :: Const a b -> Bool # isDenormalized :: Const a b -> Bool # isNegativeZero :: Const a b -> Bool # isIEEE :: Const a b -> Bool # atan2 :: Const a b -> Const a b -> Const a b #

class (Real a, Fractional a) => RealFrac a where #

Extracting components of fractions.

Minimal complete definition

properFraction

Methods

properFraction :: Integral b => a -> (b, a) #

The function properFraction takes a real fractional number x and returns a pair (n,f) such that x = n+f, and:

n is an integral number with the same sign as x; and
f is a fraction with the same type and sign as x, and with absolute value less than 1.

The default definitions of the ceiling, floor, truncate and round functions are in terms of properFraction.

truncate :: Integral b => a -> b #

truncate x returns the integer nearest x between zero and x

round :: Integral b => a -> b #

round x returns the nearest integer to x; the even integer if x is equidistant between two integers

ceiling :: Integral b => a -> b #

ceiling x returns the least integer not less than x

floor :: Integral b => a -> b #

floor x returns the greatest integer not greater than x

Instances

RealFrac CFloat
Instance details Defined in Foreign.C.Types Methods properFraction :: Integral b => CFloat -> (b, CFloat) # truncate :: Integral b => CFloat -> b # round :: Integral b => CFloat -> b # ceiling :: Integral b => CFloat -> b # floor :: Integral b => CFloat -> b #
RealFrac CDouble
Instance details Defined in Foreign.C.Types Methods properFraction :: Integral b => CDouble -> (b, CDouble) # truncate :: Integral b => CDouble -> b # round :: Integral b => CDouble -> b # ceiling :: Integral b => CDouble -> b # floor :: Integral b => CDouble -> b #
Integral a => RealFrac (Ratio a)	Since: base-2.0.1
Instance details Defined in GHC.Real Methods properFraction :: Integral b => Ratio a -> (b, Ratio a) # truncate :: Integral b => Ratio a -> b # round :: Integral b => Ratio a -> b # ceiling :: Integral b => Ratio a -> b # floor :: Integral b => Ratio a -> b #
HasResolution a => RealFrac (Fixed a)	Since: base-2.1
Instance details Defined in Data.Fixed Methods properFraction :: Integral b => Fixed a -> (b, Fixed a) # truncate :: Integral b => Fixed a -> b # round :: Integral b => Fixed a -> b # ceiling :: Integral b => Fixed a -> b # floor :: Integral b => Fixed a -> b #
RealFrac a => RealFrac (Identity a)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Identity Methods properFraction :: Integral b => Identity a -> (b, Identity a) # truncate :: Integral b => Identity a -> b # round :: Integral b => Identity a -> b # ceiling :: Integral b => Identity a -> b # floor :: Integral b => Identity a -> b #
RealFrac a => RealFrac (Const a b)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Const Methods properFraction :: Integral b0 => Const a b -> (b0, Const a b) # truncate :: Integral b0 => Const a b -> b0 # round :: Integral b0 => Const a b -> b0 # ceiling :: Integral b0 => Const a b -> b0 # floor :: Integral b0 => Const a b -> b0 #

class Show a where #

Conversion of values to readable Strings.

Derived instances of Show have the following properties, which are compatible with derived instances of Read:

The result of show is a syntactically correct Haskell expression containing only constants, given the fixity declarations in force at the point where the type is declared. It contains only the constructor names defined in the data type, parentheses, and spaces. When labelled constructor fields are used, braces, commas, field names, and equal signs are also used.
If the constructor is defined to be an infix operator, then showsPrec will produce infix applications of the constructor.
the representation will be enclosed in parentheses if the precedence of the top-level constructor in x is less than d (associativity is ignored). Thus, if d is 0 then the result is never surrounded in parentheses; if d is 11 it is always surrounded in parentheses, unless it is an atomic expression.
If the constructor is defined using record syntax, then show will produce the record-syntax form, with the fields given in the same order as the original declaration.

For example, given the declarations

infixr 5 :^:
data Tree a =  Leaf a  |  Tree a :^: Tree a

the derived instance of Show is equivalent to

instance (Show a) => Show (Tree a) where

       showsPrec d (Leaf m) = showParen (d > app_prec) $
            showString "Leaf " . showsPrec (app_prec+1) m
         where app_prec = 10

       showsPrec d (u :^: v) = showParen (d > up_prec) $
            showsPrec (up_prec+1) u .
            showString " :^: "      .
            showsPrec (up_prec+1) v
         where up_prec = 5

Note that right-associativity of :^: is ignored. For example,

show (Leaf 1 :^: Leaf 2 :^: Leaf 3) produces the string "Leaf 1 :^: (Leaf 2 :^: Leaf 3)".

Minimal complete definition

showsPrec | show

Methods

showsPrec #

Arguments

:: Int	the operator precedence of the enclosing context (a number from `0` to `11`). Function application has precedence `10`.
-> a	the value to be converted to a `String`
-> ShowS

Convert a value to a readable String.

showsPrec should satisfy the law

showsPrec d x r ++ s  ==  showsPrec d x (r ++ s)

Derived instances of Read and Show satisfy the following:

(x,"") is an element of (readsPrec d (showsPrec d x "")).

That is, readsPrec parses the string produced by showsPrec, and delivers the value that showsPrec started with.

show :: a -> String #

A specialised variant of showsPrec, using precedence context zero, and returning an ordinary String.

showList :: [a] -> ShowS #

The method showList is provided to allow the programmer to give a specialised way of showing lists of values. For example, this is used by the predefined Show instance of the Char type, where values of type String should be shown in double quotes, rather than between square brackets.

Instances

Show Bool	Since: base-2.1
Instance details Defined in GHC.Show Methods showsPrec :: Int -> Bool -> ShowS # show :: Bool -> String # showList :: [Bool] -> ShowS #
Show Char	Since: base-2.1
Instance details Defined in GHC.Show Methods showsPrec :: Int -> Char -> ShowS # show :: Char -> String # showList :: [Char] -> ShowS #
Show Int	Since: base-2.1
Instance details Defined in GHC.Show Methods showsPrec :: Int -> Int -> ShowS # show :: Int -> String # showList :: [Int] -> ShowS #
Show Int8	Since: base-2.1
Instance details Defined in GHC.Int Methods showsPrec :: Int -> Int8 -> ShowS # show :: Int8 -> String # showList :: [Int8] -> ShowS #
Show Int16	Since: base-2.1
Instance details Defined in GHC.Int Methods showsPrec :: Int -> Int16 -> ShowS # show :: Int16 -> String # showList :: [Int16] -> ShowS #
Show Int32	Since: base-2.1
Instance details Defined in GHC.Int Methods showsPrec :: Int -> Int32 -> ShowS # show :: Int32 -> String # showList :: [Int32] -> ShowS #
Show Int64	Since: base-2.1
Instance details Defined in GHC.Int Methods showsPrec :: Int -> Int64 -> ShowS # show :: Int64 -> String # showList :: [Int64] -> ShowS #
Show Integer	Since: base-2.1
Instance details Defined in GHC.Show Methods showsPrec :: Int -> Integer -> ShowS # show :: Integer -> String # showList :: [Integer] -> ShowS #
Show Natural	Since: base-4.8.0.0
Instance details Defined in GHC.Show Methods showsPrec :: Int -> Natural -> ShowS # show :: Natural -> String # showList :: [Natural] -> ShowS #
Show Ordering	Since: base-2.1
Instance details Defined in GHC.Show Methods showsPrec :: Int -> Ordering -> ShowS # show :: Ordering -> String # showList :: [Ordering] -> ShowS #
Show Word	Since: base-2.1
Instance details Defined in GHC.Show Methods showsPrec :: Int -> Word -> ShowS # show :: Word -> String # showList :: [Word] -> ShowS #
Show Word8	Since: base-2.1
Instance details Defined in GHC.Word Methods showsPrec :: Int -> Word8 -> ShowS # show :: Word8 -> String # showList :: [Word8] -> ShowS #
Show Word16	Since: base-2.1
Instance details Defined in GHC.Word Methods showsPrec :: Int -> Word16 -> ShowS # show :: Word16 -> String # showList :: [Word16] -> ShowS #
Show Word32	Since: base-2.1
Instance details Defined in GHC.Word Methods showsPrec :: Int -> Word32 -> ShowS # show :: Word32 -> String # showList :: [Word32] -> ShowS #
Show Word64	Since: base-2.1
Instance details Defined in GHC.Word Methods showsPrec :: Int -> Word64 -> ShowS # show :: Word64 -> String # showList :: [Word64] -> ShowS #
Show RuntimeRep	Since: base-4.11.0.0
Instance details Defined in GHC.Show Methods showsPrec :: Int -> RuntimeRep -> ShowS # show :: RuntimeRep -> String # showList :: [RuntimeRep] -> ShowS #
Show VecCount	Since: base-4.11.0.0
Instance details Defined in GHC.Show Methods showsPrec :: Int -> VecCount -> ShowS # show :: VecCount -> String # showList :: [VecCount] -> ShowS #
Show VecElem	Since: base-4.11.0.0
Instance details Defined in GHC.Show Methods showsPrec :: Int -> VecElem -> ShowS # show :: VecElem -> String # showList :: [VecElem] -> ShowS #
Show CallStack	Since: base-4.9.0.0
Instance details Defined in GHC.Show Methods showsPrec :: Int -> CallStack -> ShowS # show :: CallStack -> String # showList :: [CallStack] -> ShowS #
Show SomeTypeRep	Since: base-4.10.0.0
Instance details Defined in Data.Typeable.Internal Methods showsPrec :: Int -> SomeTypeRep -> ShowS # show :: SomeTypeRep -> String # showList :: [SomeTypeRep] -> ShowS #
Show ()	Since: base-2.1
Instance details Defined in GHC.Show Methods showsPrec :: Int -> () -> ShowS # show :: () -> String # showList :: [()] -> ShowS #
Show TyCon	Since: base-2.1
Instance details Defined in GHC.Show Methods showsPrec :: Int -> TyCon -> ShowS # show :: TyCon -> String # showList :: [TyCon] -> ShowS #
Show Module	Since: base-4.9.0.0
Instance details Defined in GHC.Show Methods showsPrec :: Int -> Module -> ShowS # show :: Module -> String # showList :: [Module] -> ShowS #
Show TrName	Since: base-4.9.0.0
Instance details Defined in GHC.Show Methods showsPrec :: Int -> TrName -> ShowS # show :: TrName -> String # showList :: [TrName] -> ShowS #
Show KindRep
Instance details Defined in GHC.Show Methods showsPrec :: Int -> KindRep -> ShowS # show :: KindRep -> String # showList :: [KindRep] -> ShowS #
Show TypeLitSort	Since: base-4.11.0.0
Instance details Defined in GHC.Show Methods showsPrec :: Int -> TypeLitSort -> ShowS # show :: TypeLitSort -> String # showList :: [TypeLitSort] -> ShowS #
Show Void	Since: base-4.8.0.0
Instance details Defined in Data.Void Methods showsPrec :: Int -> Void -> ShowS # show :: Void -> String # showList :: [Void] -> ShowS #
Show DataType	Since: base-4.0.0.0
Instance details Defined in Data.Data Methods showsPrec :: Int -> DataType -> ShowS # show :: DataType -> String # showList :: [DataType] -> ShowS #
Show Constr	Since: base-4.0.0.0
Instance details Defined in Data.Data Methods showsPrec :: Int -> Constr -> ShowS # show :: Constr -> String # showList :: [Constr] -> ShowS #
Show DataRep	Since: base-4.0.0.0
Instance details Defined in Data.Data Methods showsPrec :: Int -> DataRep -> ShowS # show :: DataRep -> String # showList :: [DataRep] -> ShowS #
Show ConstrRep	Since: base-4.0.0.0
Instance details Defined in Data.Data Methods showsPrec :: Int -> ConstrRep -> ShowS # show :: ConstrRep -> String # showList :: [ConstrRep] -> ShowS #
Show Fixity	Since: base-4.0.0.0
Instance details Defined in Data.Data Methods showsPrec :: Int -> Fixity -> ShowS # show :: Fixity -> String # showList :: [Fixity] -> ShowS #
Show Version	Since: base-2.1
Instance details Defined in Data.Version Methods showsPrec :: Int -> Version -> ShowS # show :: Version -> String # showList :: [Version] -> ShowS #
Show ThreadId	Since: base-4.2.0.0
Instance details Defined in GHC.Conc.Sync Methods showsPrec :: Int -> ThreadId -> ShowS # show :: ThreadId -> String # showList :: [ThreadId] -> ShowS #
Show BlockReason	Since: base-4.3.0.0
Instance details Defined in GHC.Conc.Sync Methods showsPrec :: Int -> BlockReason -> ShowS # show :: BlockReason -> String # showList :: [BlockReason] -> ShowS #
Show ThreadStatus	Since: base-4.3.0.0
Instance details Defined in GHC.Conc.Sync Methods showsPrec :: Int -> ThreadStatus -> ShowS # show :: ThreadStatus -> String # showList :: [ThreadStatus] -> ShowS #
Show BlockedIndefinitelyOnMVar	Since: base-4.1.0.0
Instance details Defined in GHC.IO.Exception Methods showsPrec :: Int -> BlockedIndefinitelyOnMVar -> ShowS # show :: BlockedIndefinitelyOnMVar -> String # showList :: [BlockedIndefinitelyOnMVar] -> ShowS #
Show BlockedIndefinitelyOnSTM	Since: base-4.1.0.0
Instance details Defined in GHC.IO.Exception Methods showsPrec :: Int -> BlockedIndefinitelyOnSTM -> ShowS # show :: BlockedIndefinitelyOnSTM -> String # showList :: [BlockedIndefinitelyOnSTM] -> ShowS #
Show Deadlock	Since: base-4.1.0.0
Instance details Defined in GHC.IO.Exception Methods showsPrec :: Int -> Deadlock -> ShowS # show :: Deadlock -> String # showList :: [Deadlock] -> ShowS #
Show AllocationLimitExceeded	Since: base-4.7.1.0
Instance details Defined in GHC.IO.Exception Methods showsPrec :: Int -> AllocationLimitExceeded -> ShowS # show :: AllocationLimitExceeded -> String # showList :: [AllocationLimitExceeded] -> ShowS #
Show CompactionFailed	Since: base-4.10.0.0
Instance details Defined in GHC.IO.Exception Methods showsPrec :: Int -> CompactionFailed -> ShowS # show :: CompactionFailed -> String # showList :: [CompactionFailed] -> ShowS #
Show AssertionFailed	Since: base-4.1.0.0
Instance details Defined in GHC.IO.Exception Methods showsPrec :: Int -> AssertionFailed -> ShowS # show :: AssertionFailed -> String # showList :: [AssertionFailed] -> ShowS #
Show SomeAsyncException	Since: base-4.7.0.0
Instance details Defined in GHC.IO.Exception Methods showsPrec :: Int -> SomeAsyncException -> ShowS # show :: SomeAsyncException -> String # showList :: [SomeAsyncException] -> ShowS #
Show AsyncException	Since: base-4.1.0.0
Instance details Defined in GHC.IO.Exception Methods showsPrec :: Int -> AsyncException -> ShowS # show :: AsyncException -> String # showList :: [AsyncException] -> ShowS #
Show ArrayException	Since: base-4.1.0.0
Instance details Defined in GHC.IO.Exception Methods showsPrec :: Int -> ArrayException -> ShowS # show :: ArrayException -> String # showList :: [ArrayException] -> ShowS #
Show FixIOException	Since: base-4.11.0.0
Instance details Defined in GHC.IO.Exception Methods showsPrec :: Int -> FixIOException -> ShowS # show :: FixIOException -> String # showList :: [FixIOException] -> ShowS #
Show ExitCode
Instance details Defined in GHC.IO.Exception Methods showsPrec :: Int -> ExitCode -> ShowS # show :: ExitCode -> String # showList :: [ExitCode] -> ShowS #
Show IOErrorType	Since: base-4.1.0.0
Instance details Defined in GHC.IO.Exception Methods showsPrec :: Int -> IOErrorType -> ShowS # show :: IOErrorType -> String # showList :: [IOErrorType] -> ShowS #
Show MaskingState	Since: base-4.3.0.0
Instance details Defined in GHC.IO Methods showsPrec :: Int -> MaskingState -> ShowS # show :: MaskingState -> String # showList :: [MaskingState] -> ShowS #
Show IOException	Since: base-4.1.0.0
Instance details Defined in GHC.IO.Exception Methods showsPrec :: Int -> IOException -> ShowS # show :: IOException -> String # showList :: [IOException] -> ShowS #
Show All	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods showsPrec :: Int -> All -> ShowS # show :: All -> String # showList :: [All] -> ShowS #
Show Any	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods showsPrec :: Int -> Any -> ShowS # show :: Any -> String # showList :: [Any] -> ShowS #
Show Fixity	Since: base-4.6.0.0
Instance details Defined in GHC.Generics Methods showsPrec :: Int -> Fixity -> ShowS # show :: Fixity -> String # showList :: [Fixity] -> ShowS #
Show Associativity	Since: base-4.6.0.0
Instance details Defined in GHC.Generics Methods showsPrec :: Int -> Associativity -> ShowS # show :: Associativity -> String # showList :: [Associativity] -> ShowS #
Show SourceUnpackedness	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods showsPrec :: Int -> SourceUnpackedness -> ShowS # show :: SourceUnpackedness -> String # showList :: [SourceUnpackedness] -> ShowS #
Show SourceStrictness	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods showsPrec :: Int -> SourceStrictness -> ShowS # show :: SourceStrictness -> String # showList :: [SourceStrictness] -> ShowS #
Show DecidedStrictness	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods showsPrec :: Int -> DecidedStrictness -> ShowS # show :: DecidedStrictness -> String # showList :: [DecidedStrictness] -> ShowS #
Show SomeSymbol	Since: base-4.7.0.0
Instance details Defined in GHC.TypeLits Methods showsPrec :: Int -> SomeSymbol -> ShowS # show :: SomeSymbol -> String # showList :: [SomeSymbol] -> ShowS #
Show SomeNat	Since: base-4.7.0.0
Instance details Defined in GHC.TypeNats Methods showsPrec :: Int -> SomeNat -> ShowS # show :: SomeNat -> String # showList :: [SomeNat] -> ShowS #
Show CChar
Instance details Defined in Foreign.C.Types Methods showsPrec :: Int -> CChar -> ShowS # show :: CChar -> String # showList :: [CChar] -> ShowS #
Show CSChar
Instance details Defined in Foreign.C.Types Methods showsPrec :: Int -> CSChar -> ShowS # show :: CSChar -> String # showList :: [CSChar] -> ShowS #
Show CUChar
Instance details Defined in Foreign.C.Types Methods showsPrec :: Int -> CUChar -> ShowS # show :: CUChar -> String # showList :: [CUChar] -> ShowS #
Show CShort
Instance details Defined in Foreign.C.Types Methods showsPrec :: Int -> CShort -> ShowS # show :: CShort -> String # showList :: [CShort] -> ShowS #
Show CUShort
Instance details Defined in Foreign.C.Types Methods showsPrec :: Int -> CUShort -> ShowS # show :: CUShort -> String # showList :: [CUShort] -> ShowS #
Show CInt
Instance details Defined in Foreign.C.Types Methods showsPrec :: Int -> CInt -> ShowS # show :: CInt -> String # showList :: [CInt] -> ShowS #
Show CUInt
Instance details Defined in Foreign.C.Types Methods showsPrec :: Int -> CUInt -> ShowS # show :: CUInt -> String # showList :: [CUInt] -> ShowS #
Show CLong
Instance details Defined in Foreign.C.Types Methods showsPrec :: Int -> CLong -> ShowS # show :: CLong -> String # showList :: [CLong] -> ShowS #
Show CULong
Instance details Defined in Foreign.C.Types Methods showsPrec :: Int -> CULong -> ShowS # show :: CULong -> String # showList :: [CULong] -> ShowS #
Show CLLong
Instance details Defined in Foreign.C.Types Methods showsPrec :: Int -> CLLong -> ShowS # show :: CLLong -> String # showList :: [CLLong] -> ShowS #
Show CULLong
Instance details Defined in Foreign.C.Types Methods showsPrec :: Int -> CULLong -> ShowS # show :: CULLong -> String # showList :: [CULLong] -> ShowS #
Show CBool
Instance details Defined in Foreign.C.Types Methods showsPrec :: Int -> CBool -> ShowS # show :: CBool -> String # showList :: [CBool] -> ShowS #
Show CFloat
Instance details Defined in Foreign.C.Types Methods showsPrec :: Int -> CFloat -> ShowS # show :: CFloat -> String # showList :: [CFloat] -> ShowS #
Show CDouble
Instance details Defined in Foreign.C.Types Methods showsPrec :: Int -> CDouble -> ShowS # show :: CDouble -> String # showList :: [CDouble] -> ShowS #
Show CPtrdiff
Instance details Defined in Foreign.C.Types Methods showsPrec :: Int -> CPtrdiff -> ShowS # show :: CPtrdiff -> String # showList :: [CPtrdiff] -> ShowS #
Show CSize
Instance details Defined in Foreign.C.Types Methods showsPrec :: Int -> CSize -> ShowS # show :: CSize -> String # showList :: [CSize] -> ShowS #
Show CWchar
Instance details Defined in Foreign.C.Types Methods showsPrec :: Int -> CWchar -> ShowS # show :: CWchar -> String # showList :: [CWchar] -> ShowS #
Show CSigAtomic
Instance details Defined in Foreign.C.Types Methods showsPrec :: Int -> CSigAtomic -> ShowS # show :: CSigAtomic -> String # showList :: [CSigAtomic] -> ShowS #
Show CClock
Instance details Defined in Foreign.C.Types Methods showsPrec :: Int -> CClock -> ShowS # show :: CClock -> String # showList :: [CClock] -> ShowS #
Show CTime
Instance details Defined in Foreign.C.Types Methods showsPrec :: Int -> CTime -> ShowS # show :: CTime -> String # showList :: [CTime] -> ShowS #
Show CUSeconds
Instance details Defined in Foreign.C.Types Methods showsPrec :: Int -> CUSeconds -> ShowS # show :: CUSeconds -> String # showList :: [CUSeconds] -> ShowS #
Show CSUSeconds
Instance details Defined in Foreign.C.Types Methods showsPrec :: Int -> CSUSeconds -> ShowS # show :: CSUSeconds -> String # showList :: [CSUSeconds] -> ShowS #
Show CIntPtr
Instance details Defined in Foreign.C.Types Methods showsPrec :: Int -> CIntPtr -> ShowS # show :: CIntPtr -> String # showList :: [CIntPtr] -> ShowS #
Show CUIntPtr
Instance details Defined in Foreign.C.Types Methods showsPrec :: Int -> CUIntPtr -> ShowS # show :: CUIntPtr -> String # showList :: [CUIntPtr] -> ShowS #
Show CIntMax
Instance details Defined in Foreign.C.Types Methods showsPrec :: Int -> CIntMax -> ShowS # show :: CIntMax -> String # showList :: [CIntMax] -> ShowS #
Show CUIntMax
Instance details Defined in Foreign.C.Types Methods showsPrec :: Int -> CUIntMax -> ShowS # show :: CUIntMax -> String # showList :: [CUIntMax] -> ShowS #
Show WordPtr
Instance details Defined in Foreign.Ptr Methods showsPrec :: Int -> WordPtr -> ShowS # show :: WordPtr -> String # showList :: [WordPtr] -> ShowS #
Show IntPtr
Instance details Defined in Foreign.Ptr Methods showsPrec :: Int -> IntPtr -> ShowS # show :: IntPtr -> String # showList :: [IntPtr] -> ShowS #
Show Fingerprint	Since: base-4.7.0.0
Instance details Defined in GHC.Fingerprint.Type Methods showsPrec :: Int -> Fingerprint -> ShowS # show :: Fingerprint -> String # showList :: [Fingerprint] -> ShowS #
Show SrcLoc	Since: base-4.9.0.0
Instance details Defined in GHC.Show Methods showsPrec :: Int -> SrcLoc -> ShowS # show :: SrcLoc -> String # showList :: [SrcLoc] -> ShowS #
Show ExactPi
Instance details Defined in Data.ExactPi Methods showsPrec :: Int -> ExactPi -> ShowS # show :: ExactPi -> String # showList :: [ExactPi] -> ShowS #
Show ByteArray	Since: primitive-0.6.3.0
Instance details Defined in Data.Primitive.ByteArray Methods showsPrec :: Int -> ByteArray -> ShowS # show :: ByteArray -> String # showList :: [ByteArray] -> ShowS #
Show Addr
Instance details Defined in Data.Primitive.Types Methods showsPrec :: Int -> Addr -> ShowS # show :: Addr -> String # showList :: [Addr] -> ShowS #
Show DynamicDimension Source #
Instance details Defined in Numeric.Units.Dimensional.Dimensions.TermLevel Methods showsPrec :: Int -> DynamicDimension -> ShowS # show :: DynamicDimension -> String # showList :: [DynamicDimension] -> ShowS #
Show Dimension' Source #
Instance details Defined in Numeric.Units.Dimensional.Dimensions.TermLevel Methods showsPrec :: Int -> Dimension' -> ShowS # show :: Dimension' -> String # showList :: [Dimension'] -> ShowS #
Show InterchangeName Source #
Instance details Defined in Numeric.Units.Dimensional.UnitNames.InterchangeNames Methods showsPrec :: Int -> InterchangeName -> ShowS # show :: InterchangeName -> String # showList :: [InterchangeName] -> ShowS #
Show InterchangeNameAuthority Source #
Instance details Defined in Numeric.Units.Dimensional.UnitNames.InterchangeNames Methods showsPrec :: Int -> InterchangeNameAuthority -> ShowS # show :: InterchangeNameAuthority -> String # showList :: [InterchangeNameAuthority] -> ShowS #
Show AnyUnit Source #
Instance details Defined in Numeric.Units.Dimensional.Dynamic Methods showsPrec :: Int -> AnyUnit -> ShowS # show :: AnyUnit -> String # showList :: [AnyUnit] -> ShowS #
Show a => Show [a]	Since: base-2.1
Instance details Defined in GHC.Show Methods showsPrec :: Int -> [a] -> ShowS # show :: [a] -> String # showList :: [[a]] -> ShowS #
Show a => Show (Maybe a)	Since: base-2.1
Instance details Defined in GHC.Show Methods showsPrec :: Int -> Maybe a -> ShowS # show :: Maybe a -> String # showList :: [Maybe a] -> ShowS #
Show a => Show (Ratio a)	Since: base-2.0.1
Instance details Defined in GHC.Real Methods showsPrec :: Int -> Ratio a -> ShowS # show :: Ratio a -> String # showList :: [Ratio a] -> ShowS #
Show (Ptr a)	Since: base-2.1
Instance details Defined in GHC.Ptr Methods showsPrec :: Int -> Ptr a -> ShowS # show :: Ptr a -> String # showList :: [Ptr a] -> ShowS #
Show (FunPtr a)	Since: base-2.1
Instance details Defined in GHC.Ptr Methods showsPrec :: Int -> FunPtr a -> ShowS # show :: FunPtr a -> String # showList :: [FunPtr a] -> ShowS #
Show p => Show (Par1 p)	Since: base-4.7.0.0
Instance details Defined in GHC.Generics Methods showsPrec :: Int -> Par1 p -> ShowS # show :: Par1 p -> String # showList :: [Par1 p] -> ShowS #
Show (ForeignPtr a)	Since: base-2.1
Instance details Defined in GHC.ForeignPtr Methods showsPrec :: Int -> ForeignPtr a -> ShowS # show :: ForeignPtr a -> String # showList :: [ForeignPtr a] -> ShowS #
Show a => Show (Complex a)	Since: base-2.1
Instance details Defined in Data.Complex Methods showsPrec :: Int -> Complex a -> ShowS # show :: Complex a -> String # showList :: [Complex a] -> ShowS #
HasResolution a => Show (Fixed a)	Since: base-2.1
Instance details Defined in Data.Fixed Methods showsPrec :: Int -> Fixed a -> ShowS # show :: Fixed a -> String # showList :: [Fixed a] -> ShowS #
Show a => Show (Min a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods showsPrec :: Int -> Min a -> ShowS # show :: Min a -> String # showList :: [Min a] -> ShowS #
Show a => Show (Max a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods showsPrec :: Int -> Max a -> ShowS # show :: Max a -> String # showList :: [Max a] -> ShowS #
Show a => Show (First a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods showsPrec :: Int -> First a -> ShowS # show :: First a -> String # showList :: [First a] -> ShowS #
Show a => Show (Last a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods showsPrec :: Int -> Last a -> ShowS # show :: Last a -> String # showList :: [Last a] -> ShowS #
Show m => Show (WrappedMonoid m)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods showsPrec :: Int -> WrappedMonoid m -> ShowS # show :: WrappedMonoid m -> String # showList :: [WrappedMonoid m] -> ShowS #
Show a => Show (Option a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods showsPrec :: Int -> Option a -> ShowS # show :: Option a -> String # showList :: [Option a] -> ShowS #
Show a => Show (ZipList a)	Since: base-4.7.0.0
Instance details Defined in Control.Applicative Methods showsPrec :: Int -> ZipList a -> ShowS # show :: ZipList a -> String # showList :: [ZipList a] -> ShowS #
Show a => Show (Identity a)	This instance would be equivalent to the derived instances of the `Identity` newtype if the `runIdentity` field were removed Since: base-4.8.0.0
Instance details Defined in Data.Functor.Identity Methods showsPrec :: Int -> Identity a -> ShowS # show :: Identity a -> String # showList :: [Identity a] -> ShowS #
Show a => Show (First a)	Since: base-2.1
Instance details Defined in Data.Monoid Methods showsPrec :: Int -> First a -> ShowS # show :: First a -> String # showList :: [First a] -> ShowS #
Show a => Show (Last a)	Since: base-2.1
Instance details Defined in Data.Monoid Methods showsPrec :: Int -> Last a -> ShowS # show :: Last a -> String # showList :: [Last a] -> ShowS #
Show a => Show (Dual a)	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods showsPrec :: Int -> Dual a -> ShowS # show :: Dual a -> String # showList :: [Dual a] -> ShowS #
Show a => Show (Sum a)	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods showsPrec :: Int -> Sum a -> ShowS # show :: Sum a -> String # showList :: [Sum a] -> ShowS #
Show a => Show (Product a)	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods showsPrec :: Int -> Product a -> ShowS # show :: Product a -> String # showList :: [Product a] -> ShowS #
Show a => Show (Down a)	Since: base-4.7.0.0
Instance details Defined in Data.Ord Methods showsPrec :: Int -> Down a -> ShowS # show :: Down a -> String # showList :: [Down a] -> ShowS #
Show a => Show (NonEmpty a)	Since: base-4.11.0.0
Instance details Defined in GHC.Show Methods showsPrec :: Int -> NonEmpty a -> ShowS # show :: NonEmpty a -> String # showList :: [NonEmpty a] -> ShowS #
(Show a, PrimUnlifted a) => Show (UnliftedArray a)	Since: primitive-0.6.4.0
Instance details Defined in Data.Primitive.UnliftedArray Methods showsPrec :: Int -> UnliftedArray a -> ShowS # show :: UnliftedArray a -> String # showList :: [UnliftedArray a] -> ShowS #
(Show a, Prim a) => Show (PrimArray a)	Since: primitive-0.6.4.0
Instance details Defined in Data.Primitive.PrimArray Methods showsPrec :: Int -> PrimArray a -> ShowS # show :: PrimArray a -> String # showList :: [PrimArray a] -> ShowS #
Show a => Show (SmallArray a)
Instance details Defined in Data.Primitive.SmallArray Methods showsPrec :: Int -> SmallArray a -> ShowS # show :: SmallArray a -> String # showList :: [SmallArray a] -> ShowS #
Show a => Show (Array a)
Instance details Defined in Data.Primitive.Array Methods showsPrec :: Int -> Array a -> ShowS # show :: Array a -> String # showList :: [Array a] -> ShowS #
(Show a, Prim a) => Show (Vector a)
Instance details Defined in Data.Vector.Primitive Methods showsPrec :: Int -> Vector a -> ShowS # show :: Vector a -> String # showList :: [Vector a] -> ShowS #
Show (UnitName m) Source #	`UnitName`s are shown with non-breaking spaces.
Instance details Defined in Numeric.Units.Dimensional.UnitNames.Internal Methods showsPrec :: Int -> UnitName m -> ShowS # show :: UnitName m -> String # showList :: [UnitName m] -> ShowS #
Show a => Show (DynQuantity a) Source #
Instance details Defined in Numeric.Units.Dimensional.Dynamic Methods showsPrec :: Int -> DynQuantity a -> ShowS # show :: DynQuantity a -> String # showList :: [DynQuantity a] -> ShowS #
Show a => Show (AnyQuantity a) Source #
Instance details Defined in Numeric.Units.Dimensional.Dynamic Methods showsPrec :: Int -> AnyQuantity a -> ShowS # show :: AnyQuantity a -> String # showList :: [AnyQuantity a] -> ShowS #
(Show a, Show b) => Show (Either a b)	Since: base-3.0
Instance details Defined in Data.Either Methods showsPrec :: Int -> Either a b -> ShowS # show :: Either a b -> String # showList :: [Either a b] -> ShowS #
Show (V1 p)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods showsPrec :: Int -> V1 p -> ShowS # show :: V1 p -> String # showList :: [V1 p] -> ShowS #
Show (U1 p)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods showsPrec :: Int -> U1 p -> ShowS # show :: U1 p -> String # showList :: [U1 p] -> ShowS #
Show (TypeRep a)
Instance details Defined in Data.Typeable.Internal Methods showsPrec :: Int -> TypeRep a -> ShowS # show :: TypeRep a -> String # showList :: [TypeRep a] -> ShowS #
(Show a, Show b) => Show (a, b)	Since: base-2.1
Instance details Defined in GHC.Show Methods showsPrec :: Int -> (a, b) -> ShowS # show :: (a, b) -> String # showList :: [(a, b)] -> ShowS #
Show (ST s a)	Since: base-2.1
Instance details Defined in GHC.ST Methods showsPrec :: Int -> ST s a -> ShowS # show :: ST s a -> String # showList :: [ST s a] -> ShowS #
(Ix a, Show a, Show b) => Show (Array a b)	Since: base-2.1
Instance details Defined in GHC.Arr Methods showsPrec :: Int -> Array a b -> ShowS # show :: Array a b -> String # showList :: [Array a b] -> ShowS #
(Show a, Show b) => Show (Arg a b)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods showsPrec :: Int -> Arg a b -> ShowS # show :: Arg a b -> String # showList :: [Arg a b] -> ShowS #
Show (Proxy s)	Since: base-4.7.0.0
Instance details Defined in Data.Proxy Methods showsPrec :: Int -> Proxy s -> ShowS # show :: Proxy s -> String # showList :: [Proxy s] -> ShowS #
(Show1 m, Show a) => Show (MaybeT m a)
Instance details Defined in Control.Monad.Trans.Maybe Methods showsPrec :: Int -> MaybeT m a -> ShowS # show :: MaybeT m a -> String # showList :: [MaybeT m a] -> ShowS #
(Show1 m, Show a) => Show (ListT m a)
Instance details Defined in Control.Monad.Trans.List Methods showsPrec :: Int -> ListT m a -> ShowS # show :: ListT m a -> String # showList :: [ListT m a] -> ShowS #
Show (f p) => Show (Rec1 f p)	Since: base-4.7.0.0
Instance details Defined in GHC.Generics Methods showsPrec :: Int -> Rec1 f p -> ShowS # show :: Rec1 f p -> String # showList :: [Rec1 f p] -> ShowS #
Show (URec Char p)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods showsPrec :: Int -> URec Char p -> ShowS # show :: URec Char p -> String # showList :: [URec Char p] -> ShowS #
Show (URec Double p)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods showsPrec :: Int -> URec Double p -> ShowS # show :: URec Double p -> String # showList :: [URec Double p] -> ShowS #
Show (URec Float p)
Instance details Defined in GHC.Generics Methods showsPrec :: Int -> URec Float p -> ShowS # show :: URec Float p -> String # showList :: [URec Float p] -> ShowS #
Show (URec Int p)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods showsPrec :: Int -> URec Int p -> ShowS # show :: URec Int p -> String # showList :: [URec Int p] -> ShowS #
Show (URec Word p)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods showsPrec :: Int -> URec Word p -> ShowS # show :: URec Word p -> String # showList :: [URec Word p] -> ShowS #
(Show a, Show b, Show c) => Show (a, b, c)	Since: base-2.1
Instance details Defined in GHC.Show Methods showsPrec :: Int -> (a, b, c) -> ShowS # show :: (a, b, c) -> String # showList :: [(a, b, c)] -> ShowS #
Show a => Show (Const a b)	This instance would be equivalent to the derived instances of the `Const` newtype if the `runConst` field were removed Since: base-4.8.0.0
Instance details Defined in Data.Functor.Const Methods showsPrec :: Int -> Const a b -> ShowS # show :: Const a b -> String # showList :: [Const a b] -> ShowS #
Show (f a) => Show (Ap f a)	Since: base-4.12.0.0
Instance details Defined in Data.Monoid Methods showsPrec :: Int -> Ap f a -> ShowS # show :: Ap f a -> String # showList :: [Ap f a] -> ShowS #
Show (f a) => Show (Alt f a)	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods showsPrec :: Int -> Alt f a -> ShowS # show :: Alt f a -> String # showList :: [Alt f a] -> ShowS #
Show (Coercion a b)	Since: base-4.7.0.0
Instance details Defined in Data.Type.Coercion Methods showsPrec :: Int -> Coercion a b -> ShowS # show :: Coercion a b -> String # showList :: [Coercion a b] -> ShowS #
Show (a :~: b)	Since: base-4.7.0.0
Instance details Defined in Data.Type.Equality Methods showsPrec :: Int -> (a :~: b) -> ShowS # show :: (a :~: b) -> String # showList :: [a :~: b] -> ShowS #
(Show w, Show1 m, Show a) => Show (WriterT w m a)
Instance details Defined in Control.Monad.Trans.Writer.Strict Methods showsPrec :: Int -> WriterT w m a -> ShowS # show :: WriterT w m a -> String # showList :: [WriterT w m a] -> ShowS #
(Show w, Show1 m, Show a) => Show (WriterT w m a)
Instance details Defined in Control.Monad.Trans.Writer.Lazy Methods showsPrec :: Int -> WriterT w m a -> ShowS # show :: WriterT w m a -> String # showList :: [WriterT w m a] -> ShowS #
(Show1 f, Show a) => Show (IdentityT f a)
Instance details Defined in Control.Monad.Trans.Identity Methods showsPrec :: Int -> IdentityT f a -> ShowS # show :: IdentityT f a -> String # showList :: [IdentityT f a] -> ShowS #
(Show e, Show1 m, Show a) => Show (ExceptT e m a)
Instance details Defined in Control.Monad.Trans.Except Methods showsPrec :: Int -> ExceptT e m a -> ShowS # show :: ExceptT e m a -> String # showList :: [ExceptT e m a] -> ShowS #
(Show e, Show1 m, Show a) => Show (ErrorT e m a)
Instance details Defined in Control.Monad.Trans.Error Methods showsPrec :: Int -> ErrorT e m a -> ShowS # show :: ErrorT e m a -> String # showList :: [ErrorT e m a] -> ShowS #
(KnownDimension d, KnownExactPi s, Show a, Real a) => Show (SQuantity s d a) Source #	Uses non-breaking spaces between the value and the unit, and within the unit name.
Instance details Defined in Numeric.Units.Dimensional.Internal Methods showsPrec :: Int -> SQuantity s d a -> ShowS # show :: SQuantity s d a -> String # showList :: [SQuantity s d a] -> ShowS #
Show a => Show (Unit m d a) Source #	Unit names are shown with non-breaking spaces.
Instance details Defined in Numeric.Units.Dimensional.Internal Methods showsPrec :: Int -> Unit m d a -> ShowS # show :: Unit m d a -> String # showList :: [Unit m d a] -> ShowS #
Show c => Show (K1 i c p)	Since: base-4.7.0.0
Instance details Defined in GHC.Generics Methods showsPrec :: Int -> K1 i c p -> ShowS # show :: K1 i c p -> String # showList :: [K1 i c p] -> ShowS #
(Show (f p), Show (g p)) => Show ((f :+: g) p)	Since: base-4.7.0.0
Instance details Defined in GHC.Generics Methods showsPrec :: Int -> (f :+: g) p -> ShowS # show :: (f :+: g) p -> String # showList :: [(f :+: g) p] -> ShowS #
(Show (f p), Show (g p)) => Show ((f :*: g) p)	Since: base-4.7.0.0
Instance details Defined in GHC.Generics Methods showsPrec :: Int -> (f :: g) p -> ShowS # show :: (f :: g) p -> String # showList :: [(f :*: g) p] -> ShowS #
(Show a, Show b, Show c, Show d) => Show (a, b, c, d)	Since: base-2.1
Instance details Defined in GHC.Show Methods showsPrec :: Int -> (a, b, c, d) -> ShowS # show :: (a, b, c, d) -> String # showList :: [(a, b, c, d)] -> ShowS #
(Show1 f, Show1 g, Show a) => Show (Product f g a)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Product Methods showsPrec :: Int -> Product f g a -> ShowS # show :: Product f g a -> String # showList :: [Product f g a] -> ShowS #
(Show1 f, Show1 g, Show a) => Show (Sum f g a)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Sum Methods showsPrec :: Int -> Sum f g a -> ShowS # show :: Sum f g a -> String # showList :: [Sum f g a] -> ShowS #
Show (a :~~: b)	Since: base-4.10.0.0
Instance details Defined in Data.Type.Equality Methods showsPrec :: Int -> (a :~~: b) -> ShowS # show :: (a :~~: b) -> String # showList :: [a :~~: b] -> ShowS #
Show (f p) => Show (M1 i c f p)	Since: base-4.7.0.0
Instance details Defined in GHC.Generics Methods showsPrec :: Int -> M1 i c f p -> ShowS # show :: M1 i c f p -> String # showList :: [M1 i c f p] -> ShowS #
Show (f (g p)) => Show ((f :.: g) p)	Since: base-4.7.0.0
Instance details Defined in GHC.Generics Methods showsPrec :: Int -> (f :.: g) p -> ShowS # show :: (f :.: g) p -> String # showList :: [(f :.: g) p] -> ShowS #
(Show a, Show b, Show c, Show d, Show e) => Show (a, b, c, d, e)	Since: base-2.1
Instance details Defined in GHC.Show Methods showsPrec :: Int -> (a, b, c, d, e) -> ShowS # show :: (a, b, c, d, e) -> String # showList :: [(a, b, c, d, e)] -> ShowS #
(Show1 f, Show1 g, Show a) => Show (Compose f g a)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Compose Methods showsPrec :: Int -> Compose f g a -> ShowS # show :: Compose f g a -> String # showList :: [Compose f g a] -> ShowS #
(Show a, Show b, Show c, Show d, Show e, Show f) => Show (a, b, c, d, e, f)	Since: base-2.1
Instance details Defined in GHC.Show Methods showsPrec :: Int -> (a, b, c, d, e, f) -> ShowS # show :: (a, b, c, d, e, f) -> String # showList :: [(a, b, c, d, e, f)] -> ShowS #
(Show a, Show b, Show c, Show d, Show e, Show f, Show g) => Show (a, b, c, d, e, f, g)	Since: base-2.1
Instance details Defined in GHC.Show Methods showsPrec :: Int -> (a, b, c, d, e, f, g) -> ShowS # show :: (a, b, c, d, e, f, g) -> String # showList :: [(a, b, c, d, e, f, g)] -> ShowS #
(Show a, Show b, Show c, Show d, Show e, Show f, Show g, Show h) => Show (a, b, c, d, e, f, g, h)	Since: base-2.1
Instance details Defined in GHC.Show Methods showsPrec :: Int -> (a, b, c, d, e, f, g, h) -> ShowS # show :: (a, b, c, d, e, f, g, h) -> String # showList :: [(a, b, c, d, e, f, g, h)] -> ShowS #
(Show a, Show b, Show c, Show d, Show e, Show f, Show g, Show h, Show i) => Show (a, b, c, d, e, f, g, h, i)	Since: base-2.1
Instance details Defined in GHC.Show Methods showsPrec :: Int -> (a, b, c, d, e, f, g, h, i) -> ShowS # show :: (a, b, c, d, e, f, g, h, i) -> String # showList :: [(a, b, c, d, e, f, g, h, i)] -> ShowS #
(Show a, Show b, Show c, Show d, Show e, Show f, Show g, Show h, Show i, Show j) => Show (a, b, c, d, e, f, g, h, i, j)	Since: base-2.1
Instance details Defined in GHC.Show Methods showsPrec :: Int -> (a, b, c, d, e, f, g, h, i, j) -> ShowS # show :: (a, b, c, d, e, f, g, h, i, j) -> String # showList :: [(a, b, c, d, e, f, g, h, i, j)] -> ShowS #
(Show a, Show b, Show c, Show d, Show e, Show f, Show g, Show h, Show i, Show j, Show k) => Show (a, b, c, d, e, f, g, h, i, j, k)	Since: base-2.1
Instance details Defined in GHC.Show Methods showsPrec :: Int -> (a, b, c, d, e, f, g, h, i, j, k) -> ShowS # show :: (a, b, c, d, e, f, g, h, i, j, k) -> String # showList :: [(a, b, c, d, e, f, g, h, i, j, k)] -> ShowS #
(Show a, Show b, Show c, Show d, Show e, Show f, Show g, Show h, Show i, Show j, Show k, Show l) => Show (a, b, c, d, e, f, g, h, i, j, k, l)	Since: base-2.1
Instance details Defined in GHC.Show Methods showsPrec :: Int -> (a, b, c, d, e, f, g, h, i, j, k, l) -> ShowS # show :: (a, b, c, d, e, f, g, h, i, j, k, l) -> String # showList :: [(a, b, c, d, e, f, g, h, i, j, k, l)] -> ShowS #
(Show a, Show b, Show c, Show d, Show e, Show f, Show g, Show h, Show i, Show j, Show k, Show l, Show m) => Show (a, b, c, d, e, f, g, h, i, j, k, l, m)	Since: base-2.1
Instance details Defined in GHC.Show Methods showsPrec :: Int -> (a, b, c, d, e, f, g, h, i, j, k, l, m) -> ShowS # show :: (a, b, c, d, e, f, g, h, i, j, k, l, m) -> String # showList :: [(a, b, c, d, e, f, g, h, i, j, k, l, m)] -> ShowS #
(Show a, Show b, Show c, Show d, Show e, Show f, Show g, Show h, Show i, Show j, Show k, Show l, Show m, Show n) => Show (a, b, c, d, e, f, g, h, i, j, k, l, m, n)	Since: base-2.1
Instance details Defined in GHC.Show Methods showsPrec :: Int -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> ShowS # show :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> String # showList :: [(a, b, c, d, e, f, g, h, i, j, k, l, m, n)] -> ShowS #
(Show a, Show b, Show c, Show d, Show e, Show f, Show g, Show h, Show i, Show j, Show k, Show l, Show m, Show n, Show o) => Show (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o)	Since: base-2.1
Instance details Defined in GHC.Show Methods showsPrec :: Int -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> ShowS # show :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> String # showList :: [(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o)] -> ShowS #

class Functor f => Applicative (f :: Type -> Type) where #

A functor with application, providing operations to

embed pure expressions (pure), and
sequence computations and combine their results (<*> and liftA2).

A minimal complete definition must include implementations of pure and of either <*> or liftA2. If it defines both, then they must behave the same as their default definitions:

(<*>) = liftA2 id

liftA2 f x y = f <$> x <*> y

Further, any definition must satisfy the following:

identity

pure id <*> v = v

composition

pure (.) <*> u <*> v <*> w = u <*> (v <*> w)

homomorphism

pure f <*> pure x = pure (f x)

interchange

u <*> pure y = pure ($ y) <*> u

The other methods have the following default definitions, which may be overridden with equivalent specialized implementations:

```
u *> v = (id <$ u) <*> v
```
```
u <* v = liftA2 const u v
```

As a consequence of these laws, the Functor instance for f will satisfy

```
fmap f x = pure f <*> x
```

It may be useful to note that supposing

forall x y. p (q x y) = f x . g y

it follows from the above that

liftA2 p (liftA2 q u v) = liftA2 f u . liftA2 g v

If f is also a Monad, it should satisfy

```
pure = return
```
```
(<*>) = ap
```
```
(*>) = (>>)
```

(which implies that pure and <*> satisfy the applicative functor laws).

Minimal complete definition

pure, ((<*>) | liftA2)

Methods

pure :: a -> f a #

Lift a value.

(<*>) :: f (a -> b) -> f a -> f b infixl 4 #

Sequential application.

A few functors support an implementation of <*> that is more efficient than the default one.

(*>) :: f a -> f b -> f b infixl 4 #

Sequence actions, discarding the value of the first argument.

(<*) :: f a -> f b -> f a infixl 4 #

Sequence actions, discarding the value of the second argument.

Instances

Applicative []	Since: base-2.1
Instance details Defined in GHC.Base Methods pure :: a -> [a] # (<>) :: [a -> b] -> [a] -> [b] # liftA2 :: (a -> b -> c) -> [a] -> [b] -> [c] # (>) :: [a] -> [b] -> [b] # (<*) :: [a] -> [b] -> [a] #
Applicative Maybe	Since: base-2.1
Instance details Defined in GHC.Base Methods pure :: a -> Maybe a # (<>) :: Maybe (a -> b) -> Maybe a -> Maybe b # liftA2 :: (a -> b -> c) -> Maybe a -> Maybe b -> Maybe c # (>) :: Maybe a -> Maybe b -> Maybe b # (<*) :: Maybe a -> Maybe b -> Maybe a #
Applicative IO	Since: base-2.1
Instance details Defined in GHC.Base Methods pure :: a -> IO a # (<>) :: IO (a -> b) -> IO a -> IO b # liftA2 :: (a -> b -> c) -> IO a -> IO b -> IO c # (>) :: IO a -> IO b -> IO b # (<*) :: IO a -> IO b -> IO a #
Applicative Par1	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods pure :: a -> Par1 a # (<>) :: Par1 (a -> b) -> Par1 a -> Par1 b # liftA2 :: (a -> b -> c) -> Par1 a -> Par1 b -> Par1 c # (>) :: Par1 a -> Par1 b -> Par1 b # (<*) :: Par1 a -> Par1 b -> Par1 a #
Applicative Complex	Since: base-4.9.0.0
Instance details Defined in Data.Complex Methods pure :: a -> Complex a # (<>) :: Complex (a -> b) -> Complex a -> Complex b # liftA2 :: (a -> b -> c) -> Complex a -> Complex b -> Complex c # (>) :: Complex a -> Complex b -> Complex b # (<*) :: Complex a -> Complex b -> Complex a #
Applicative Min	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods pure :: a -> Min a # (<>) :: Min (a -> b) -> Min a -> Min b # liftA2 :: (a -> b -> c) -> Min a -> Min b -> Min c # (>) :: Min a -> Min b -> Min b # (<*) :: Min a -> Min b -> Min a #
Applicative Max	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods pure :: a -> Max a # (<>) :: Max (a -> b) -> Max a -> Max b # liftA2 :: (a -> b -> c) -> Max a -> Max b -> Max c # (>) :: Max a -> Max b -> Max b # (<*) :: Max a -> Max b -> Max a #
Applicative First	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods pure :: a -> First a # (<>) :: First (a -> b) -> First a -> First b # liftA2 :: (a -> b -> c) -> First a -> First b -> First c # (>) :: First a -> First b -> First b # (<*) :: First a -> First b -> First a #
Applicative Last	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods pure :: a -> Last a # (<>) :: Last (a -> b) -> Last a -> Last b # liftA2 :: (a -> b -> c) -> Last a -> Last b -> Last c # (>) :: Last a -> Last b -> Last b # (<*) :: Last a -> Last b -> Last a #
Applicative Option	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods pure :: a -> Option a # (<>) :: Option (a -> b) -> Option a -> Option b # liftA2 :: (a -> b -> c) -> Option a -> Option b -> Option c # (>) :: Option a -> Option b -> Option b # (<*) :: Option a -> Option b -> Option a #
Applicative ZipList	f '<$>' 'ZipList' xs1 '<>' ... '<>' 'ZipList' xsN = 'ZipList' (zipWithN f xs1 ... xsN) where `zipWithN` refers to the `zipWith` function of the appropriate arity (`zipWith`, `zipWith3`, `zipWith4`, ...). For example: (\a b c -> stimes c [a, b]) <$> ZipList "abcd" <> ZipList "567" <> ZipList [1..] = ZipList (zipWith3 (\a b c -> stimes c [a, b]) "abcd" "567" [1..]) = ZipList {getZipList = ["a5","b6b6","c7c7c7"]} Since: base-2.1
Instance details Defined in Control.Applicative Methods pure :: a -> ZipList a # (<>) :: ZipList (a -> b) -> ZipList a -> ZipList b # liftA2 :: (a -> b -> c) -> ZipList a -> ZipList b -> ZipList c # (>) :: ZipList a -> ZipList b -> ZipList b # (<*) :: ZipList a -> ZipList b -> ZipList a #
Applicative Identity	Since: base-4.8.0.0
Instance details Defined in Data.Functor.Identity Methods pure :: a -> Identity a # (<>) :: Identity (a -> b) -> Identity a -> Identity b # liftA2 :: (a -> b -> c) -> Identity a -> Identity b -> Identity c # (>) :: Identity a -> Identity b -> Identity b # (<*) :: Identity a -> Identity b -> Identity a #
Applicative STM	Since: base-4.8.0.0
Instance details Defined in GHC.Conc.Sync Methods pure :: a -> STM a # (<>) :: STM (a -> b) -> STM a -> STM b # liftA2 :: (a -> b -> c) -> STM a -> STM b -> STM c # (>) :: STM a -> STM b -> STM b # (<*) :: STM a -> STM b -> STM a #
Applicative First	Since: base-4.8.0.0
Instance details Defined in Data.Monoid Methods pure :: a -> First a # (<>) :: First (a -> b) -> First a -> First b # liftA2 :: (a -> b -> c) -> First a -> First b -> First c # (>) :: First a -> First b -> First b # (<*) :: First a -> First b -> First a #
Applicative Last	Since: base-4.8.0.0
Instance details Defined in Data.Monoid Methods pure :: a -> Last a # (<>) :: Last (a -> b) -> Last a -> Last b # liftA2 :: (a -> b -> c) -> Last a -> Last b -> Last c # (>) :: Last a -> Last b -> Last b # (<*) :: Last a -> Last b -> Last a #
Applicative Dual	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods pure :: a -> Dual a # (<>) :: Dual (a -> b) -> Dual a -> Dual b # liftA2 :: (a -> b -> c) -> Dual a -> Dual b -> Dual c # (>) :: Dual a -> Dual b -> Dual b # (<*) :: Dual a -> Dual b -> Dual a #
Applicative Sum	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods pure :: a -> Sum a # (<>) :: Sum (a -> b) -> Sum a -> Sum b # liftA2 :: (a -> b -> c) -> Sum a -> Sum b -> Sum c # (>) :: Sum a -> Sum b -> Sum b # (<*) :: Sum a -> Sum b -> Sum a #
Applicative Product	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods pure :: a -> Product a # (<>) :: Product (a -> b) -> Product a -> Product b # liftA2 :: (a -> b -> c) -> Product a -> Product b -> Product c # (>) :: Product a -> Product b -> Product b # (<*) :: Product a -> Product b -> Product a #
Applicative Down	Since: base-4.11.0.0
Instance details Defined in Data.Ord Methods pure :: a -> Down a # (<>) :: Down (a -> b) -> Down a -> Down b # liftA2 :: (a -> b -> c) -> Down a -> Down b -> Down c # (>) :: Down a -> Down b -> Down b # (<*) :: Down a -> Down b -> Down a #
Applicative ReadP	Since: base-4.6.0.0
Instance details Defined in Text.ParserCombinators.ReadP Methods pure :: a -> ReadP a # (<>) :: ReadP (a -> b) -> ReadP a -> ReadP b # liftA2 :: (a -> b -> c) -> ReadP a -> ReadP b -> ReadP c # (>) :: ReadP a -> ReadP b -> ReadP b # (<*) :: ReadP a -> ReadP b -> ReadP a #
Applicative NonEmpty	Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods pure :: a -> NonEmpty a # (<>) :: NonEmpty (a -> b) -> NonEmpty a -> NonEmpty b # liftA2 :: (a -> b -> c) -> NonEmpty a -> NonEmpty b -> NonEmpty c # (>) :: NonEmpty a -> NonEmpty b -> NonEmpty b # (<*) :: NonEmpty a -> NonEmpty b -> NonEmpty a #
Applicative SmallArray
Instance details Defined in Data.Primitive.SmallArray Methods pure :: a -> SmallArray a # (<>) :: SmallArray (a -> b) -> SmallArray a -> SmallArray b # liftA2 :: (a -> b -> c) -> SmallArray a -> SmallArray b -> SmallArray c # (>) :: SmallArray a -> SmallArray b -> SmallArray b # (<*) :: SmallArray a -> SmallArray b -> SmallArray a #
Applicative Array
Instance details Defined in Data.Primitive.Array Methods pure :: a -> Array a # (<>) :: Array (a -> b) -> Array a -> Array b # liftA2 :: (a -> b -> c) -> Array a -> Array b -> Array c # (>) :: Array a -> Array b -> Array b # (<*) :: Array a -> Array b -> Array a #
Applicative Id
Instance details Defined in Data.Vector.Fusion.Util Methods pure :: a -> Id a # (<>) :: Id (a -> b) -> Id a -> Id b # liftA2 :: (a -> b -> c) -> Id a -> Id b -> Id c # (>) :: Id a -> Id b -> Id b # (<*) :: Id a -> Id b -> Id a #
Applicative Box
Instance details Defined in Data.Vector.Fusion.Util Methods pure :: a -> Box a # (<>) :: Box (a -> b) -> Box a -> Box b # liftA2 :: (a -> b -> c) -> Box a -> Box b -> Box c # (>) :: Box a -> Box b -> Box b # (<*) :: Box a -> Box b -> Box a #
Applicative P	Since: base-4.5.0.0
Instance details Defined in Text.ParserCombinators.ReadP Methods pure :: a -> P a # (<>) :: P (a -> b) -> P a -> P b # liftA2 :: (a -> b -> c) -> P a -> P b -> P c # (>) :: P a -> P b -> P b # (<*) :: P a -> P b -> P a #
Applicative (Either e)	Since: base-3.0
Instance details Defined in Data.Either Methods pure :: a -> Either e a # (<>) :: Either e (a -> b) -> Either e a -> Either e b # liftA2 :: (a -> b -> c) -> Either e a -> Either e b -> Either e c # (>) :: Either e a -> Either e b -> Either e b # (<*) :: Either e a -> Either e b -> Either e a #
Applicative (U1 :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods pure :: a -> U1 a # (<>) :: U1 (a -> b) -> U1 a -> U1 b # liftA2 :: (a -> b -> c) -> U1 a -> U1 b -> U1 c # (>) :: U1 a -> U1 b -> U1 b # (<*) :: U1 a -> U1 b -> U1 a #
Monoid a => Applicative ((,) a)	For tuples, the `Monoid` constraint on `a` determines how the first values merge. For example, `String`s concatenate: ("hello ", (+15)) <> ("world!", 2002) ("hello world!",2017) Since: base-2.1*
Instance details Defined in GHC.Base Methods pure :: a0 -> (a, a0) # (<>) :: (a, a0 -> b) -> (a, a0) -> (a, b) # liftA2 :: (a0 -> b -> c) -> (a, a0) -> (a, b) -> (a, c) # (>) :: (a, a0) -> (a, b) -> (a, b) # (<*) :: (a, a0) -> (a, b) -> (a, a0) #
Applicative (ST s)	Since: base-4.4.0.0
Instance details Defined in GHC.ST Methods pure :: a -> ST s a # (<>) :: ST s (a -> b) -> ST s a -> ST s b # liftA2 :: (a -> b -> c) -> ST s a -> ST s b -> ST s c # (>) :: ST s a -> ST s b -> ST s b # (<*) :: ST s a -> ST s b -> ST s a #
Monad m => Applicative (WrappedMonad m)	Since: base-2.1
Instance details Defined in Control.Applicative Methods pure :: a -> WrappedMonad m a # (<>) :: WrappedMonad m (a -> b) -> WrappedMonad m a -> WrappedMonad m b # liftA2 :: (a -> b -> c) -> WrappedMonad m a -> WrappedMonad m b -> WrappedMonad m c # (>) :: WrappedMonad m a -> WrappedMonad m b -> WrappedMonad m b # (<*) :: WrappedMonad m a -> WrappedMonad m b -> WrappedMonad m a #
Applicative (Proxy :: Type -> Type)	Since: base-4.7.0.0
Instance details Defined in Data.Proxy Methods pure :: a -> Proxy a # (<>) :: Proxy (a -> b) -> Proxy a -> Proxy b # liftA2 :: (a -> b -> c) -> Proxy a -> Proxy b -> Proxy c # (>) :: Proxy a -> Proxy b -> Proxy b # (<*) :: Proxy a -> Proxy b -> Proxy a #
(Functor m, Monad m) => Applicative (MaybeT m)
Instance details Defined in Control.Monad.Trans.Maybe Methods pure :: a -> MaybeT m a # (<>) :: MaybeT m (a -> b) -> MaybeT m a -> MaybeT m b # liftA2 :: (a -> b -> c) -> MaybeT m a -> MaybeT m b -> MaybeT m c # (>) :: MaybeT m a -> MaybeT m b -> MaybeT m b # (<*) :: MaybeT m a -> MaybeT m b -> MaybeT m a #
Applicative m => Applicative (ListT m)
Instance details Defined in Control.Monad.Trans.List Methods pure :: a -> ListT m a # (<>) :: ListT m (a -> b) -> ListT m a -> ListT m b # liftA2 :: (a -> b -> c) -> ListT m a -> ListT m b -> ListT m c # (>) :: ListT m a -> ListT m b -> ListT m b # (<*) :: ListT m a -> ListT m b -> ListT m a #
Applicative f => Applicative (Rec1 f)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods pure :: a -> Rec1 f a # (<>) :: Rec1 f (a -> b) -> Rec1 f a -> Rec1 f b # liftA2 :: (a -> b -> c) -> Rec1 f a -> Rec1 f b -> Rec1 f c # (>) :: Rec1 f a -> Rec1 f b -> Rec1 f b # (<*) :: Rec1 f a -> Rec1 f b -> Rec1 f a #
Arrow a => Applicative (WrappedArrow a b)	Since: base-2.1
Instance details Defined in Control.Applicative Methods pure :: a0 -> WrappedArrow a b a0 # (<>) :: WrappedArrow a b (a0 -> b0) -> WrappedArrow a b a0 -> WrappedArrow a b b0 # liftA2 :: (a0 -> b0 -> c) -> WrappedArrow a b a0 -> WrappedArrow a b b0 -> WrappedArrow a b c # (>) :: WrappedArrow a b a0 -> WrappedArrow a b b0 -> WrappedArrow a b b0 # (<*) :: WrappedArrow a b a0 -> WrappedArrow a b b0 -> WrappedArrow a b a0 #
Monoid m => Applicative (Const m :: Type -> Type)	Since: base-2.0.1
Instance details Defined in Data.Functor.Const Methods pure :: a -> Const m a # (<>) :: Const m (a -> b) -> Const m a -> Const m b # liftA2 :: (a -> b -> c) -> Const m a -> Const m b -> Const m c # (>) :: Const m a -> Const m b -> Const m b # (<*) :: Const m a -> Const m b -> Const m a #
Applicative f => Applicative (Ap f)	Since: base-4.12.0.0
Instance details Defined in Data.Monoid Methods pure :: a -> Ap f a # (<>) :: Ap f (a -> b) -> Ap f a -> Ap f b # liftA2 :: (a -> b -> c) -> Ap f a -> Ap f b -> Ap f c # (>) :: Ap f a -> Ap f b -> Ap f b # (<*) :: Ap f a -> Ap f b -> Ap f a #
Applicative f => Applicative (Alt f)	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods pure :: a -> Alt f a # (<>) :: Alt f (a -> b) -> Alt f a -> Alt f b # liftA2 :: (a -> b -> c) -> Alt f a -> Alt f b -> Alt f c # (>) :: Alt f a -> Alt f b -> Alt f b # (<*) :: Alt f a -> Alt f b -> Alt f a #
(Monoid w, Applicative m) => Applicative (WriterT w m)
Instance details Defined in Control.Monad.Trans.Writer.Strict Methods pure :: a -> WriterT w m a # (<>) :: WriterT w m (a -> b) -> WriterT w m a -> WriterT w m b # liftA2 :: (a -> b -> c) -> WriterT w m a -> WriterT w m b -> WriterT w m c # (>) :: WriterT w m a -> WriterT w m b -> WriterT w m b # (<*) :: WriterT w m a -> WriterT w m b -> WriterT w m a #
(Monoid w, Functor m, Monad m) => Applicative (AccumT w m)
Instance details Defined in Control.Monad.Trans.Accum Methods pure :: a -> AccumT w m a # (<>) :: AccumT w m (a -> b) -> AccumT w m a -> AccumT w m b # liftA2 :: (a -> b -> c) -> AccumT w m a -> AccumT w m b -> AccumT w m c # (>) :: AccumT w m a -> AccumT w m b -> AccumT w m b # (<*) :: AccumT w m a -> AccumT w m b -> AccumT w m a #
(Monoid w, Applicative m) => Applicative (WriterT w m)
Instance details Defined in Control.Monad.Trans.Writer.Lazy Methods pure :: a -> WriterT w m a # (<>) :: WriterT w m (a -> b) -> WriterT w m a -> WriterT w m b # liftA2 :: (a -> b -> c) -> WriterT w m a -> WriterT w m b -> WriterT w m c # (>) :: WriterT w m a -> WriterT w m b -> WriterT w m b # (<*) :: WriterT w m a -> WriterT w m b -> WriterT w m a #
(Functor m, Monad m) => Applicative (StateT s m)
Instance details Defined in Control.Monad.Trans.State.Strict Methods pure :: a -> StateT s m a # (<>) :: StateT s m (a -> b) -> StateT s m a -> StateT s m b # liftA2 :: (a -> b -> c) -> StateT s m a -> StateT s m b -> StateT s m c # (>) :: StateT s m a -> StateT s m b -> StateT s m b # (<*) :: StateT s m a -> StateT s m b -> StateT s m a #
(Functor m, Monad m) => Applicative (StateT s m)
Instance details Defined in Control.Monad.Trans.State.Lazy Methods pure :: a -> StateT s m a # (<>) :: StateT s m (a -> b) -> StateT s m a -> StateT s m b # liftA2 :: (a -> b -> c) -> StateT s m a -> StateT s m b -> StateT s m c # (>) :: StateT s m a -> StateT s m b -> StateT s m b # (<*) :: StateT s m a -> StateT s m b -> StateT s m a #
(Functor m, Monad m) => Applicative (SelectT r m)
Instance details Defined in Control.Monad.Trans.Select Methods pure :: a -> SelectT r m a # (<>) :: SelectT r m (a -> b) -> SelectT r m a -> SelectT r m b # liftA2 :: (a -> b -> c) -> SelectT r m a -> SelectT r m b -> SelectT r m c # (>) :: SelectT r m a -> SelectT r m b -> SelectT r m b # (<*) :: SelectT r m a -> SelectT r m b -> SelectT r m a #
Applicative m => Applicative (IdentityT m)
Instance details Defined in Control.Monad.Trans.Identity Methods pure :: a -> IdentityT m a # (<>) :: IdentityT m (a -> b) -> IdentityT m a -> IdentityT m b # liftA2 :: (a -> b -> c) -> IdentityT m a -> IdentityT m b -> IdentityT m c # (>) :: IdentityT m a -> IdentityT m b -> IdentityT m b # (<*) :: IdentityT m a -> IdentityT m b -> IdentityT m a #
(Functor m, Monad m) => Applicative (ExceptT e m)
Instance details Defined in Control.Monad.Trans.Except Methods pure :: a -> ExceptT e m a # (<>) :: ExceptT e m (a -> b) -> ExceptT e m a -> ExceptT e m b # liftA2 :: (a -> b -> c) -> ExceptT e m a -> ExceptT e m b -> ExceptT e m c # (>) :: ExceptT e m a -> ExceptT e m b -> ExceptT e m b # (<*) :: ExceptT e m a -> ExceptT e m b -> ExceptT e m a #
(Functor m, Monad m) => Applicative (ErrorT e m)
Instance details Defined in Control.Monad.Trans.Error Methods pure :: a -> ErrorT e m a # (<>) :: ErrorT e m (a -> b) -> ErrorT e m a -> ErrorT e m b # liftA2 :: (a -> b -> c) -> ErrorT e m a -> ErrorT e m b -> ErrorT e m c # (>) :: ErrorT e m a -> ErrorT e m b -> ErrorT e m b # (<*) :: ErrorT e m a -> ErrorT e m b -> ErrorT e m a #
Applicative ((->) a :: Type -> Type)	Since: base-2.1
Instance details Defined in GHC.Base Methods pure :: a0 -> a -> a0 # (<>) :: (a -> (a0 -> b)) -> (a -> a0) -> a -> b # liftA2 :: (a0 -> b -> c) -> (a -> a0) -> (a -> b) -> a -> c # (>) :: (a -> a0) -> (a -> b) -> a -> b # (<*) :: (a -> a0) -> (a -> b) -> a -> a0 #
Monoid c => Applicative (K1 i c :: Type -> Type)	Since: base-4.12.0.0
Instance details Defined in GHC.Generics Methods pure :: a -> K1 i c a # (<>) :: K1 i c (a -> b) -> K1 i c a -> K1 i c b # liftA2 :: (a -> b -> c0) -> K1 i c a -> K1 i c b -> K1 i c c0 # (>) :: K1 i c a -> K1 i c b -> K1 i c b # (<*) :: K1 i c a -> K1 i c b -> K1 i c a #
(Applicative f, Applicative g) => Applicative (f :*: g)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods pure :: a -> (f :: g) a # (<>) :: (f :: g) (a -> b) -> (f :: g) a -> (f :: g) b # liftA2 :: (a -> b -> c) -> (f :: g) a -> (f :: g) b -> (f :: g) c # (>) :: (f :: g) a -> (f :: g) b -> (f :: g) b # (<) :: (f :: g) a -> (f :: g) b -> (f :: g) a #
(Applicative f, Applicative g) => Applicative (Product f g)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Product Methods pure :: a -> Product f g a # (<>) :: Product f g (a -> b) -> Product f g a -> Product f g b # liftA2 :: (a -> b -> c) -> Product f g a -> Product f g b -> Product f g c # (>) :: Product f g a -> Product f g b -> Product f g b # (<*) :: Product f g a -> Product f g b -> Product f g a #
Applicative m => Applicative (ReaderT r m)
Instance details Defined in Control.Monad.Trans.Reader Methods pure :: a -> ReaderT r m a # (<>) :: ReaderT r m (a -> b) -> ReaderT r m a -> ReaderT r m b # liftA2 :: (a -> b -> c) -> ReaderT r m a -> ReaderT r m b -> ReaderT r m c # (>) :: ReaderT r m a -> ReaderT r m b -> ReaderT r m b # (<*) :: ReaderT r m a -> ReaderT r m b -> ReaderT r m a #
Applicative (ContT r m)
Instance details Defined in Control.Monad.Trans.Cont Methods pure :: a -> ContT r m a # (<>) :: ContT r m (a -> b) -> ContT r m a -> ContT r m b # liftA2 :: (a -> b -> c) -> ContT r m a -> ContT r m b -> ContT r m c # (>) :: ContT r m a -> ContT r m b -> ContT r m b # (<*) :: ContT r m a -> ContT r m b -> ContT r m a #
Applicative f => Applicative (M1 i c f)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods pure :: a -> M1 i c f a # (<>) :: M1 i c f (a -> b) -> M1 i c f a -> M1 i c f b # liftA2 :: (a -> b -> c0) -> M1 i c f a -> M1 i c f b -> M1 i c f c0 # (>) :: M1 i c f a -> M1 i c f b -> M1 i c f b # (<*) :: M1 i c f a -> M1 i c f b -> M1 i c f a #
(Applicative f, Applicative g) => Applicative (f :.: g)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods pure :: a -> (f :.: g) a # (<>) :: (f :.: g) (a -> b) -> (f :.: g) a -> (f :.: g) b # liftA2 :: (a -> b -> c) -> (f :.: g) a -> (f :.: g) b -> (f :.: g) c # (>) :: (f :.: g) a -> (f :.: g) b -> (f :.: g) b # (<*) :: (f :.: g) a -> (f :.: g) b -> (f :.: g) a #
(Applicative f, Applicative g) => Applicative (Compose f g)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Compose Methods pure :: a -> Compose f g a # (<>) :: Compose f g (a -> b) -> Compose f g a -> Compose f g b # liftA2 :: (a -> b -> c) -> Compose f g a -> Compose f g b -> Compose f g c # (>) :: Compose f g a -> Compose f g b -> Compose f g b # (<*) :: Compose f g a -> Compose f g b -> Compose f g a #
(Monoid w, Functor m, Monad m) => Applicative (RWST r w s m)
Instance details Defined in Control.Monad.Trans.RWS.Strict Methods pure :: a -> RWST r w s m a # (<>) :: RWST r w s m (a -> b) -> RWST r w s m a -> RWST r w s m b # liftA2 :: (a -> b -> c) -> RWST r w s m a -> RWST r w s m b -> RWST r w s m c # (>) :: RWST r w s m a -> RWST r w s m b -> RWST r w s m b # (<*) :: RWST r w s m a -> RWST r w s m b -> RWST r w s m a #
(Monoid w, Functor m, Monad m) => Applicative (RWST r w s m)
Instance details Defined in Control.Monad.Trans.RWS.Lazy Methods pure :: a -> RWST r w s m a # (<>) :: RWST r w s m (a -> b) -> RWST r w s m a -> RWST r w s m b # liftA2 :: (a -> b -> c) -> RWST r w s m a -> RWST r w s m b -> RWST r w s m c # (>) :: RWST r w s m a -> RWST r w s m b -> RWST r w s m b # (<*) :: RWST r w s m a -> RWST r w s m b -> RWST r w s m a #

class Foldable (t :: Type -> Type) where #

Data structures that can be folded.

For example, given a data type

data Tree a = Empty | Leaf a | Node (Tree a) a (Tree a)

a suitable instance would be

instance Foldable Tree where
   foldMap f Empty = mempty
   foldMap f (Leaf x) = f x
   foldMap f (Node l k r) = foldMap f l `mappend` f k `mappend` foldMap f r

This is suitable even for abstract types, as the monoid is assumed to satisfy the monoid laws. Alternatively, one could define foldr:

instance Foldable Tree where
   foldr f z Empty = z
   foldr f z (Leaf x) = f x z
   foldr f z (Node l k r) = foldr f (f k (foldr f z r)) l

Foldable instances are expected to satisfy the following laws:

foldr f z t = appEndo (foldMap (Endo . f) t ) z

foldl f z t = appEndo (getDual (foldMap (Dual . Endo . flip f) t)) z

fold = foldMap id

length = getSum . foldMap (Sum . const  1)

sum, product, maximum, and minimum should all be essentially equivalent to foldMap forms, such as

sum = getSum . foldMap Sum

but may be less defined.

If the type is also a Functor instance, it should satisfy

foldMap f = fold . fmap f

which implies that

foldMap f . fmap g = foldMap (f . g)

Minimal complete definition

foldMap | foldr

Methods

foldMap :: Monoid m => (a -> m) -> t a -> m #

Map each element of the structure to a monoid, and combine the results.

foldr :: (a -> b -> b) -> b -> t a -> b #

Right-associative fold of a structure.

In the case of lists, foldr, when applied to a binary operator, a starting value (typically the right-identity of the operator), and a list, reduces the list using the binary operator, from right to left:

foldr f z [x1, x2, ..., xn] == x1 `f` (x2 `f` ... (xn `f` z)...)

Note that, since the head of the resulting expression is produced by an application of the operator to the first element of the list, foldr can produce a terminating expression from an infinite list.

For a general Foldable structure this should be semantically identical to,

foldr f z = foldr f z . toList

foldl :: (b -> a -> b) -> b -> t a -> b #

Left-associative fold of a structure.

In the case of lists, foldl, when applied to a binary operator, a starting value (typically the left-identity of the operator), and a list, reduces the list using the binary operator, from left to right:

foldl f z [x1, x2, ..., xn] == (...((z `f` x1) `f` x2) `f`...) `f` xn

Note that to produce the outermost application of the operator the entire input list must be traversed. This means that foldl' will diverge if given an infinite list.

Also note that if you want an efficient left-fold, you probably want to use foldl' instead of foldl. The reason for this is that latter does not force the "inner" results (e.g. z f x1 in the above example) before applying them to the operator (e.g. to (f x2)). This results in a thunk chain O(n) elements long, which then must be evaluated from the outside-in.

For a general Foldable structure this should be semantically identical to,

foldl f z = foldl f z . toList

foldr1 :: (a -> a -> a) -> t a -> a #

A variant of foldr that has no base case, and thus may only be applied to non-empty structures.

foldr1 f = foldr1 f . toList

foldl1 :: (a -> a -> a) -> t a -> a #

A variant of foldl that has no base case, and thus may only be applied to non-empty structures.

foldl1 f = foldl1 f . toList

null :: t a -> Bool #

Test whether the structure is empty. The default implementation is optimized for structures that are similar to cons-lists, because there is no general way to do better.

length :: t a -> Int #

Returns the size/length of a finite structure as an Int. The default implementation is optimized for structures that are similar to cons-lists, because there is no general way to do better.

elem :: Eq a => a -> t a -> Bool infix 4 #

Does the element occur in the structure?

Instances

Foldable []	Since: base-2.1
Instance details Defined in Data.Foldable Methods fold :: Monoid m => [m] -> m # foldMap :: Monoid m => (a -> m) -> [a] -> m # foldr :: (a -> b -> b) -> b -> [a] -> b # foldr' :: (a -> b -> b) -> b -> [a] -> b # foldl :: (b -> a -> b) -> b -> [a] -> b # foldl' :: (b -> a -> b) -> b -> [a] -> b # foldr1 :: (a -> a -> a) -> [a] -> a # foldl1 :: (a -> a -> a) -> [a] -> a # toList :: [a] -> [a] # null :: [a] -> Bool # length :: [a] -> Int # elem :: Eq a => a -> [a] -> Bool # maximum :: Ord a => [a] -> a # minimum :: Ord a => [a] -> a # sum :: Num a => [a] -> a # product :: Num a => [a] -> a #
Foldable Maybe	Since: base-2.1
Instance details Defined in Data.Foldable Methods fold :: Monoid m => Maybe m -> m # foldMap :: Monoid m => (a -> m) -> Maybe a -> m # foldr :: (a -> b -> b) -> b -> Maybe a -> b # foldr' :: (a -> b -> b) -> b -> Maybe a -> b # foldl :: (b -> a -> b) -> b -> Maybe a -> b # foldl' :: (b -> a -> b) -> b -> Maybe a -> b # foldr1 :: (a -> a -> a) -> Maybe a -> a # foldl1 :: (a -> a -> a) -> Maybe a -> a # toList :: Maybe a -> [a] # null :: Maybe a -> Bool # length :: Maybe a -> Int # elem :: Eq a => a -> Maybe a -> Bool # maximum :: Ord a => Maybe a -> a # minimum :: Ord a => Maybe a -> a # sum :: Num a => Maybe a -> a # product :: Num a => Maybe a -> a #
Foldable Par1	Since: base-4.9.0.0
Instance details Defined in Data.Foldable Methods fold :: Monoid m => Par1 m -> m # foldMap :: Monoid m => (a -> m) -> Par1 a -> m # foldr :: (a -> b -> b) -> b -> Par1 a -> b # foldr' :: (a -> b -> b) -> b -> Par1 a -> b # foldl :: (b -> a -> b) -> b -> Par1 a -> b # foldl' :: (b -> a -> b) -> b -> Par1 a -> b # foldr1 :: (a -> a -> a) -> Par1 a -> a # foldl1 :: (a -> a -> a) -> Par1 a -> a # toList :: Par1 a -> [a] # null :: Par1 a -> Bool # length :: Par1 a -> Int # elem :: Eq a => a -> Par1 a -> Bool # maximum :: Ord a => Par1 a -> a # minimum :: Ord a => Par1 a -> a # sum :: Num a => Par1 a -> a # product :: Num a => Par1 a -> a #
Foldable Complex	Since: base-4.9.0.0
Instance details Defined in Data.Complex Methods fold :: Monoid m => Complex m -> m # foldMap :: Monoid m => (a -> m) -> Complex a -> m # foldr :: (a -> b -> b) -> b -> Complex a -> b # foldr' :: (a -> b -> b) -> b -> Complex a -> b # foldl :: (b -> a -> b) -> b -> Complex a -> b # foldl' :: (b -> a -> b) -> b -> Complex a -> b # foldr1 :: (a -> a -> a) -> Complex a -> a # foldl1 :: (a -> a -> a) -> Complex a -> a # toList :: Complex a -> [a] # null :: Complex a -> Bool # length :: Complex a -> Int # elem :: Eq a => a -> Complex a -> Bool # maximum :: Ord a => Complex a -> a # minimum :: Ord a => Complex a -> a # sum :: Num a => Complex a -> a # product :: Num a => Complex a -> a #
Foldable Min	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods fold :: Monoid m => Min m -> m # foldMap :: Monoid m => (a -> m) -> Min a -> m # foldr :: (a -> b -> b) -> b -> Min a -> b # foldr' :: (a -> b -> b) -> b -> Min a -> b # foldl :: (b -> a -> b) -> b -> Min a -> b # foldl' :: (b -> a -> b) -> b -> Min a -> b # foldr1 :: (a -> a -> a) -> Min a -> a # foldl1 :: (a -> a -> a) -> Min a -> a # toList :: Min a -> [a] # null :: Min a -> Bool # length :: Min a -> Int # elem :: Eq a => a -> Min a -> Bool # maximum :: Ord a => Min a -> a # minimum :: Ord a => Min a -> a # sum :: Num a => Min a -> a # product :: Num a => Min a -> a #
Foldable Max	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods fold :: Monoid m => Max m -> m # foldMap :: Monoid m => (a -> m) -> Max a -> m # foldr :: (a -> b -> b) -> b -> Max a -> b # foldr' :: (a -> b -> b) -> b -> Max a -> b # foldl :: (b -> a -> b) -> b -> Max a -> b # foldl' :: (b -> a -> b) -> b -> Max a -> b # foldr1 :: (a -> a -> a) -> Max a -> a # foldl1 :: (a -> a -> a) -> Max a -> a # toList :: Max a -> [a] # null :: Max a -> Bool # length :: Max a -> Int # elem :: Eq a => a -> Max a -> Bool # maximum :: Ord a => Max a -> a # minimum :: Ord a => Max a -> a # sum :: Num a => Max a -> a # product :: Num a => Max a -> a #
Foldable First	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods fold :: Monoid m => First m -> m # foldMap :: Monoid m => (a -> m) -> First a -> m # foldr :: (a -> b -> b) -> b -> First a -> b # foldr' :: (a -> b -> b) -> b -> First a -> b # foldl :: (b -> a -> b) -> b -> First a -> b # foldl' :: (b -> a -> b) -> b -> First a -> b # foldr1 :: (a -> a -> a) -> First a -> a # foldl1 :: (a -> a -> a) -> First a -> a # toList :: First a -> [a] # null :: First a -> Bool # length :: First a -> Int # elem :: Eq a => a -> First a -> Bool # maximum :: Ord a => First a -> a # minimum :: Ord a => First a -> a # sum :: Num a => First a -> a # product :: Num a => First a -> a #
Foldable Last	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods fold :: Monoid m => Last m -> m # foldMap :: Monoid m => (a -> m) -> Last a -> m # foldr :: (a -> b -> b) -> b -> Last a -> b # foldr' :: (a -> b -> b) -> b -> Last a -> b # foldl :: (b -> a -> b) -> b -> Last a -> b # foldl' :: (b -> a -> b) -> b -> Last a -> b # foldr1 :: (a -> a -> a) -> Last a -> a # foldl1 :: (a -> a -> a) -> Last a -> a # toList :: Last a -> [a] # null :: Last a -> Bool # length :: Last a -> Int # elem :: Eq a => a -> Last a -> Bool # maximum :: Ord a => Last a -> a # minimum :: Ord a => Last a -> a # sum :: Num a => Last a -> a # product :: Num a => Last a -> a #
Foldable Option	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods fold :: Monoid m => Option m -> m # foldMap :: Monoid m => (a -> m) -> Option a -> m # foldr :: (a -> b -> b) -> b -> Option a -> b # foldr' :: (a -> b -> b) -> b -> Option a -> b # foldl :: (b -> a -> b) -> b -> Option a -> b # foldl' :: (b -> a -> b) -> b -> Option a -> b # foldr1 :: (a -> a -> a) -> Option a -> a # foldl1 :: (a -> a -> a) -> Option a -> a # toList :: Option a -> [a] # null :: Option a -> Bool # length :: Option a -> Int # elem :: Eq a => a -> Option a -> Bool # maximum :: Ord a => Option a -> a # minimum :: Ord a => Option a -> a # sum :: Num a => Option a -> a # product :: Num a => Option a -> a #
Foldable ZipList	Since: base-4.9.0.0
Instance details Defined in Control.Applicative Methods fold :: Monoid m => ZipList m -> m # foldMap :: Monoid m => (a -> m) -> ZipList a -> m # foldr :: (a -> b -> b) -> b -> ZipList a -> b # foldr' :: (a -> b -> b) -> b -> ZipList a -> b # foldl :: (b -> a -> b) -> b -> ZipList a -> b # foldl' :: (b -> a -> b) -> b -> ZipList a -> b # foldr1 :: (a -> a -> a) -> ZipList a -> a # foldl1 :: (a -> a -> a) -> ZipList a -> a # toList :: ZipList a -> [a] # null :: ZipList a -> Bool # length :: ZipList a -> Int # elem :: Eq a => a -> ZipList a -> Bool # maximum :: Ord a => ZipList a -> a # minimum :: Ord a => ZipList a -> a # sum :: Num a => ZipList a -> a # product :: Num a => ZipList a -> a #
Foldable Identity	Since: base-4.8.0.0
Instance details Defined in Data.Functor.Identity Methods fold :: Monoid m => Identity m -> m # foldMap :: Monoid m => (a -> m) -> Identity a -> m # foldr :: (a -> b -> b) -> b -> Identity a -> b # foldr' :: (a -> b -> b) -> b -> Identity a -> b # foldl :: (b -> a -> b) -> b -> Identity a -> b # foldl' :: (b -> a -> b) -> b -> Identity a -> b # foldr1 :: (a -> a -> a) -> Identity a -> a # foldl1 :: (a -> a -> a) -> Identity a -> a # toList :: Identity a -> [a] # null :: Identity a -> Bool # length :: Identity a -> Int # elem :: Eq a => a -> Identity a -> Bool # maximum :: Ord a => Identity a -> a # minimum :: Ord a => Identity a -> a # sum :: Num a => Identity a -> a # product :: Num a => Identity a -> a #
Foldable First	Since: base-4.8.0.0
Instance details Defined in Data.Foldable Methods fold :: Monoid m => First m -> m # foldMap :: Monoid m => (a -> m) -> First a -> m # foldr :: (a -> b -> b) -> b -> First a -> b # foldr' :: (a -> b -> b) -> b -> First a -> b # foldl :: (b -> a -> b) -> b -> First a -> b # foldl' :: (b -> a -> b) -> b -> First a -> b # foldr1 :: (a -> a -> a) -> First a -> a # foldl1 :: (a -> a -> a) -> First a -> a # toList :: First a -> [a] # null :: First a -> Bool # length :: First a -> Int # elem :: Eq a => a -> First a -> Bool # maximum :: Ord a => First a -> a # minimum :: Ord a => First a -> a # sum :: Num a => First a -> a # product :: Num a => First a -> a #
Foldable Last	Since: base-4.8.0.0
Instance details Defined in Data.Foldable Methods fold :: Monoid m => Last m -> m # foldMap :: Monoid m => (a -> m) -> Last a -> m # foldr :: (a -> b -> b) -> b -> Last a -> b # foldr' :: (a -> b -> b) -> b -> Last a -> b # foldl :: (b -> a -> b) -> b -> Last a -> b # foldl' :: (b -> a -> b) -> b -> Last a -> b # foldr1 :: (a -> a -> a) -> Last a -> a # foldl1 :: (a -> a -> a) -> Last a -> a # toList :: Last a -> [a] # null :: Last a -> Bool # length :: Last a -> Int # elem :: Eq a => a -> Last a -> Bool # maximum :: Ord a => Last a -> a # minimum :: Ord a => Last a -> a # sum :: Num a => Last a -> a # product :: Num a => Last a -> a #
Foldable Dual	Since: base-4.8.0.0
Instance details Defined in Data.Foldable Methods fold :: Monoid m => Dual m -> m # foldMap :: Monoid m => (a -> m) -> Dual a -> m # foldr :: (a -> b -> b) -> b -> Dual a -> b # foldr' :: (a -> b -> b) -> b -> Dual a -> b # foldl :: (b -> a -> b) -> b -> Dual a -> b # foldl' :: (b -> a -> b) -> b -> Dual a -> b # foldr1 :: (a -> a -> a) -> Dual a -> a # foldl1 :: (a -> a -> a) -> Dual a -> a # toList :: Dual a -> [a] # null :: Dual a -> Bool # length :: Dual a -> Int # elem :: Eq a => a -> Dual a -> Bool # maximum :: Ord a => Dual a -> a # minimum :: Ord a => Dual a -> a # sum :: Num a => Dual a -> a # product :: Num a => Dual a -> a #
Foldable Sum	Since: base-4.8.0.0
Instance details Defined in Data.Foldable Methods fold :: Monoid m => Sum m -> m # foldMap :: Monoid m => (a -> m) -> Sum a -> m # foldr :: (a -> b -> b) -> b -> Sum a -> b # foldr' :: (a -> b -> b) -> b -> Sum a -> b # foldl :: (b -> a -> b) -> b -> Sum a -> b # foldl' :: (b -> a -> b) -> b -> Sum a -> b # foldr1 :: (a -> a -> a) -> Sum a -> a # foldl1 :: (a -> a -> a) -> Sum a -> a # toList :: Sum a -> [a] # null :: Sum a -> Bool # length :: Sum a -> Int # elem :: Eq a => a -> Sum a -> Bool # maximum :: Ord a => Sum a -> a # minimum :: Ord a => Sum a -> a # sum :: Num a => Sum a -> a # product :: Num a => Sum a -> a #
Foldable Product	Since: base-4.8.0.0
Instance details Defined in Data.Foldable Methods fold :: Monoid m => Product m -> m # foldMap :: Monoid m => (a -> m) -> Product a -> m # foldr :: (a -> b -> b) -> b -> Product a -> b # foldr' :: (a -> b -> b) -> b -> Product a -> b # foldl :: (b -> a -> b) -> b -> Product a -> b # foldl' :: (b -> a -> b) -> b -> Product a -> b # foldr1 :: (a -> a -> a) -> Product a -> a # foldl1 :: (a -> a -> a) -> Product a -> a # toList :: Product a -> [a] # null :: Product a -> Bool # length :: Product a -> Int # elem :: Eq a => a -> Product a -> Bool # maximum :: Ord a => Product a -> a # minimum :: Ord a => Product a -> a # sum :: Num a => Product a -> a # product :: Num a => Product a -> a #
Foldable Down	Since: base-4.12.0.0
Instance details Defined in Data.Foldable Methods fold :: Monoid m => Down m -> m # foldMap :: Monoid m => (a -> m) -> Down a -> m # foldr :: (a -> b -> b) -> b -> Down a -> b # foldr' :: (a -> b -> b) -> b -> Down a -> b # foldl :: (b -> a -> b) -> b -> Down a -> b # foldl' :: (b -> a -> b) -> b -> Down a -> b # foldr1 :: (a -> a -> a) -> Down a -> a # foldl1 :: (a -> a -> a) -> Down a -> a # toList :: Down a -> [a] # null :: Down a -> Bool # length :: Down a -> Int # elem :: Eq a => a -> Down a -> Bool # maximum :: Ord a => Down a -> a # minimum :: Ord a => Down a -> a # sum :: Num a => Down a -> a # product :: Num a => Down a -> a #
Foldable NonEmpty	Since: base-4.9.0.0
Instance details Defined in Data.Foldable Methods fold :: Monoid m => NonEmpty m -> m # foldMap :: Monoid m => (a -> m) -> NonEmpty a -> m # foldr :: (a -> b -> b) -> b -> NonEmpty a -> b # foldr' :: (a -> b -> b) -> b -> NonEmpty a -> b # foldl :: (b -> a -> b) -> b -> NonEmpty a -> b # foldl' :: (b -> a -> b) -> b -> NonEmpty a -> b # foldr1 :: (a -> a -> a) -> NonEmpty a -> a # foldl1 :: (a -> a -> a) -> NonEmpty a -> a # toList :: NonEmpty a -> [a] # null :: NonEmpty a -> Bool # length :: NonEmpty a -> Int # elem :: Eq a => a -> NonEmpty a -> Bool # maximum :: Ord a => NonEmpty a -> a # minimum :: Ord a => NonEmpty a -> a # sum :: Num a => NonEmpty a -> a # product :: Num a => NonEmpty a -> a #
Foldable SmallArray
Instance details Defined in Data.Primitive.SmallArray Methods fold :: Monoid m => SmallArray m -> m # foldMap :: Monoid m => (a -> m) -> SmallArray a -> m # foldr :: (a -> b -> b) -> b -> SmallArray a -> b # foldr' :: (a -> b -> b) -> b -> SmallArray a -> b # foldl :: (b -> a -> b) -> b -> SmallArray a -> b # foldl' :: (b -> a -> b) -> b -> SmallArray a -> b # foldr1 :: (a -> a -> a) -> SmallArray a -> a # foldl1 :: (a -> a -> a) -> SmallArray a -> a # toList :: SmallArray a -> [a] # null :: SmallArray a -> Bool # length :: SmallArray a -> Int # elem :: Eq a => a -> SmallArray a -> Bool # maximum :: Ord a => SmallArray a -> a # minimum :: Ord a => SmallArray a -> a # sum :: Num a => SmallArray a -> a # product :: Num a => SmallArray a -> a #
Foldable Array
Instance details Defined in Data.Primitive.Array Methods fold :: Monoid m => Array m -> m # foldMap :: Monoid m => (a -> m) -> Array a -> m # foldr :: (a -> b -> b) -> b -> Array a -> b # foldr' :: (a -> b -> b) -> b -> Array a -> b # foldl :: (b -> a -> b) -> b -> Array a -> b # foldl' :: (b -> a -> b) -> b -> Array a -> b # foldr1 :: (a -> a -> a) -> Array a -> a # foldl1 :: (a -> a -> a) -> Array a -> a # toList :: Array a -> [a] # null :: Array a -> Bool # length :: Array a -> Int # elem :: Eq a => a -> Array a -> Bool # maximum :: Ord a => Array a -> a # minimum :: Ord a => Array a -> a # sum :: Num a => Array a -> a # product :: Num a => Array a -> a #
Foldable (Either a)	Since: base-4.7.0.0
Instance details Defined in Data.Foldable Methods fold :: Monoid m => Either a m -> m # foldMap :: Monoid m => (a0 -> m) -> Either a a0 -> m # foldr :: (a0 -> b -> b) -> b -> Either a a0 -> b # foldr' :: (a0 -> b -> b) -> b -> Either a a0 -> b # foldl :: (b -> a0 -> b) -> b -> Either a a0 -> b # foldl' :: (b -> a0 -> b) -> b -> Either a a0 -> b # foldr1 :: (a0 -> a0 -> a0) -> Either a a0 -> a0 # foldl1 :: (a0 -> a0 -> a0) -> Either a a0 -> a0 # toList :: Either a a0 -> [a0] # null :: Either a a0 -> Bool # length :: Either a a0 -> Int # elem :: Eq a0 => a0 -> Either a a0 -> Bool # maximum :: Ord a0 => Either a a0 -> a0 # minimum :: Ord a0 => Either a a0 -> a0 # sum :: Num a0 => Either a a0 -> a0 # product :: Num a0 => Either a a0 -> a0 #
Foldable (V1 :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Foldable Methods fold :: Monoid m => V1 m -> m # foldMap :: Monoid m => (a -> m) -> V1 a -> m # foldr :: (a -> b -> b) -> b -> V1 a -> b # foldr' :: (a -> b -> b) -> b -> V1 a -> b # foldl :: (b -> a -> b) -> b -> V1 a -> b # foldl' :: (b -> a -> b) -> b -> V1 a -> b # foldr1 :: (a -> a -> a) -> V1 a -> a # foldl1 :: (a -> a -> a) -> V1 a -> a # toList :: V1 a -> [a] # null :: V1 a -> Bool # length :: V1 a -> Int # elem :: Eq a => a -> V1 a -> Bool # maximum :: Ord a => V1 a -> a # minimum :: Ord a => V1 a -> a # sum :: Num a => V1 a -> a # product :: Num a => V1 a -> a #
Foldable (U1 :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Foldable Methods fold :: Monoid m => U1 m -> m # foldMap :: Monoid m => (a -> m) -> U1 a -> m # foldr :: (a -> b -> b) -> b -> U1 a -> b # foldr' :: (a -> b -> b) -> b -> U1 a -> b # foldl :: (b -> a -> b) -> b -> U1 a -> b # foldl' :: (b -> a -> b) -> b -> U1 a -> b # foldr1 :: (a -> a -> a) -> U1 a -> a # foldl1 :: (a -> a -> a) -> U1 a -> a # toList :: U1 a -> [a] # null :: U1 a -> Bool # length :: U1 a -> Int # elem :: Eq a => a -> U1 a -> Bool # maximum :: Ord a => U1 a -> a # minimum :: Ord a => U1 a -> a # sum :: Num a => U1 a -> a # product :: Num a => U1 a -> a #
Foldable ((,) a)	Since: base-4.7.0.0
Instance details Defined in Data.Foldable Methods fold :: Monoid m => (a, m) -> m # foldMap :: Monoid m => (a0 -> m) -> (a, a0) -> m # foldr :: (a0 -> b -> b) -> b -> (a, a0) -> b # foldr' :: (a0 -> b -> b) -> b -> (a, a0) -> b # foldl :: (b -> a0 -> b) -> b -> (a, a0) -> b # foldl' :: (b -> a0 -> b) -> b -> (a, a0) -> b # foldr1 :: (a0 -> a0 -> a0) -> (a, a0) -> a0 # foldl1 :: (a0 -> a0 -> a0) -> (a, a0) -> a0 # toList :: (a, a0) -> [a0] # null :: (a, a0) -> Bool # length :: (a, a0) -> Int # elem :: Eq a0 => a0 -> (a, a0) -> Bool # maximum :: Ord a0 => (a, a0) -> a0 # minimum :: Ord a0 => (a, a0) -> a0 # sum :: Num a0 => (a, a0) -> a0 # product :: Num a0 => (a, a0) -> a0 #
Foldable (Array i)	Since: base-4.8.0.0
Instance details Defined in Data.Foldable Methods fold :: Monoid m => Array i m -> m # foldMap :: Monoid m => (a -> m) -> Array i a -> m # foldr :: (a -> b -> b) -> b -> Array i a -> b # foldr' :: (a -> b -> b) -> b -> Array i a -> b # foldl :: (b -> a -> b) -> b -> Array i a -> b # foldl' :: (b -> a -> b) -> b -> Array i a -> b # foldr1 :: (a -> a -> a) -> Array i a -> a # foldl1 :: (a -> a -> a) -> Array i a -> a # toList :: Array i a -> [a] # null :: Array i a -> Bool # length :: Array i a -> Int # elem :: Eq a => a -> Array i a -> Bool # maximum :: Ord a => Array i a -> a # minimum :: Ord a => Array i a -> a # sum :: Num a => Array i a -> a # product :: Num a => Array i a -> a #
Foldable (Arg a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods fold :: Monoid m => Arg a m -> m # foldMap :: Monoid m => (a0 -> m) -> Arg a a0 -> m # foldr :: (a0 -> b -> b) -> b -> Arg a a0 -> b # foldr' :: (a0 -> b -> b) -> b -> Arg a a0 -> b # foldl :: (b -> a0 -> b) -> b -> Arg a a0 -> b # foldl' :: (b -> a0 -> b) -> b -> Arg a a0 -> b # foldr1 :: (a0 -> a0 -> a0) -> Arg a a0 -> a0 # foldl1 :: (a0 -> a0 -> a0) -> Arg a a0 -> a0 # toList :: Arg a a0 -> [a0] # null :: Arg a a0 -> Bool # length :: Arg a a0 -> Int # elem :: Eq a0 => a0 -> Arg a a0 -> Bool # maximum :: Ord a0 => Arg a a0 -> a0 # minimum :: Ord a0 => Arg a a0 -> a0 # sum :: Num a0 => Arg a a0 -> a0 # product :: Num a0 => Arg a a0 -> a0 #
Foldable (Proxy :: Type -> Type)	Since: base-4.7.0.0
Instance details Defined in Data.Foldable Methods fold :: Monoid m => Proxy m -> m # foldMap :: Monoid m => (a -> m) -> Proxy a -> m # foldr :: (a -> b -> b) -> b -> Proxy a -> b # foldr' :: (a -> b -> b) -> b -> Proxy a -> b # foldl :: (b -> a -> b) -> b -> Proxy a -> b # foldl' :: (b -> a -> b) -> b -> Proxy a -> b # foldr1 :: (a -> a -> a) -> Proxy a -> a # foldl1 :: (a -> a -> a) -> Proxy a -> a # toList :: Proxy a -> [a] # null :: Proxy a -> Bool # length :: Proxy a -> Int # elem :: Eq a => a -> Proxy a -> Bool # maximum :: Ord a => Proxy a -> a # minimum :: Ord a => Proxy a -> a # sum :: Num a => Proxy a -> a # product :: Num a => Proxy a -> a #
Foldable f => Foldable (MaybeT f)
Instance details Defined in Control.Monad.Trans.Maybe Methods fold :: Monoid m => MaybeT f m -> m # foldMap :: Monoid m => (a -> m) -> MaybeT f a -> m # foldr :: (a -> b -> b) -> b -> MaybeT f a -> b # foldr' :: (a -> b -> b) -> b -> MaybeT f a -> b # foldl :: (b -> a -> b) -> b -> MaybeT f a -> b # foldl' :: (b -> a -> b) -> b -> MaybeT f a -> b # foldr1 :: (a -> a -> a) -> MaybeT f a -> a # foldl1 :: (a -> a -> a) -> MaybeT f a -> a # toList :: MaybeT f a -> [a] # null :: MaybeT f a -> Bool # length :: MaybeT f a -> Int # elem :: Eq a => a -> MaybeT f a -> Bool # maximum :: Ord a => MaybeT f a -> a # minimum :: Ord a => MaybeT f a -> a # sum :: Num a => MaybeT f a -> a # product :: Num a => MaybeT f a -> a #
Foldable f => Foldable (ListT f)
Instance details Defined in Control.Monad.Trans.List Methods fold :: Monoid m => ListT f m -> m # foldMap :: Monoid m => (a -> m) -> ListT f a -> m # foldr :: (a -> b -> b) -> b -> ListT f a -> b # foldr' :: (a -> b -> b) -> b -> ListT f a -> b # foldl :: (b -> a -> b) -> b -> ListT f a -> b # foldl' :: (b -> a -> b) -> b -> ListT f a -> b # foldr1 :: (a -> a -> a) -> ListT f a -> a # foldl1 :: (a -> a -> a) -> ListT f a -> a # toList :: ListT f a -> [a] # null :: ListT f a -> Bool # length :: ListT f a -> Int # elem :: Eq a => a -> ListT f a -> Bool # maximum :: Ord a => ListT f a -> a # minimum :: Ord a => ListT f a -> a # sum :: Num a => ListT f a -> a # product :: Num a => ListT f a -> a #
Foldable f => Foldable (Rec1 f)	Since: base-4.9.0.0
Instance details Defined in Data.Foldable Methods fold :: Monoid m => Rec1 f m -> m # foldMap :: Monoid m => (a -> m) -> Rec1 f a -> m # foldr :: (a -> b -> b) -> b -> Rec1 f a -> b # foldr' :: (a -> b -> b) -> b -> Rec1 f a -> b # foldl :: (b -> a -> b) -> b -> Rec1 f a -> b # foldl' :: (b -> a -> b) -> b -> Rec1 f a -> b # foldr1 :: (a -> a -> a) -> Rec1 f a -> a # foldl1 :: (a -> a -> a) -> Rec1 f a -> a # toList :: Rec1 f a -> [a] # null :: Rec1 f a -> Bool # length :: Rec1 f a -> Int # elem :: Eq a => a -> Rec1 f a -> Bool # maximum :: Ord a => Rec1 f a -> a # minimum :: Ord a => Rec1 f a -> a # sum :: Num a => Rec1 f a -> a # product :: Num a => Rec1 f a -> a #
Foldable (URec Char :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Foldable Methods fold :: Monoid m => URec Char m -> m # foldMap :: Monoid m => (a -> m) -> URec Char a -> m # foldr :: (a -> b -> b) -> b -> URec Char a -> b # foldr' :: (a -> b -> b) -> b -> URec Char a -> b # foldl :: (b -> a -> b) -> b -> URec Char a -> b # foldl' :: (b -> a -> b) -> b -> URec Char a -> b # foldr1 :: (a -> a -> a) -> URec Char a -> a # foldl1 :: (a -> a -> a) -> URec Char a -> a # toList :: URec Char a -> [a] # null :: URec Char a -> Bool # length :: URec Char a -> Int # elem :: Eq a => a -> URec Char a -> Bool # maximum :: Ord a => URec Char a -> a # minimum :: Ord a => URec Char a -> a # sum :: Num a => URec Char a -> a # product :: Num a => URec Char a -> a #
Foldable (URec Double :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Foldable Methods fold :: Monoid m => URec Double m -> m # foldMap :: Monoid m => (a -> m) -> URec Double a -> m # foldr :: (a -> b -> b) -> b -> URec Double a -> b # foldr' :: (a -> b -> b) -> b -> URec Double a -> b # foldl :: (b -> a -> b) -> b -> URec Double a -> b # foldl' :: (b -> a -> b) -> b -> URec Double a -> b # foldr1 :: (a -> a -> a) -> URec Double a -> a # foldl1 :: (a -> a -> a) -> URec Double a -> a # toList :: URec Double a -> [a] # null :: URec Double a -> Bool # length :: URec Double a -> Int # elem :: Eq a => a -> URec Double a -> Bool # maximum :: Ord a => URec Double a -> a # minimum :: Ord a => URec Double a -> a # sum :: Num a => URec Double a -> a # product :: Num a => URec Double a -> a #
Foldable (URec Float :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Foldable Methods fold :: Monoid m => URec Float m -> m # foldMap :: Monoid m => (a -> m) -> URec Float a -> m # foldr :: (a -> b -> b) -> b -> URec Float a -> b # foldr' :: (a -> b -> b) -> b -> URec Float a -> b # foldl :: (b -> a -> b) -> b -> URec Float a -> b # foldl' :: (b -> a -> b) -> b -> URec Float a -> b # foldr1 :: (a -> a -> a) -> URec Float a -> a # foldl1 :: (a -> a -> a) -> URec Float a -> a # toList :: URec Float a -> [a] # null :: URec Float a -> Bool # length :: URec Float a -> Int # elem :: Eq a => a -> URec Float a -> Bool # maximum :: Ord a => URec Float a -> a # minimum :: Ord a => URec Float a -> a # sum :: Num a => URec Float a -> a # product :: Num a => URec Float a -> a #
Foldable (URec Int :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Foldable Methods fold :: Monoid m => URec Int m -> m # foldMap :: Monoid m => (a -> m) -> URec Int a -> m # foldr :: (a -> b -> b) -> b -> URec Int a -> b # foldr' :: (a -> b -> b) -> b -> URec Int a -> b # foldl :: (b -> a -> b) -> b -> URec Int a -> b # foldl' :: (b -> a -> b) -> b -> URec Int a -> b # foldr1 :: (a -> a -> a) -> URec Int a -> a # foldl1 :: (a -> a -> a) -> URec Int a -> a # toList :: URec Int a -> [a] # null :: URec Int a -> Bool # length :: URec Int a -> Int # elem :: Eq a => a -> URec Int a -> Bool # maximum :: Ord a => URec Int a -> a # minimum :: Ord a => URec Int a -> a # sum :: Num a => URec Int a -> a # product :: Num a => URec Int a -> a #
Foldable (URec Word :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Foldable Methods fold :: Monoid m => URec Word m -> m # foldMap :: Monoid m => (a -> m) -> URec Word a -> m # foldr :: (a -> b -> b) -> b -> URec Word a -> b # foldr' :: (a -> b -> b) -> b -> URec Word a -> b # foldl :: (b -> a -> b) -> b -> URec Word a -> b # foldl' :: (b -> a -> b) -> b -> URec Word a -> b # foldr1 :: (a -> a -> a) -> URec Word a -> a # foldl1 :: (a -> a -> a) -> URec Word a -> a # toList :: URec Word a -> [a] # null :: URec Word a -> Bool # length :: URec Word a -> Int # elem :: Eq a => a -> URec Word a -> Bool # maximum :: Ord a => URec Word a -> a # minimum :: Ord a => URec Word a -> a # sum :: Num a => URec Word a -> a # product :: Num a => URec Word a -> a #
Foldable (URec (Ptr ()) :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Foldable Methods fold :: Monoid m => URec (Ptr ()) m -> m # foldMap :: Monoid m => (a -> m) -> URec (Ptr ()) a -> m # foldr :: (a -> b -> b) -> b -> URec (Ptr ()) a -> b # foldr' :: (a -> b -> b) -> b -> URec (Ptr ()) a -> b # foldl :: (b -> a -> b) -> b -> URec (Ptr ()) a -> b # foldl' :: (b -> a -> b) -> b -> URec (Ptr ()) a -> b # foldr1 :: (a -> a -> a) -> URec (Ptr ()) a -> a # foldl1 :: (a -> a -> a) -> URec (Ptr ()) a -> a # toList :: URec (Ptr ()) a -> [a] # null :: URec (Ptr ()) a -> Bool # length :: URec (Ptr ()) a -> Int # elem :: Eq a => a -> URec (Ptr ()) a -> Bool # maximum :: Ord a => URec (Ptr ()) a -> a # minimum :: Ord a => URec (Ptr ()) a -> a # sum :: Num a => URec (Ptr ()) a -> a # product :: Num a => URec (Ptr ()) a -> a #
Foldable (Const m :: Type -> Type)	Since: base-4.7.0.0
Instance details Defined in Data.Functor.Const Methods fold :: Monoid m0 => Const m m0 -> m0 # foldMap :: Monoid m0 => (a -> m0) -> Const m a -> m0 # foldr :: (a -> b -> b) -> b -> Const m a -> b # foldr' :: (a -> b -> b) -> b -> Const m a -> b # foldl :: (b -> a -> b) -> b -> Const m a -> b # foldl' :: (b -> a -> b) -> b -> Const m a -> b # foldr1 :: (a -> a -> a) -> Const m a -> a # foldl1 :: (a -> a -> a) -> Const m a -> a # toList :: Const m a -> [a] # null :: Const m a -> Bool # length :: Const m a -> Int # elem :: Eq a => a -> Const m a -> Bool # maximum :: Ord a => Const m a -> a # minimum :: Ord a => Const m a -> a # sum :: Num a => Const m a -> a # product :: Num a => Const m a -> a #
Foldable f => Foldable (Ap f)	Since: base-4.12.0.0
Instance details Defined in Data.Foldable Methods fold :: Monoid m => Ap f m -> m # foldMap :: Monoid m => (a -> m) -> Ap f a -> m # foldr :: (a -> b -> b) -> b -> Ap f a -> b # foldr' :: (a -> b -> b) -> b -> Ap f a -> b # foldl :: (b -> a -> b) -> b -> Ap f a -> b # foldl' :: (b -> a -> b) -> b -> Ap f a -> b # foldr1 :: (a -> a -> a) -> Ap f a -> a # foldl1 :: (a -> a -> a) -> Ap f a -> a # toList :: Ap f a -> [a] # null :: Ap f a -> Bool # length :: Ap f a -> Int # elem :: Eq a => a -> Ap f a -> Bool # maximum :: Ord a => Ap f a -> a # minimum :: Ord a => Ap f a -> a # sum :: Num a => Ap f a -> a # product :: Num a => Ap f a -> a #
Foldable f => Foldable (Alt f)	Since: base-4.12.0.0
Instance details Defined in Data.Foldable Methods fold :: Monoid m => Alt f m -> m # foldMap :: Monoid m => (a -> m) -> Alt f a -> m # foldr :: (a -> b -> b) -> b -> Alt f a -> b # foldr' :: (a -> b -> b) -> b -> Alt f a -> b # foldl :: (b -> a -> b) -> b -> Alt f a -> b # foldl' :: (b -> a -> b) -> b -> Alt f a -> b # foldr1 :: (a -> a -> a) -> Alt f a -> a # foldl1 :: (a -> a -> a) -> Alt f a -> a # toList :: Alt f a -> [a] # null :: Alt f a -> Bool # length :: Alt f a -> Int # elem :: Eq a => a -> Alt f a -> Bool # maximum :: Ord a => Alt f a -> a # minimum :: Ord a => Alt f a -> a # sum :: Num a => Alt f a -> a # product :: Num a => Alt f a -> a #
Foldable f => Foldable (WriterT w f)
Instance details Defined in Control.Monad.Trans.Writer.Strict Methods fold :: Monoid m => WriterT w f m -> m # foldMap :: Monoid m => (a -> m) -> WriterT w f a -> m # foldr :: (a -> b -> b) -> b -> WriterT w f a -> b # foldr' :: (a -> b -> b) -> b -> WriterT w f a -> b # foldl :: (b -> a -> b) -> b -> WriterT w f a -> b # foldl' :: (b -> a -> b) -> b -> WriterT w f a -> b # foldr1 :: (a -> a -> a) -> WriterT w f a -> a # foldl1 :: (a -> a -> a) -> WriterT w f a -> a # toList :: WriterT w f a -> [a] # null :: WriterT w f a -> Bool # length :: WriterT w f a -> Int # elem :: Eq a => a -> WriterT w f a -> Bool # maximum :: Ord a => WriterT w f a -> a # minimum :: Ord a => WriterT w f a -> a # sum :: Num a => WriterT w f a -> a # product :: Num a => WriterT w f a -> a #
Foldable f => Foldable (WriterT w f)
Instance details Defined in Control.Monad.Trans.Writer.Lazy Methods fold :: Monoid m => WriterT w f m -> m # foldMap :: Monoid m => (a -> m) -> WriterT w f a -> m # foldr :: (a -> b -> b) -> b -> WriterT w f a -> b # foldr' :: (a -> b -> b) -> b -> WriterT w f a -> b # foldl :: (b -> a -> b) -> b -> WriterT w f a -> b # foldl' :: (b -> a -> b) -> b -> WriterT w f a -> b # foldr1 :: (a -> a -> a) -> WriterT w f a -> a # foldl1 :: (a -> a -> a) -> WriterT w f a -> a # toList :: WriterT w f a -> [a] # null :: WriterT w f a -> Bool # length :: WriterT w f a -> Int # elem :: Eq a => a -> WriterT w f a -> Bool # maximum :: Ord a => WriterT w f a -> a # minimum :: Ord a => WriterT w f a -> a # sum :: Num a => WriterT w f a -> a # product :: Num a => WriterT w f a -> a #
Foldable f => Foldable (IdentityT f)
Instance details Defined in Control.Monad.Trans.Identity Methods fold :: Monoid m => IdentityT f m -> m # foldMap :: Monoid m => (a -> m) -> IdentityT f a -> m # foldr :: (a -> b -> b) -> b -> IdentityT f a -> b # foldr' :: (a -> b -> b) -> b -> IdentityT f a -> b # foldl :: (b -> a -> b) -> b -> IdentityT f a -> b # foldl' :: (b -> a -> b) -> b -> IdentityT f a -> b # foldr1 :: (a -> a -> a) -> IdentityT f a -> a # foldl1 :: (a -> a -> a) -> IdentityT f a -> a # toList :: IdentityT f a -> [a] # null :: IdentityT f a -> Bool # length :: IdentityT f a -> Int # elem :: Eq a => a -> IdentityT f a -> Bool # maximum :: Ord a => IdentityT f a -> a # minimum :: Ord a => IdentityT f a -> a # sum :: Num a => IdentityT f a -> a # product :: Num a => IdentityT f a -> a #
Foldable f => Foldable (ExceptT e f)
Instance details Defined in Control.Monad.Trans.Except Methods fold :: Monoid m => ExceptT e f m -> m # foldMap :: Monoid m => (a -> m) -> ExceptT e f a -> m # foldr :: (a -> b -> b) -> b -> ExceptT e f a -> b # foldr' :: (a -> b -> b) -> b -> ExceptT e f a -> b # foldl :: (b -> a -> b) -> b -> ExceptT e f a -> b # foldl' :: (b -> a -> b) -> b -> ExceptT e f a -> b # foldr1 :: (a -> a -> a) -> ExceptT e f a -> a # foldl1 :: (a -> a -> a) -> ExceptT e f a -> a # toList :: ExceptT e f a -> [a] # null :: ExceptT e f a -> Bool # length :: ExceptT e f a -> Int # elem :: Eq a => a -> ExceptT e f a -> Bool # maximum :: Ord a => ExceptT e f a -> a # minimum :: Ord a => ExceptT e f a -> a # sum :: Num a => ExceptT e f a -> a # product :: Num a => ExceptT e f a -> a #
Foldable f => Foldable (ErrorT e f)
Instance details Defined in Control.Monad.Trans.Error Methods fold :: Monoid m => ErrorT e f m -> m # foldMap :: Monoid m => (a -> m) -> ErrorT e f a -> m # foldr :: (a -> b -> b) -> b -> ErrorT e f a -> b # foldr' :: (a -> b -> b) -> b -> ErrorT e f a -> b # foldl :: (b -> a -> b) -> b -> ErrorT e f a -> b # foldl' :: (b -> a -> b) -> b -> ErrorT e f a -> b # foldr1 :: (a -> a -> a) -> ErrorT e f a -> a # foldl1 :: (a -> a -> a) -> ErrorT e f a -> a # toList :: ErrorT e f a -> [a] # null :: ErrorT e f a -> Bool # length :: ErrorT e f a -> Int # elem :: Eq a => a -> ErrorT e f a -> Bool # maximum :: Ord a => ErrorT e f a -> a # minimum :: Ord a => ErrorT e f a -> a # sum :: Num a => ErrorT e f a -> a # product :: Num a => ErrorT e f a -> a #
Foldable (K1 i c :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Foldable Methods fold :: Monoid m => K1 i c m -> m # foldMap :: Monoid m => (a -> m) -> K1 i c a -> m # foldr :: (a -> b -> b) -> b -> K1 i c a -> b # foldr' :: (a -> b -> b) -> b -> K1 i c a -> b # foldl :: (b -> a -> b) -> b -> K1 i c a -> b # foldl' :: (b -> a -> b) -> b -> K1 i c a -> b # foldr1 :: (a -> a -> a) -> K1 i c a -> a # foldl1 :: (a -> a -> a) -> K1 i c a -> a # toList :: K1 i c a -> [a] # null :: K1 i c a -> Bool # length :: K1 i c a -> Int # elem :: Eq a => a -> K1 i c a -> Bool # maximum :: Ord a => K1 i c a -> a # minimum :: Ord a => K1 i c a -> a # sum :: Num a => K1 i c a -> a # product :: Num a => K1 i c a -> a #
(Foldable f, Foldable g) => Foldable (f :+: g)	Since: base-4.9.0.0
Instance details Defined in Data.Foldable Methods fold :: Monoid m => (f :+: g) m -> m # foldMap :: Monoid m => (a -> m) -> (f :+: g) a -> m # foldr :: (a -> b -> b) -> b -> (f :+: g) a -> b # foldr' :: (a -> b -> b) -> b -> (f :+: g) a -> b # foldl :: (b -> a -> b) -> b -> (f :+: g) a -> b # foldl' :: (b -> a -> b) -> b -> (f :+: g) a -> b # foldr1 :: (a -> a -> a) -> (f :+: g) a -> a # foldl1 :: (a -> a -> a) -> (f :+: g) a -> a # toList :: (f :+: g) a -> [a] # null :: (f :+: g) a -> Bool # length :: (f :+: g) a -> Int # elem :: Eq a => a -> (f :+: g) a -> Bool # maximum :: Ord a => (f :+: g) a -> a # minimum :: Ord a => (f :+: g) a -> a # sum :: Num a => (f :+: g) a -> a # product :: Num a => (f :+: g) a -> a #
(Foldable f, Foldable g) => Foldable (f :*: g)	Since: base-4.9.0.0
Instance details Defined in Data.Foldable Methods fold :: Monoid m => (f :: g) m -> m # foldMap :: Monoid m => (a -> m) -> (f :: g) a -> m # foldr :: (a -> b -> b) -> b -> (f :: g) a -> b # foldr' :: (a -> b -> b) -> b -> (f :: g) a -> b # foldl :: (b -> a -> b) -> b -> (f :: g) a -> b # foldl' :: (b -> a -> b) -> b -> (f :: g) a -> b # foldr1 :: (a -> a -> a) -> (f :: g) a -> a # foldl1 :: (a -> a -> a) -> (f :: g) a -> a # toList :: (f :: g) a -> [a] # null :: (f :: g) a -> Bool # length :: (f :: g) a -> Int # elem :: Eq a => a -> (f :: g) a -> Bool # maximum :: Ord a => (f :: g) a -> a # minimum :: Ord a => (f :: g) a -> a # sum :: Num a => (f :: g) a -> a # product :: Num a => (f :: g) a -> a #
(Foldable f, Foldable g) => Foldable (Product f g)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Product Methods fold :: Monoid m => Product f g m -> m # foldMap :: Monoid m => (a -> m) -> Product f g a -> m # foldr :: (a -> b -> b) -> b -> Product f g a -> b # foldr' :: (a -> b -> b) -> b -> Product f g a -> b # foldl :: (b -> a -> b) -> b -> Product f g a -> b # foldl' :: (b -> a -> b) -> b -> Product f g a -> b # foldr1 :: (a -> a -> a) -> Product f g a -> a # foldl1 :: (a -> a -> a) -> Product f g a -> a # toList :: Product f g a -> [a] # null :: Product f g a -> Bool # length :: Product f g a -> Int # elem :: Eq a => a -> Product f g a -> Bool # maximum :: Ord a => Product f g a -> a # minimum :: Ord a => Product f g a -> a # sum :: Num a => Product f g a -> a # product :: Num a => Product f g a -> a #
(Foldable f, Foldable g) => Foldable (Sum f g)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Sum Methods fold :: Monoid m => Sum f g m -> m # foldMap :: Monoid m => (a -> m) -> Sum f g a -> m # foldr :: (a -> b -> b) -> b -> Sum f g a -> b # foldr' :: (a -> b -> b) -> b -> Sum f g a -> b # foldl :: (b -> a -> b) -> b -> Sum f g a -> b # foldl' :: (b -> a -> b) -> b -> Sum f g a -> b # foldr1 :: (a -> a -> a) -> Sum f g a -> a # foldl1 :: (a -> a -> a) -> Sum f g a -> a # toList :: Sum f g a -> [a] # null :: Sum f g a -> Bool # length :: Sum f g a -> Int # elem :: Eq a => a -> Sum f g a -> Bool # maximum :: Ord a => Sum f g a -> a # minimum :: Ord a => Sum f g a -> a # sum :: Num a => Sum f g a -> a # product :: Num a => Sum f g a -> a #
Foldable f => Foldable (M1 i c f)	Since: base-4.9.0.0
Instance details Defined in Data.Foldable Methods fold :: Monoid m => M1 i c f m -> m # foldMap :: Monoid m => (a -> m) -> M1 i c f a -> m # foldr :: (a -> b -> b) -> b -> M1 i c f a -> b # foldr' :: (a -> b -> b) -> b -> M1 i c f a -> b # foldl :: (b -> a -> b) -> b -> M1 i c f a -> b # foldl' :: (b -> a -> b) -> b -> M1 i c f a -> b # foldr1 :: (a -> a -> a) -> M1 i c f a -> a # foldl1 :: (a -> a -> a) -> M1 i c f a -> a # toList :: M1 i c f a -> [a] # null :: M1 i c f a -> Bool # length :: M1 i c f a -> Int # elem :: Eq a => a -> M1 i c f a -> Bool # maximum :: Ord a => M1 i c f a -> a # minimum :: Ord a => M1 i c f a -> a # sum :: Num a => M1 i c f a -> a # product :: Num a => M1 i c f a -> a #
(Foldable f, Foldable g) => Foldable (f :.: g)	Since: base-4.9.0.0
Instance details Defined in Data.Foldable Methods fold :: Monoid m => (f :.: g) m -> m # foldMap :: Monoid m => (a -> m) -> (f :.: g) a -> m # foldr :: (a -> b -> b) -> b -> (f :.: g) a -> b # foldr' :: (a -> b -> b) -> b -> (f :.: g) a -> b # foldl :: (b -> a -> b) -> b -> (f :.: g) a -> b # foldl' :: (b -> a -> b) -> b -> (f :.: g) a -> b # foldr1 :: (a -> a -> a) -> (f :.: g) a -> a # foldl1 :: (a -> a -> a) -> (f :.: g) a -> a # toList :: (f :.: g) a -> [a] # null :: (f :.: g) a -> Bool # length :: (f :.: g) a -> Int # elem :: Eq a => a -> (f :.: g) a -> Bool # maximum :: Ord a => (f :.: g) a -> a # minimum :: Ord a => (f :.: g) a -> a # sum :: Num a => (f :.: g) a -> a # product :: Num a => (f :.: g) a -> a #
(Foldable f, Foldable g) => Foldable (Compose f g)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Compose Methods fold :: Monoid m => Compose f g m -> m # foldMap :: Monoid m => (a -> m) -> Compose f g a -> m # foldr :: (a -> b -> b) -> b -> Compose f g a -> b # foldr' :: (a -> b -> b) -> b -> Compose f g a -> b # foldl :: (b -> a -> b) -> b -> Compose f g a -> b # foldl' :: (b -> a -> b) -> b -> Compose f g a -> b # foldr1 :: (a -> a -> a) -> Compose f g a -> a # foldl1 :: (a -> a -> a) -> Compose f g a -> a # toList :: Compose f g a -> [a] # null :: Compose f g a -> Bool # length :: Compose f g a -> Int # elem :: Eq a => a -> Compose f g a -> Bool # maximum :: Ord a => Compose f g a -> a # minimum :: Ord a => Compose f g a -> a # sum :: Num a => Compose f g a -> a # product :: Num a => Compose f g a -> a #

class (Functor t, Foldable t) => Traversable (t :: Type -> Type) where #

Functors representing data structures that can be traversed from left to right.

A definition of traverse must satisfy the following laws:

naturality: t . traverse f = traverse (t . f) for every applicative transformation t
identity: traverse Identity = Identity
composition: traverse (Compose . fmap g . f) = Compose . fmap (traverse g) . traverse f

A definition of sequenceA must satisfy the following laws:

naturality: t . sequenceA = sequenceA . fmap t for every applicative transformation t
identity: sequenceA . fmap Identity = Identity
composition: sequenceA . fmap Compose = Compose . fmap sequenceA . sequenceA

where an applicative transformation is a function

t :: (Applicative f, Applicative g) => f a -> g a

preserving the Applicative operations, i.e.

```
t (pure x) = pure x
```
```
t (x <*> y) = t x <*> t y
```

and the identity functor Identity and composition of functors Compose are defined as

  newtype Identity a = Identity a

  instance Functor Identity where
    fmap f (Identity x) = Identity (f x)

  instance Applicative Identity where
    pure x = Identity x
    Identity f <*> Identity x = Identity (f x)

  newtype Compose f g a = Compose (f (g a))

  instance (Functor f, Functor g) => Functor (Compose f g) where
    fmap f (Compose x) = Compose (fmap (fmap f) x)

  instance (Applicative f, Applicative g) => Applicative (Compose f g) where
    pure x = Compose (pure (pure x))
    Compose f <*> Compose x = Compose ((<*>) <$> f <*> x)

(The naturality law is implied by parametricity.)

Instances are similar to Functor, e.g. given a data type

data Tree a = Empty | Leaf a | Node (Tree a) a (Tree a)

a suitable instance would be

instance Traversable Tree where
   traverse f Empty = pure Empty
   traverse f (Leaf x) = Leaf <$> f x
   traverse f (Node l k r) = Node <$> traverse f l <*> f k <*> traverse f r

This is suitable even for abstract types, as the laws for <*> imply a form of associativity.

The superclass instances should satisfy the following:

In the Functor instance, fmap should be equivalent to traversal with the identity applicative functor (fmapDefault).
In the Foldable instance, foldMap should be equivalent to traversal with a constant applicative functor (foldMapDefault).

Minimal complete definition

traverse | sequenceA

Methods

traverse :: Applicative f => (a -> f b) -> t a -> f (t b) #

Map each element of a structure to an action, evaluate these actions from left to right, and collect the results. For a version that ignores the results see traverse_.

sequenceA :: Applicative f => t (f a) -> f (t a) #

Evaluate each action in the structure from left to right, and collect the results. For a version that ignores the results see sequenceA_.

mapM :: Monad m => (a -> m b) -> t a -> m (t b) #

Map each element of a structure to a monadic action, evaluate these actions from left to right, and collect the results. For a version that ignores the results see mapM_.

sequence :: Monad m => t (m a) -> m (t a) #

Evaluate each monadic action in the structure from left to right, and collect the results. For a version that ignores the results see sequence_.

Instances

Traversable []	Since: base-2.1
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> [a] -> f [b] # sequenceA :: Applicative f => [f a] -> f [a] # mapM :: Monad m => (a -> m b) -> [a] -> m [b] # sequence :: Monad m => [m a] -> m [a] #
Traversable Maybe	Since: base-2.1
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> Maybe a -> f (Maybe b) # sequenceA :: Applicative f => Maybe (f a) -> f (Maybe a) # mapM :: Monad m => (a -> m b) -> Maybe a -> m (Maybe b) # sequence :: Monad m => Maybe (m a) -> m (Maybe a) #
Traversable Par1	Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> Par1 a -> f (Par1 b) # sequenceA :: Applicative f => Par1 (f a) -> f (Par1 a) # mapM :: Monad m => (a -> m b) -> Par1 a -> m (Par1 b) # sequence :: Monad m => Par1 (m a) -> m (Par1 a) #
Traversable Complex	Since: base-4.9.0.0
Instance details Defined in Data.Complex Methods traverse :: Applicative f => (a -> f b) -> Complex a -> f (Complex b) # sequenceA :: Applicative f => Complex (f a) -> f (Complex a) # mapM :: Monad m => (a -> m b) -> Complex a -> m (Complex b) # sequence :: Monad m => Complex (m a) -> m (Complex a) #
Traversable Min	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods traverse :: Applicative f => (a -> f b) -> Min a -> f (Min b) # sequenceA :: Applicative f => Min (f a) -> f (Min a) # mapM :: Monad m => (a -> m b) -> Min a -> m (Min b) # sequence :: Monad m => Min (m a) -> m (Min a) #
Traversable Max	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods traverse :: Applicative f => (a -> f b) -> Max a -> f (Max b) # sequenceA :: Applicative f => Max (f a) -> f (Max a) # mapM :: Monad m => (a -> m b) -> Max a -> m (Max b) # sequence :: Monad m => Max (m a) -> m (Max a) #
Traversable First	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods traverse :: Applicative f => (a -> f b) -> First a -> f (First b) # sequenceA :: Applicative f => First (f a) -> f (First a) # mapM :: Monad m => (a -> m b) -> First a -> m (First b) # sequence :: Monad m => First (m a) -> m (First a) #
Traversable Last	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods traverse :: Applicative f => (a -> f b) -> Last a -> f (Last b) # sequenceA :: Applicative f => Last (f a) -> f (Last a) # mapM :: Monad m => (a -> m b) -> Last a -> m (Last b) # sequence :: Monad m => Last (m a) -> m (Last a) #
Traversable Option	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods traverse :: Applicative f => (a -> f b) -> Option a -> f (Option b) # sequenceA :: Applicative f => Option (f a) -> f (Option a) # mapM :: Monad m => (a -> m b) -> Option a -> m (Option b) # sequence :: Monad m => Option (m a) -> m (Option a) #
Traversable ZipList	Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> ZipList a -> f (ZipList b) # sequenceA :: Applicative f => ZipList (f a) -> f (ZipList a) # mapM :: Monad m => (a -> m b) -> ZipList a -> m (ZipList b) # sequence :: Monad m => ZipList (m a) -> m (ZipList a) #
Traversable Identity	Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> Identity a -> f (Identity b) # sequenceA :: Applicative f => Identity (f a) -> f (Identity a) # mapM :: Monad m => (a -> m b) -> Identity a -> m (Identity b) # sequence :: Monad m => Identity (m a) -> m (Identity a) #
Traversable First	Since: base-4.8.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> First a -> f (First b) # sequenceA :: Applicative f => First (f a) -> f (First a) # mapM :: Monad m => (a -> m b) -> First a -> m (First b) # sequence :: Monad m => First (m a) -> m (First a) #
Traversable Last	Since: base-4.8.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> Last a -> f (Last b) # sequenceA :: Applicative f => Last (f a) -> f (Last a) # mapM :: Monad m => (a -> m b) -> Last a -> m (Last b) # sequence :: Monad m => Last (m a) -> m (Last a) #
Traversable Dual	Since: base-4.8.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> Dual a -> f (Dual b) # sequenceA :: Applicative f => Dual (f a) -> f (Dual a) # mapM :: Monad m => (a -> m b) -> Dual a -> m (Dual b) # sequence :: Monad m => Dual (m a) -> m (Dual a) #
Traversable Sum	Since: base-4.8.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> Sum a -> f (Sum b) # sequenceA :: Applicative f => Sum (f a) -> f (Sum a) # mapM :: Monad m => (a -> m b) -> Sum a -> m (Sum b) # sequence :: Monad m => Sum (m a) -> m (Sum a) #
Traversable Product	Since: base-4.8.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> Product a -> f (Product b) # sequenceA :: Applicative f => Product (f a) -> f (Product a) # mapM :: Monad m => (a -> m b) -> Product a -> m (Product b) # sequence :: Monad m => Product (m a) -> m (Product a) #
Traversable Down	Since: base-4.12.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> Down a -> f (Down b) # sequenceA :: Applicative f => Down (f a) -> f (Down a) # mapM :: Monad m => (a -> m b) -> Down a -> m (Down b) # sequence :: Monad m => Down (m a) -> m (Down a) #
Traversable NonEmpty	Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> NonEmpty a -> f (NonEmpty b) # sequenceA :: Applicative f => NonEmpty (f a) -> f (NonEmpty a) # mapM :: Monad m => (a -> m b) -> NonEmpty a -> m (NonEmpty b) # sequence :: Monad m => NonEmpty (m a) -> m (NonEmpty a) #
Traversable SmallArray
Instance details Defined in Data.Primitive.SmallArray Methods traverse :: Applicative f => (a -> f b) -> SmallArray a -> f (SmallArray b) # sequenceA :: Applicative f => SmallArray (f a) -> f (SmallArray a) # mapM :: Monad m => (a -> m b) -> SmallArray a -> m (SmallArray b) # sequence :: Monad m => SmallArray (m a) -> m (SmallArray a) #
Traversable Array
Instance details Defined in Data.Primitive.Array Methods traverse :: Applicative f => (a -> f b) -> Array a -> f (Array b) # sequenceA :: Applicative f => Array (f a) -> f (Array a) # mapM :: Monad m => (a -> m b) -> Array a -> m (Array b) # sequence :: Monad m => Array (m a) -> m (Array a) #
Traversable (Either a)	Since: base-4.7.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a0 -> f b) -> Either a a0 -> f (Either a b) # sequenceA :: Applicative f => Either a (f a0) -> f (Either a a0) # mapM :: Monad m => (a0 -> m b) -> Either a a0 -> m (Either a b) # sequence :: Monad m => Either a (m a0) -> m (Either a a0) #
Traversable (V1 :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> V1 a -> f (V1 b) # sequenceA :: Applicative f => V1 (f a) -> f (V1 a) # mapM :: Monad m => (a -> m b) -> V1 a -> m (V1 b) # sequence :: Monad m => V1 (m a) -> m (V1 a) #
Traversable (U1 :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> U1 a -> f (U1 b) # sequenceA :: Applicative f => U1 (f a) -> f (U1 a) # mapM :: Monad m => (a -> m b) -> U1 a -> m (U1 b) # sequence :: Monad m => U1 (m a) -> m (U1 a) #
Traversable ((,) a)	Since: base-4.7.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a0 -> f b) -> (a, a0) -> f (a, b) # sequenceA :: Applicative f => (a, f a0) -> f (a, a0) # mapM :: Monad m => (a0 -> m b) -> (a, a0) -> m (a, b) # sequence :: Monad m => (a, m a0) -> m (a, a0) #
Ix i => Traversable (Array i)	Since: base-2.1
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> Array i a -> f (Array i b) # sequenceA :: Applicative f => Array i (f a) -> f (Array i a) # mapM :: Monad m => (a -> m b) -> Array i a -> m (Array i b) # sequence :: Monad m => Array i (m a) -> m (Array i a) #
Traversable (Arg a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods traverse :: Applicative f => (a0 -> f b) -> Arg a a0 -> f (Arg a b) # sequenceA :: Applicative f => Arg a (f a0) -> f (Arg a a0) # mapM :: Monad m => (a0 -> m b) -> Arg a a0 -> m (Arg a b) # sequence :: Monad m => Arg a (m a0) -> m (Arg a a0) #
Traversable (Proxy :: Type -> Type)	Since: base-4.7.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> Proxy a -> f (Proxy b) # sequenceA :: Applicative f => Proxy (f a) -> f (Proxy a) # mapM :: Monad m => (a -> m b) -> Proxy a -> m (Proxy b) # sequence :: Monad m => Proxy (m a) -> m (Proxy a) #
Traversable f => Traversable (MaybeT f)
Instance details Defined in Control.Monad.Trans.Maybe Methods traverse :: Applicative f0 => (a -> f0 b) -> MaybeT f a -> f0 (MaybeT f b) # sequenceA :: Applicative f0 => MaybeT f (f0 a) -> f0 (MaybeT f a) # mapM :: Monad m => (a -> m b) -> MaybeT f a -> m (MaybeT f b) # sequence :: Monad m => MaybeT f (m a) -> m (MaybeT f a) #
Traversable f => Traversable (ListT f)
Instance details Defined in Control.Monad.Trans.List Methods traverse :: Applicative f0 => (a -> f0 b) -> ListT f a -> f0 (ListT f b) # sequenceA :: Applicative f0 => ListT f (f0 a) -> f0 (ListT f a) # mapM :: Monad m => (a -> m b) -> ListT f a -> m (ListT f b) # sequence :: Monad m => ListT f (m a) -> m (ListT f a) #
Traversable f => Traversable (Rec1 f)	Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f0 => (a -> f0 b) -> Rec1 f a -> f0 (Rec1 f b) # sequenceA :: Applicative f0 => Rec1 f (f0 a) -> f0 (Rec1 f a) # mapM :: Monad m => (a -> m b) -> Rec1 f a -> m (Rec1 f b) # sequence :: Monad m => Rec1 f (m a) -> m (Rec1 f a) #
Traversable (URec Char :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> URec Char a -> f (URec Char b) # sequenceA :: Applicative f => URec Char (f a) -> f (URec Char a) # mapM :: Monad m => (a -> m b) -> URec Char a -> m (URec Char b) # sequence :: Monad m => URec Char (m a) -> m (URec Char a) #
Traversable (URec Double :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> URec Double a -> f (URec Double b) # sequenceA :: Applicative f => URec Double (f a) -> f (URec Double a) # mapM :: Monad m => (a -> m b) -> URec Double a -> m (URec Double b) # sequence :: Monad m => URec Double (m a) -> m (URec Double a) #
Traversable (URec Float :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> URec Float a -> f (URec Float b) # sequenceA :: Applicative f => URec Float (f a) -> f (URec Float a) # mapM :: Monad m => (a -> m b) -> URec Float a -> m (URec Float b) # sequence :: Monad m => URec Float (m a) -> m (URec Float a) #
Traversable (URec Int :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> URec Int a -> f (URec Int b) # sequenceA :: Applicative f => URec Int (f a) -> f (URec Int a) # mapM :: Monad m => (a -> m b) -> URec Int a -> m (URec Int b) # sequence :: Monad m => URec Int (m a) -> m (URec Int a) #
Traversable (URec Word :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> URec Word a -> f (URec Word b) # sequenceA :: Applicative f => URec Word (f a) -> f (URec Word a) # mapM :: Monad m => (a -> m b) -> URec Word a -> m (URec Word b) # sequence :: Monad m => URec Word (m a) -> m (URec Word a) #
Traversable (URec (Ptr ()) :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> URec (Ptr ()) a -> f (URec (Ptr ()) b) # sequenceA :: Applicative f => URec (Ptr ()) (f a) -> f (URec (Ptr ()) a) # mapM :: Monad m => (a -> m b) -> URec (Ptr ()) a -> m (URec (Ptr ()) b) # sequence :: Monad m => URec (Ptr ()) (m a) -> m (URec (Ptr ()) a) #
Traversable (Const m :: Type -> Type)	Since: base-4.7.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> Const m a -> f (Const m b) # sequenceA :: Applicative f => Const m (f a) -> f (Const m a) # mapM :: Monad m0 => (a -> m0 b) -> Const m a -> m0 (Const m b) # sequence :: Monad m0 => Const m (m0 a) -> m0 (Const m a) #
Traversable f => Traversable (Ap f)	Since: base-4.12.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f0 => (a -> f0 b) -> Ap f a -> f0 (Ap f b) # sequenceA :: Applicative f0 => Ap f (f0 a) -> f0 (Ap f a) # mapM :: Monad m => (a -> m b) -> Ap f a -> m (Ap f b) # sequence :: Monad m => Ap f (m a) -> m (Ap f a) #
Traversable f => Traversable (Alt f)	Since: base-4.12.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f0 => (a -> f0 b) -> Alt f a -> f0 (Alt f b) # sequenceA :: Applicative f0 => Alt f (f0 a) -> f0 (Alt f a) # mapM :: Monad m => (a -> m b) -> Alt f a -> m (Alt f b) # sequence :: Monad m => Alt f (m a) -> m (Alt f a) #
Traversable f => Traversable (WriterT w f)
Instance details Defined in Control.Monad.Trans.Writer.Strict Methods traverse :: Applicative f0 => (a -> f0 b) -> WriterT w f a -> f0 (WriterT w f b) # sequenceA :: Applicative f0 => WriterT w f (f0 a) -> f0 (WriterT w f a) # mapM :: Monad m => (a -> m b) -> WriterT w f a -> m (WriterT w f b) # sequence :: Monad m => WriterT w f (m a) -> m (WriterT w f a) #
Traversable f => Traversable (WriterT w f)
Instance details Defined in Control.Monad.Trans.Writer.Lazy Methods traverse :: Applicative f0 => (a -> f0 b) -> WriterT w f a -> f0 (WriterT w f b) # sequenceA :: Applicative f0 => WriterT w f (f0 a) -> f0 (WriterT w f a) # mapM :: Monad m => (a -> m b) -> WriterT w f a -> m (WriterT w f b) # sequence :: Monad m => WriterT w f (m a) -> m (WriterT w f a) #
Traversable f => Traversable (IdentityT f)
Instance details Defined in Control.Monad.Trans.Identity Methods traverse :: Applicative f0 => (a -> f0 b) -> IdentityT f a -> f0 (IdentityT f b) # sequenceA :: Applicative f0 => IdentityT f (f0 a) -> f0 (IdentityT f a) # mapM :: Monad m => (a -> m b) -> IdentityT f a -> m (IdentityT f b) # sequence :: Monad m => IdentityT f (m a) -> m (IdentityT f a) #
Traversable f => Traversable (ExceptT e f)
Instance details Defined in Control.Monad.Trans.Except Methods traverse :: Applicative f0 => (a -> f0 b) -> ExceptT e f a -> f0 (ExceptT e f b) # sequenceA :: Applicative f0 => ExceptT e f (f0 a) -> f0 (ExceptT e f a) # mapM :: Monad m => (a -> m b) -> ExceptT e f a -> m (ExceptT e f b) # sequence :: Monad m => ExceptT e f (m a) -> m (ExceptT e f a) #
Traversable f => Traversable (ErrorT e f)
Instance details Defined in Control.Monad.Trans.Error Methods traverse :: Applicative f0 => (a -> f0 b) -> ErrorT e f a -> f0 (ErrorT e f b) # sequenceA :: Applicative f0 => ErrorT e f (f0 a) -> f0 (ErrorT e f a) # mapM :: Monad m => (a -> m b) -> ErrorT e f a -> m (ErrorT e f b) # sequence :: Monad m => ErrorT e f (m a) -> m (ErrorT e f a) #
Traversable (K1 i c :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> K1 i c a -> f (K1 i c b) # sequenceA :: Applicative f => K1 i c (f a) -> f (K1 i c a) # mapM :: Monad m => (a -> m b) -> K1 i c a -> m (K1 i c b) # sequence :: Monad m => K1 i c (m a) -> m (K1 i c a) #
(Traversable f, Traversable g) => Traversable (f :+: g)	Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f0 => (a -> f0 b) -> (f :+: g) a -> f0 ((f :+: g) b) # sequenceA :: Applicative f0 => (f :+: g) (f0 a) -> f0 ((f :+: g) a) # mapM :: Monad m => (a -> m b) -> (f :+: g) a -> m ((f :+: g) b) # sequence :: Monad m => (f :+: g) (m a) -> m ((f :+: g) a) #
(Traversable f, Traversable g) => Traversable (f :*: g)	Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f0 => (a -> f0 b) -> (f :: g) a -> f0 ((f :: g) b) # sequenceA :: Applicative f0 => (f :: g) (f0 a) -> f0 ((f :: g) a) # mapM :: Monad m => (a -> m b) -> (f :: g) a -> m ((f :: g) b) # sequence :: Monad m => (f :: g) (m a) -> m ((f :: g) a) #
(Traversable f, Traversable g) => Traversable (Product f g)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Product Methods traverse :: Applicative f0 => (a -> f0 b) -> Product f g a -> f0 (Product f g b) # sequenceA :: Applicative f0 => Product f g (f0 a) -> f0 (Product f g a) # mapM :: Monad m => (a -> m b) -> Product f g a -> m (Product f g b) # sequence :: Monad m => Product f g (m a) -> m (Product f g a) #
(Traversable f, Traversable g) => Traversable (Sum f g)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Sum Methods traverse :: Applicative f0 => (a -> f0 b) -> Sum f g a -> f0 (Sum f g b) # sequenceA :: Applicative f0 => Sum f g (f0 a) -> f0 (Sum f g a) # mapM :: Monad m => (a -> m b) -> Sum f g a -> m (Sum f g b) # sequence :: Monad m => Sum f g (m a) -> m (Sum f g a) #
Traversable f => Traversable (M1 i c f)	Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f0 => (a -> f0 b) -> M1 i c f a -> f0 (M1 i c f b) # sequenceA :: Applicative f0 => M1 i c f (f0 a) -> f0 (M1 i c f a) # mapM :: Monad m => (a -> m b) -> M1 i c f a -> m (M1 i c f b) # sequence :: Monad m => M1 i c f (m a) -> m (M1 i c f a) #
(Traversable f, Traversable g) => Traversable (f :.: g)	Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f0 => (a -> f0 b) -> (f :.: g) a -> f0 ((f :.: g) b) # sequenceA :: Applicative f0 => (f :.: g) (f0 a) -> f0 ((f :.: g) a) # mapM :: Monad m => (a -> m b) -> (f :.: g) a -> m ((f :.: g) b) # sequence :: Monad m => (f :.: g) (m a) -> m ((f :.: g) a) #
(Traversable f, Traversable g) => Traversable (Compose f g)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Compose Methods traverse :: Applicative f0 => (a -> f0 b) -> Compose f g a -> f0 (Compose f g b) # sequenceA :: Applicative f0 => Compose f g (f0 a) -> f0 (Compose f g a) # mapM :: Monad m => (a -> m b) -> Compose f g a -> m (Compose f g b) # sequence :: Monad m => Compose f g (m a) -> m (Compose f g a) #

class Semigroup a where #

The class of semigroups (types with an associative binary operation).

Instances should satisfy the associativity law:

```
x <> (y <> z) = (x <> y) <> z
```

Since: base-4.9.0.0

Methods

(<>) :: a -> a -> a infixr 6 #

An associative operation.

Instances

Semigroup Ordering	Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods (<>) :: Ordering -> Ordering -> Ordering # sconcat :: NonEmpty Ordering -> Ordering # stimes :: Integral b => b -> Ordering -> Ordering #
Semigroup ()	Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods (<>) :: () -> () -> () # sconcat :: NonEmpty () -> () # stimes :: Integral b => b -> () -> () #
Semigroup Void	Since: base-4.9.0.0
Instance details Defined in Data.Void Methods (<>) :: Void -> Void -> Void # sconcat :: NonEmpty Void -> Void # stimes :: Integral b => b -> Void -> Void #
Semigroup All	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup.Internal Methods (<>) :: All -> All -> All # sconcat :: NonEmpty All -> All # stimes :: Integral b => b -> All -> All #
Semigroup Any	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup.Internal Methods (<>) :: Any -> Any -> Any # sconcat :: NonEmpty Any -> Any # stimes :: Integral b => b -> Any -> Any #
Semigroup ExactPi	The multiplicative semigroup over `Rational`s augmented with multiples of `pi`.
Instance details Defined in Data.ExactPi Methods (<>) :: ExactPi -> ExactPi -> ExactPi # sconcat :: NonEmpty ExactPi -> ExactPi # stimes :: Integral b => b -> ExactPi -> ExactPi #
Semigroup ByteArray
Instance details Defined in Data.Primitive.ByteArray Methods (<>) :: ByteArray -> ByteArray -> ByteArray # sconcat :: NonEmpty ByteArray -> ByteArray # stimes :: Integral b => b -> ByteArray -> ByteArray #
Semigroup Dimension' Source #
Instance details Defined in Numeric.Units.Dimensional.Dimensions.TermLevel Methods (<>) :: Dimension' -> Dimension' -> Dimension' # sconcat :: NonEmpty Dimension' -> Dimension' # stimes :: Integral b => b -> Dimension' -> Dimension' #
Semigroup AnyUnit Source #	`AnyUnit`s form a `Semigroup` under multiplication.
Instance details Defined in Numeric.Units.Dimensional.Dynamic Methods (<>) :: AnyUnit -> AnyUnit -> AnyUnit # sconcat :: NonEmpty AnyUnit -> AnyUnit # stimes :: Integral b => b -> AnyUnit -> AnyUnit #
Semigroup [a]	Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods (<>) :: [a] -> [a] -> [a] # sconcat :: NonEmpty [a] -> [a] # stimes :: Integral b => b -> [a] -> [a] #
Semigroup a => Semigroup (Maybe a)	Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods (<>) :: Maybe a -> Maybe a -> Maybe a # sconcat :: NonEmpty (Maybe a) -> Maybe a # stimes :: Integral b => b -> Maybe a -> Maybe a #
Semigroup a => Semigroup (IO a)	Since: base-4.10.0.0
Instance details Defined in GHC.Base Methods (<>) :: IO a -> IO a -> IO a # sconcat :: NonEmpty (IO a) -> IO a # stimes :: Integral b => b -> IO a -> IO a #
Semigroup p => Semigroup (Par1 p)	Since: base-4.12.0.0
Instance details Defined in GHC.Generics Methods (<>) :: Par1 p -> Par1 p -> Par1 p # sconcat :: NonEmpty (Par1 p) -> Par1 p # stimes :: Integral b => b -> Par1 p -> Par1 p #
Ord a => Semigroup (Min a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods (<>) :: Min a -> Min a -> Min a # sconcat :: NonEmpty (Min a) -> Min a # stimes :: Integral b => b -> Min a -> Min a #
Ord a => Semigroup (Max a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods (<>) :: Max a -> Max a -> Max a # sconcat :: NonEmpty (Max a) -> Max a # stimes :: Integral b => b -> Max a -> Max a #
Semigroup (First a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods (<>) :: First a -> First a -> First a # sconcat :: NonEmpty (First a) -> First a # stimes :: Integral b => b -> First a -> First a #
Semigroup (Last a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods (<>) :: Last a -> Last a -> Last a # sconcat :: NonEmpty (Last a) -> Last a # stimes :: Integral b => b -> Last a -> Last a #
Monoid m => Semigroup (WrappedMonoid m)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods (<>) :: WrappedMonoid m -> WrappedMonoid m -> WrappedMonoid m # sconcat :: NonEmpty (WrappedMonoid m) -> WrappedMonoid m # stimes :: Integral b => b -> WrappedMonoid m -> WrappedMonoid m #
Semigroup a => Semigroup (Option a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods (<>) :: Option a -> Option a -> Option a # sconcat :: NonEmpty (Option a) -> Option a # stimes :: Integral b => b -> Option a -> Option a #
Semigroup a => Semigroup (Identity a)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Identity Methods (<>) :: Identity a -> Identity a -> Identity a # sconcat :: NonEmpty (Identity a) -> Identity a # stimes :: Integral b => b -> Identity a -> Identity a #
Semigroup (First a)	Since: base-4.9.0.0
Instance details Defined in Data.Monoid Methods (<>) :: First a -> First a -> First a # sconcat :: NonEmpty (First a) -> First a # stimes :: Integral b => b -> First a -> First a #
Semigroup (Last a)	Since: base-4.9.0.0
Instance details Defined in Data.Monoid Methods (<>) :: Last a -> Last a -> Last a # sconcat :: NonEmpty (Last a) -> Last a # stimes :: Integral b => b -> Last a -> Last a #
Semigroup a => Semigroup (Dual a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup.Internal Methods (<>) :: Dual a -> Dual a -> Dual a # sconcat :: NonEmpty (Dual a) -> Dual a # stimes :: Integral b => b -> Dual a -> Dual a #
Semigroup (Endo a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup.Internal Methods (<>) :: Endo a -> Endo a -> Endo a # sconcat :: NonEmpty (Endo a) -> Endo a # stimes :: Integral b => b -> Endo a -> Endo a #
Num a => Semigroup (Sum a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup.Internal Methods (<>) :: Sum a -> Sum a -> Sum a # sconcat :: NonEmpty (Sum a) -> Sum a # stimes :: Integral b => b -> Sum a -> Sum a #
Num a => Semigroup (Product a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup.Internal Methods (<>) :: Product a -> Product a -> Product a # sconcat :: NonEmpty (Product a) -> Product a # stimes :: Integral b => b -> Product a -> Product a #
Semigroup a => Semigroup (Down a)	Since: base-4.11.0.0
Instance details Defined in Data.Ord Methods (<>) :: Down a -> Down a -> Down a # sconcat :: NonEmpty (Down a) -> Down a # stimes :: Integral b => b -> Down a -> Down a #
Semigroup (NonEmpty a)	Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods (<>) :: NonEmpty a -> NonEmpty a -> NonEmpty a # sconcat :: NonEmpty (NonEmpty a) -> NonEmpty a # stimes :: Integral b => b -> NonEmpty a -> NonEmpty a #
PrimUnlifted a => Semigroup (UnliftedArray a)	Since: primitive-0.6.4.0
Instance details Defined in Data.Primitive.UnliftedArray Methods (<>) :: UnliftedArray a -> UnliftedArray a -> UnliftedArray a # sconcat :: NonEmpty (UnliftedArray a) -> UnliftedArray a # stimes :: Integral b => b -> UnliftedArray a -> UnliftedArray a #
Semigroup (PrimArray a)	Since: primitive-0.6.4.0
Instance details Defined in Data.Primitive.PrimArray Methods (<>) :: PrimArray a -> PrimArray a -> PrimArray a # sconcat :: NonEmpty (PrimArray a) -> PrimArray a # stimes :: Integral b => b -> PrimArray a -> PrimArray a #
Semigroup (SmallArray a)	Since: primitive-0.6.3.0
Instance details Defined in Data.Primitive.SmallArray Methods (<>) :: SmallArray a -> SmallArray a -> SmallArray a # sconcat :: NonEmpty (SmallArray a) -> SmallArray a # stimes :: Integral b => b -> SmallArray a -> SmallArray a #
Semigroup (Array a)	Since: primitive-0.6.3.0
Instance details Defined in Data.Primitive.Array Methods (<>) :: Array a -> Array a -> Array a # sconcat :: NonEmpty (Array a) -> Array a # stimes :: Integral b => b -> Array a -> Array a #
Prim a => Semigroup (Vector a)
Instance details Defined in Data.Vector.Primitive Methods (<>) :: Vector a -> Vector a -> Vector a # sconcat :: NonEmpty (Vector a) -> Vector a # stimes :: Integral b => b -> Vector a -> Vector a #
Num a => Semigroup (DynQuantity a) Source #	`DynQuantity`s form a `Semigroup` under multiplication, but not under addition because they may not be added together if their dimensions do not match.
Instance details Defined in Numeric.Units.Dimensional.Dynamic Methods (<>) :: DynQuantity a -> DynQuantity a -> DynQuantity a # sconcat :: NonEmpty (DynQuantity a) -> DynQuantity a # stimes :: Integral b => b -> DynQuantity a -> DynQuantity a #
Num a => Semigroup (AnyQuantity a) Source #	`AnyQuantity`s form a `Semigroup` under multiplication, but not under addition because they may not be added together if their dimensions do not match.
Instance details Defined in Numeric.Units.Dimensional.Dynamic Methods (<>) :: AnyQuantity a -> AnyQuantity a -> AnyQuantity a # sconcat :: NonEmpty (AnyQuantity a) -> AnyQuantity a # stimes :: Integral b => b -> AnyQuantity a -> AnyQuantity a #
Semigroup b => Semigroup (a -> b)	Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods (<>) :: (a -> b) -> (a -> b) -> a -> b # sconcat :: NonEmpty (a -> b) -> a -> b # stimes :: Integral b0 => b0 -> (a -> b) -> a -> b #
Semigroup (Either a b)	Since: base-4.9.0.0
Instance details Defined in Data.Either Methods (<>) :: Either a b -> Either a b -> Either a b # sconcat :: NonEmpty (Either a b) -> Either a b # stimes :: Integral b0 => b0 -> Either a b -> Either a b #
Semigroup (V1 p)	Since: base-4.12.0.0
Instance details Defined in GHC.Generics Methods (<>) :: V1 p -> V1 p -> V1 p # sconcat :: NonEmpty (V1 p) -> V1 p # stimes :: Integral b => b -> V1 p -> V1 p #
Semigroup (U1 p)	Since: base-4.12.0.0
Instance details Defined in GHC.Generics Methods (<>) :: U1 p -> U1 p -> U1 p # sconcat :: NonEmpty (U1 p) -> U1 p # stimes :: Integral b => b -> U1 p -> U1 p #
(Semigroup a, Semigroup b) => Semigroup (a, b)	Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods (<>) :: (a, b) -> (a, b) -> (a, b) # sconcat :: NonEmpty (a, b) -> (a, b) # stimes :: Integral b0 => b0 -> (a, b) -> (a, b) #
Semigroup a => Semigroup (ST s a)	Since: base-4.11.0.0
Instance details Defined in GHC.ST Methods (<>) :: ST s a -> ST s a -> ST s a # sconcat :: NonEmpty (ST s a) -> ST s a # stimes :: Integral b => b -> ST s a -> ST s a #
Semigroup (Proxy s)	Since: base-4.9.0.0
Instance details Defined in Data.Proxy Methods (<>) :: Proxy s -> Proxy s -> Proxy s # sconcat :: NonEmpty (Proxy s) -> Proxy s # stimes :: Integral b => b -> Proxy s -> Proxy s #
Semigroup (f p) => Semigroup (Rec1 f p)	Since: base-4.12.0.0
Instance details Defined in GHC.Generics Methods (<>) :: Rec1 f p -> Rec1 f p -> Rec1 f p # sconcat :: NonEmpty (Rec1 f p) -> Rec1 f p # stimes :: Integral b => b -> Rec1 f p -> Rec1 f p #
(Semigroup a, Semigroup b, Semigroup c) => Semigroup (a, b, c)	Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods (<>) :: (a, b, c) -> (a, b, c) -> (a, b, c) # sconcat :: NonEmpty (a, b, c) -> (a, b, c) # stimes :: Integral b0 => b0 -> (a, b, c) -> (a, b, c) #
Semigroup a => Semigroup (Const a b)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Const Methods (<>) :: Const a b -> Const a b -> Const a b # sconcat :: NonEmpty (Const a b) -> Const a b # stimes :: Integral b0 => b0 -> Const a b -> Const a b #
(Applicative f, Semigroup a) => Semigroup (Ap f a)	Since: base-4.12.0.0
Instance details Defined in Data.Monoid Methods (<>) :: Ap f a -> Ap f a -> Ap f a # sconcat :: NonEmpty (Ap f a) -> Ap f a # stimes :: Integral b => b -> Ap f a -> Ap f a #
Alternative f => Semigroup (Alt f a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup.Internal Methods (<>) :: Alt f a -> Alt f a -> Alt f a # sconcat :: NonEmpty (Alt f a) -> Alt f a # stimes :: Integral b => b -> Alt f a -> Alt f a #
Num a => Semigroup (SQuantity s d a) Source #	`Quantity`s of a given `Dimension` form a `Semigroup` under addition.
Instance details Defined in Numeric.Units.Dimensional.Internal Methods (<>) :: SQuantity s d a -> SQuantity s d a -> SQuantity s d a # sconcat :: NonEmpty (SQuantity s d a) -> SQuantity s d a # stimes :: Integral b => b -> SQuantity s d a -> SQuantity s d a #
Semigroup c => Semigroup (K1 i c p)	Since: base-4.12.0.0
Instance details Defined in GHC.Generics Methods (<>) :: K1 i c p -> K1 i c p -> K1 i c p # sconcat :: NonEmpty (K1 i c p) -> K1 i c p # stimes :: Integral b => b -> K1 i c p -> K1 i c p #
(Semigroup (f p), Semigroup (g p)) => Semigroup ((f :*: g) p)	Since: base-4.12.0.0
Instance details Defined in GHC.Generics Methods (<>) :: (f :: g) p -> (f :: g) p -> (f :: g) p # sconcat :: NonEmpty ((f :: g) p) -> (f :: g) p # stimes :: Integral b => b -> (f :: g) p -> (f :*: g) p #
(Semigroup a, Semigroup b, Semigroup c, Semigroup d) => Semigroup (a, b, c, d)	Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods (<>) :: (a, b, c, d) -> (a, b, c, d) -> (a, b, c, d) # sconcat :: NonEmpty (a, b, c, d) -> (a, b, c, d) # stimes :: Integral b0 => b0 -> (a, b, c, d) -> (a, b, c, d) #
Semigroup (f p) => Semigroup (M1 i c f p)	Since: base-4.12.0.0
Instance details Defined in GHC.Generics Methods (<>) :: M1 i c f p -> M1 i c f p -> M1 i c f p # sconcat :: NonEmpty (M1 i c f p) -> M1 i c f p # stimes :: Integral b => b -> M1 i c f p -> M1 i c f p #
Semigroup (f (g p)) => Semigroup ((f :.: g) p)	Since: base-4.12.0.0
Instance details Defined in GHC.Generics Methods (<>) :: (f :.: g) p -> (f :.: g) p -> (f :.: g) p # sconcat :: NonEmpty ((f :.: g) p) -> (f :.: g) p # stimes :: Integral b => b -> (f :.: g) p -> (f :.: g) p #
(Semigroup a, Semigroup b, Semigroup c, Semigroup d, Semigroup e) => Semigroup (a, b, c, d, e)	Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods (<>) :: (a, b, c, d, e) -> (a, b, c, d, e) -> (a, b, c, d, e) # sconcat :: NonEmpty (a, b, c, d, e) -> (a, b, c, d, e) # stimes :: Integral b0 => b0 -> (a, b, c, d, e) -> (a, b, c, d, e) #

class Semigroup a => Monoid a where #

The class of monoids (types with an associative binary operation that has an identity). Instances should satisfy the following laws:

```
x <> mempty = x
```
```
mempty <> x = x
```
x <> (y <> z) = (x <> y) <> z (Semigroup law)
```
mconcat = foldr '(<>)' mempty
```

The method names refer to the monoid of lists under concatenation, but there are many other instances.

Some types can be viewed as a monoid in more than one way, e.g. both addition and multiplication on numbers. In such cases we often define newtypes and make those instances of Monoid, e.g. Sum and Product.

NOTE: Semigroup is a superclass of Monoid since base-4.11.0.0.

Minimal complete definition

mempty

Methods

mempty :: a #

Identity of mappend

mappend :: a -> a -> a #

An associative operation

NOTE: This method is redundant and has the default implementation mappend = '(<>)' since base-4.11.0.0.

mconcat :: [a] -> a #

Fold a list using the monoid.

For most types, the default definition for mconcat will be used, but the function is included in the class definition so that an optimized version can be provided for specific types.

Instances

Monoid Ordering	Since: base-2.1
Instance details Defined in GHC.Base Methods mempty :: Ordering # mappend :: Ordering -> Ordering -> Ordering # mconcat :: [Ordering] -> Ordering #
Monoid ()	Since: base-2.1
Instance details Defined in GHC.Base Methods mempty :: () # mappend :: () -> () -> () # mconcat :: [()] -> () #
Monoid All	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods mempty :: All # mappend :: All -> All -> All # mconcat :: [All] -> All #
Monoid Any	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods mempty :: Any # mappend :: Any -> Any -> Any # mconcat :: [Any] -> Any #
Monoid ExactPi	The multiplicative monoid over `Rational`s augmented with multiples of `pi`.
Instance details Defined in Data.ExactPi Methods mempty :: ExactPi # mappend :: ExactPi -> ExactPi -> ExactPi # mconcat :: [ExactPi] -> ExactPi #
Monoid ByteArray
Instance details Defined in Data.Primitive.ByteArray Methods mempty :: ByteArray # mappend :: ByteArray -> ByteArray -> ByteArray # mconcat :: [ByteArray] -> ByteArray #
Monoid Dimension' Source #	The monoid of dimensions under multiplication.
Instance details Defined in Numeric.Units.Dimensional.Dimensions.TermLevel Methods mempty :: Dimension' # mappend :: Dimension' -> Dimension' -> Dimension' # mconcat :: [Dimension'] -> Dimension' #
Monoid AnyUnit Source #	`AnyUnit`s form a `Monoid` under multiplication.
Instance details Defined in Numeric.Units.Dimensional.Dynamic Methods mempty :: AnyUnit # mappend :: AnyUnit -> AnyUnit -> AnyUnit # mconcat :: [AnyUnit] -> AnyUnit #
Monoid [a]	Since: base-2.1
Instance details Defined in GHC.Base Methods mempty :: [a] # mappend :: [a] -> [a] -> [a] # mconcat :: [[a]] -> [a] #
Semigroup a => Monoid (Maybe a)	Lift a semigroup into `Maybe` forming a `Monoid` according to http://en.wikipedia.org/wiki/Monoid: "Any semigroup `S` may be turned into a monoid simply by adjoining an element `e` not in `S` and defining `ee = e` and `es = s = se` for all `s ∈ S`." Since 4.11.0: constraint on inner `a` value generalised from `Monoid` to `Semigroup`. Since: base-2.1*
Instance details Defined in GHC.Base Methods mempty :: Maybe a # mappend :: Maybe a -> Maybe a -> Maybe a # mconcat :: [Maybe a] -> Maybe a #
Monoid a => Monoid (IO a)	Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods mempty :: IO a # mappend :: IO a -> IO a -> IO a # mconcat :: [IO a] -> IO a #
Monoid p => Monoid (Par1 p)	Since: base-4.12.0.0
Instance details Defined in GHC.Generics Methods mempty :: Par1 p # mappend :: Par1 p -> Par1 p -> Par1 p # mconcat :: [Par1 p] -> Par1 p #
(Ord a, Bounded a) => Monoid (Min a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods mempty :: Min a # mappend :: Min a -> Min a -> Min a # mconcat :: [Min a] -> Min a #
(Ord a, Bounded a) => Monoid (Max a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods mempty :: Max a # mappend :: Max a -> Max a -> Max a # mconcat :: [Max a] -> Max a #
Monoid m => Monoid (WrappedMonoid m)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods mempty :: WrappedMonoid m # mappend :: WrappedMonoid m -> WrappedMonoid m -> WrappedMonoid m # mconcat :: [WrappedMonoid m] -> WrappedMonoid m #
Semigroup a => Monoid (Option a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods mempty :: Option a # mappend :: Option a -> Option a -> Option a # mconcat :: [Option a] -> Option a #
Monoid a => Monoid (Identity a)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Identity Methods mempty :: Identity a # mappend :: Identity a -> Identity a -> Identity a # mconcat :: [Identity a] -> Identity a #
Monoid (First a)	Since: base-2.1
Instance details Defined in Data.Monoid Methods mempty :: First a # mappend :: First a -> First a -> First a # mconcat :: [First a] -> First a #
Monoid (Last a)	Since: base-2.1
Instance details Defined in Data.Monoid Methods mempty :: Last a # mappend :: Last a -> Last a -> Last a # mconcat :: [Last a] -> Last a #
Monoid a => Monoid (Dual a)	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods mempty :: Dual a # mappend :: Dual a -> Dual a -> Dual a # mconcat :: [Dual a] -> Dual a #
Monoid (Endo a)	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods mempty :: Endo a # mappend :: Endo a -> Endo a -> Endo a # mconcat :: [Endo a] -> Endo a #
Num a => Monoid (Sum a)	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods mempty :: Sum a # mappend :: Sum a -> Sum a -> Sum a # mconcat :: [Sum a] -> Sum a #
Num a => Monoid (Product a)	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods mempty :: Product a # mappend :: Product a -> Product a -> Product a # mconcat :: [Product a] -> Product a #
Monoid a => Monoid (Down a)	Since: base-4.11.0.0
Instance details Defined in Data.Ord Methods mempty :: Down a # mappend :: Down a -> Down a -> Down a # mconcat :: [Down a] -> Down a #
PrimUnlifted a => Monoid (UnliftedArray a)	Since: primitive-0.6.4.0
Instance details Defined in Data.Primitive.UnliftedArray Methods mempty :: UnliftedArray a # mappend :: UnliftedArray a -> UnliftedArray a -> UnliftedArray a # mconcat :: [UnliftedArray a] -> UnliftedArray a #
Monoid (PrimArray a)	Since: primitive-0.6.4.0
Instance details Defined in Data.Primitive.PrimArray Methods mempty :: PrimArray a # mappend :: PrimArray a -> PrimArray a -> PrimArray a # mconcat :: [PrimArray a] -> PrimArray a #
Monoid (SmallArray a)
Instance details Defined in Data.Primitive.SmallArray Methods mempty :: SmallArray a # mappend :: SmallArray a -> SmallArray a -> SmallArray a # mconcat :: [SmallArray a] -> SmallArray a #
Monoid (Array a)
Instance details Defined in Data.Primitive.Array Methods mempty :: Array a # mappend :: Array a -> Array a -> Array a # mconcat :: [Array a] -> Array a #
Prim a => Monoid (Vector a)
Instance details Defined in Data.Vector.Primitive Methods mempty :: Vector a # mappend :: Vector a -> Vector a -> Vector a # mconcat :: [Vector a] -> Vector a #
Num a => Monoid (DynQuantity a) Source #	`DynQuantity`s form a `Monoid` under multiplication, but not under addition because they may not be added together if their dimensions do not match.
Instance details Defined in Numeric.Units.Dimensional.Dynamic Methods mempty :: DynQuantity a # mappend :: DynQuantity a -> DynQuantity a -> DynQuantity a # mconcat :: [DynQuantity a] -> DynQuantity a #
Num a => Monoid (AnyQuantity a) Source #	`AnyQuantity`s form a `Monoid` under multiplication, but not under addition because they may not be added together if their dimensions do not match.
Instance details Defined in Numeric.Units.Dimensional.Dynamic Methods mempty :: AnyQuantity a # mappend :: AnyQuantity a -> AnyQuantity a -> AnyQuantity a # mconcat :: [AnyQuantity a] -> AnyQuantity a #
Monoid b => Monoid (a -> b)	Since: base-2.1
Instance details Defined in GHC.Base Methods mempty :: a -> b # mappend :: (a -> b) -> (a -> b) -> a -> b # mconcat :: [a -> b] -> a -> b #
Monoid (U1 p)	Since: base-4.12.0.0
Instance details Defined in GHC.Generics Methods mempty :: U1 p # mappend :: U1 p -> U1 p -> U1 p # mconcat :: [U1 p] -> U1 p #
(Monoid a, Monoid b) => Monoid (a, b)	Since: base-2.1
Instance details Defined in GHC.Base Methods mempty :: (a, b) # mappend :: (a, b) -> (a, b) -> (a, b) # mconcat :: [(a, b)] -> (a, b) #
Monoid a => Monoid (ST s a)	Since: base-4.11.0.0
Instance details Defined in GHC.ST Methods mempty :: ST s a # mappend :: ST s a -> ST s a -> ST s a # mconcat :: [ST s a] -> ST s a #
Monoid (Proxy s)	Since: base-4.7.0.0
Instance details Defined in Data.Proxy Methods mempty :: Proxy s # mappend :: Proxy s -> Proxy s -> Proxy s # mconcat :: [Proxy s] -> Proxy s #
Monoid (f p) => Monoid (Rec1 f p)	Since: base-4.12.0.0
Instance details Defined in GHC.Generics Methods mempty :: Rec1 f p # mappend :: Rec1 f p -> Rec1 f p -> Rec1 f p # mconcat :: [Rec1 f p] -> Rec1 f p #
(Monoid a, Monoid b, Monoid c) => Monoid (a, b, c)	Since: base-2.1
Instance details Defined in GHC.Base Methods mempty :: (a, b, c) # mappend :: (a, b, c) -> (a, b, c) -> (a, b, c) # mconcat :: [(a, b, c)] -> (a, b, c) #
Monoid a => Monoid (Const a b)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Const Methods mempty :: Const a b # mappend :: Const a b -> Const a b -> Const a b # mconcat :: [Const a b] -> Const a b #
(Applicative f, Monoid a) => Monoid (Ap f a)	Since: base-4.12.0.0
Instance details Defined in Data.Monoid Methods mempty :: Ap f a # mappend :: Ap f a -> Ap f a -> Ap f a # mconcat :: [Ap f a] -> Ap f a #
Alternative f => Monoid (Alt f a)	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods mempty :: Alt f a # mappend :: Alt f a -> Alt f a -> Alt f a # mconcat :: [Alt f a] -> Alt f a #
Num a => Monoid (SQuantity s d a) Source #	`Quantity`s of a given `Dimension` form a `Monoid` under addition.
Instance details Defined in Numeric.Units.Dimensional.Internal Methods mempty :: SQuantity s d a # mappend :: SQuantity s d a -> SQuantity s d a -> SQuantity s d a # mconcat :: [SQuantity s d a] -> SQuantity s d a #
Monoid c => Monoid (K1 i c p)	Since: base-4.12.0.0
Instance details Defined in GHC.Generics Methods mempty :: K1 i c p # mappend :: K1 i c p -> K1 i c p -> K1 i c p # mconcat :: [K1 i c p] -> K1 i c p #
(Monoid (f p), Monoid (g p)) => Monoid ((f :*: g) p)	Since: base-4.12.0.0
Instance details Defined in GHC.Generics Methods mempty :: (f :: g) p # mappend :: (f :: g) p -> (f :: g) p -> (f :: g) p # mconcat :: [(f :: g) p] -> (f :: g) p #
(Monoid a, Monoid b, Monoid c, Monoid d) => Monoid (a, b, c, d)	Since: base-2.1
Instance details Defined in GHC.Base Methods mempty :: (a, b, c, d) # mappend :: (a, b, c, d) -> (a, b, c, d) -> (a, b, c, d) # mconcat :: [(a, b, c, d)] -> (a, b, c, d) #
Monoid (f p) => Monoid (M1 i c f p)	Since: base-4.12.0.0
Instance details Defined in GHC.Generics Methods mempty :: M1 i c f p # mappend :: M1 i c f p -> M1 i c f p -> M1 i c f p # mconcat :: [M1 i c f p] -> M1 i c f p #
Monoid (f (g p)) => Monoid ((f :.: g) p)	Since: base-4.12.0.0
Instance details Defined in GHC.Generics Methods mempty :: (f :.: g) p # mappend :: (f :.: g) p -> (f :.: g) p -> (f :.: g) p # mconcat :: [(f :.: g) p] -> (f :.: g) p #
(Monoid a, Monoid b, Monoid c, Monoid d, Monoid e) => Monoid (a, b, c, d, e)	Since: base-2.1
Instance details Defined in GHC.Base Methods mempty :: (a, b, c, d, e) # mappend :: (a, b, c, d, e) -> (a, b, c, d, e) -> (a, b, c, d, e) # mconcat :: [(a, b, c, d, e)] -> (a, b, c, d, e) #

data Bool #

Constructors

False
True

Instances

Bounded Bool	Since: base-2.1
Instance details Defined in GHC.Enum Methods minBound :: Bool # maxBound :: Bool #
Enum Bool	Since: base-2.1
Instance details Defined in GHC.Enum Methods succ :: Bool -> Bool # pred :: Bool -> Bool # toEnum :: Int -> Bool # fromEnum :: Bool -> Int # enumFrom :: Bool -> [Bool] # enumFromThen :: Bool -> Bool -> [Bool] # enumFromTo :: Bool -> Bool -> [Bool] # enumFromThenTo :: Bool -> Bool -> Bool -> [Bool] #
Eq Bool
Instance details Defined in GHC.Classes Methods (==) :: Bool -> Bool -> Bool # (/=) :: Bool -> Bool -> Bool #
Data Bool	Since: base-4.0.0.0
Instance details Defined in Data.Data Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Bool -> c Bool # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Bool # toConstr :: Bool -> Constr # dataTypeOf :: Bool -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c Bool) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Bool) # gmapT :: (forall b. Data b => b -> b) -> Bool -> Bool # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Bool -> r # gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Bool -> r # gmapQ :: (forall d. Data d => d -> u) -> Bool -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> Bool -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Bool -> m Bool # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Bool -> m Bool # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Bool -> m Bool #
Ord Bool
Instance details Defined in GHC.Classes Methods compare :: Bool -> Bool -> Ordering # (<) :: Bool -> Bool -> Bool # (<=) :: Bool -> Bool -> Bool # (>) :: Bool -> Bool -> Bool # (>=) :: Bool -> Bool -> Bool # max :: Bool -> Bool -> Bool # min :: Bool -> Bool -> Bool #
Read Bool	Since: base-2.1
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS Bool # readList :: ReadS [Bool] # readPrec :: ReadPrec Bool # readListPrec :: ReadPrec [Bool] #
Show Bool	Since: base-2.1
Instance details Defined in GHC.Show Methods showsPrec :: Int -> Bool -> ShowS # show :: Bool -> String # showList :: [Bool] -> ShowS #
Ix Bool	Since: base-2.1
Instance details Defined in GHC.Arr Methods range :: (Bool, Bool) -> [Bool] # index :: (Bool, Bool) -> Bool -> Int # unsafeIndex :: (Bool, Bool) -> Bool -> Int inRange :: (Bool, Bool) -> Bool -> Bool # rangeSize :: (Bool, Bool) -> Int # unsafeRangeSize :: (Bool, Bool) -> Int
Generic Bool
Instance details Defined in GHC.Generics Associated Types type Rep Bool :: Type -> Type # Methods from :: Bool -> Rep Bool x # to :: Rep Bool x -> Bool #
SingKind Bool	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Associated Types type DemoteRep Bool :: Type Methods fromSing :: Sing a -> DemoteRep Bool
Storable Bool	Since: base-2.1
Instance details Defined in Foreign.Storable Methods sizeOf :: Bool -> Int # alignment :: Bool -> Int # peekElemOff :: Ptr Bool -> Int -> IO Bool # pokeElemOff :: Ptr Bool -> Int -> Bool -> IO () # peekByteOff :: Ptr b -> Int -> IO Bool # pokeByteOff :: Ptr b -> Int -> Bool -> IO () # peek :: Ptr Bool -> IO Bool # poke :: Ptr Bool -> Bool -> IO () #
Bits Bool	Interpret `Bool` as 1-bit bit-field Since: base-4.7.0.0
Instance details Defined in Data.Bits Methods (.&.) :: Bool -> Bool -> Bool # (.\|.) :: Bool -> Bool -> Bool # xor :: Bool -> Bool -> Bool # complement :: Bool -> Bool # shift :: Bool -> Int -> Bool # rotate :: Bool -> Int -> Bool # zeroBits :: Bool # bit :: Int -> Bool # setBit :: Bool -> Int -> Bool # clearBit :: Bool -> Int -> Bool # complementBit :: Bool -> Int -> Bool # testBit :: Bool -> Int -> Bool # bitSizeMaybe :: Bool -> Maybe Int # bitSize :: Bool -> Int # isSigned :: Bool -> Bool # shiftL :: Bool -> Int -> Bool # unsafeShiftL :: Bool -> Int -> Bool # shiftR :: Bool -> Int -> Bool # unsafeShiftR :: Bool -> Int -> Bool # rotateL :: Bool -> Int -> Bool # rotateR :: Bool -> Int -> Bool # popCount :: Bool -> Int #
FiniteBits Bool	Since: base-4.7.0.0
Instance details Defined in Data.Bits Methods finiteBitSize :: Bool -> Int # countLeadingZeros :: Bool -> Int # countTrailingZeros :: Bool -> Int #
NFData Bool
Instance details Defined in Control.DeepSeq Methods rnf :: Bool -> () #
AEq Bool
Instance details Defined in Data.AEq Methods (===) :: Bool -> Bool -> Bool # (~==) :: Bool -> Bool -> Bool #
Unbox Bool
Instance details Defined in Data.Vector.Unboxed.Base
SingI False	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods sing :: Sing False
SingI True	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods sing :: Sing True
Vector Vector Bool
Instance details Defined in Data.Vector.Unboxed.Base Methods basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) Bool -> m (Vector Bool) # basicUnsafeThaw :: PrimMonad m => Vector Bool -> m (Mutable Vector (PrimState m) Bool) # basicLength :: Vector Bool -> Int # basicUnsafeSlice :: Int -> Int -> Vector Bool -> Vector Bool # basicUnsafeIndexM :: Monad m => Vector Bool -> Int -> m Bool # basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) Bool -> Vector Bool -> m () # elemseq :: Vector Bool -> Bool -> b -> b #
MVector MVector Bool
Instance details Defined in Data.Vector.Unboxed.Base Methods basicLength :: MVector s Bool -> Int # basicUnsafeSlice :: Int -> Int -> MVector s Bool -> MVector s Bool # basicOverlaps :: MVector s Bool -> MVector s Bool -> Bool # basicUnsafeNew :: PrimMonad m => Int -> m (MVector (PrimState m) Bool) # basicInitialize :: PrimMonad m => MVector (PrimState m) Bool -> m () # basicUnsafeReplicate :: PrimMonad m => Int -> Bool -> m (MVector (PrimState m) Bool) # basicUnsafeRead :: PrimMonad m => MVector (PrimState m) Bool -> Int -> m Bool # basicUnsafeWrite :: PrimMonad m => MVector (PrimState m) Bool -> Int -> Bool -> m () # basicClear :: PrimMonad m => MVector (PrimState m) Bool -> m () # basicSet :: PrimMonad m => MVector (PrimState m) Bool -> Bool -> m () # basicUnsafeCopy :: PrimMonad m => MVector (PrimState m) Bool -> MVector (PrimState m) Bool -> m () # basicUnsafeMove :: PrimMonad m => MVector (PrimState m) Bool -> MVector (PrimState m) Bool -> m () # basicUnsafeGrow :: PrimMonad m => MVector (PrimState m) Bool -> Int -> m (MVector (PrimState m) Bool) #
type Rep Bool	Since: base-4.6.0.0
Instance details Defined in GHC.Generics type Rep Bool = D1 (MetaData "Bool" "GHC.Types" "ghc-prim" False) (C1 (MetaCons "False" PrefixI False) (U1 :: Type -> Type) :+: C1 (MetaCons "True" PrefixI False) (U1 :: Type -> Type))
data Sing (a :: Bool)
Instance details Defined in GHC.Generics data Sing (a :: Bool) where STrue :: forall (a :: Bool). Sing True SFalse :: forall (a :: Bool). Sing False
type DemoteRep Bool
Instance details Defined in GHC.Generics type DemoteRep Bool = Bool
data Vector Bool
Instance details Defined in Data.Vector.Unboxed.Base data Vector Bool = V_Bool (Vector Word8)
data MVector s Bool
Instance details Defined in Data.Vector.Unboxed.Base data MVector s Bool = MV_Bool (MVector s Word8)

data Char #

The character type Char is an enumeration whose values represent Unicode (or equivalently ISO/IEC 10646) code points (i.e. characters, see http://www.unicode.org/ for details). This set extends the ISO 8859-1 (Latin-1) character set (the first 256 characters), which is itself an extension of the ASCII character set (the first 128 characters). A character literal in Haskell has type Char.

To convert a Char to or from the corresponding Int value defined by Unicode, use toEnum and fromEnum from the Enum class respectively (or equivalently ord and chr).

Instances

Bounded Char	Since: base-2.1
Instance details Defined in GHC.Enum Methods minBound :: Char # maxBound :: Char #
Enum Char	Since: base-2.1
Instance details Defined in GHC.Enum Methods succ :: Char -> Char # pred :: Char -> Char # toEnum :: Int -> Char # fromEnum :: Char -> Int # enumFrom :: Char -> [Char] # enumFromThen :: Char -> Char -> [Char] # enumFromTo :: Char -> Char -> [Char] # enumFromThenTo :: Char -> Char -> Char -> [Char] #
Eq Char
Instance details Defined in GHC.Classes Methods (==) :: Char -> Char -> Bool # (/=) :: Char -> Char -> Bool #
Data Char	Since: base-4.0.0.0
Instance details Defined in Data.Data Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Char -> c Char # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Char # toConstr :: Char -> Constr # dataTypeOf :: Char -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c Char) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Char) # gmapT :: (forall b. Data b => b -> b) -> Char -> Char # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Char -> r # gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Char -> r # gmapQ :: (forall d. Data d => d -> u) -> Char -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> Char -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Char -> m Char # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Char -> m Char # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Char -> m Char #
Ord Char
Instance details Defined in GHC.Classes Methods compare :: Char -> Char -> Ordering # (<) :: Char -> Char -> Bool # (<=) :: Char -> Char -> Bool # (>) :: Char -> Char -> Bool # (>=) :: Char -> Char -> Bool # max :: Char -> Char -> Char # min :: Char -> Char -> Char #
Read Char	Since: base-2.1
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS Char # readList :: ReadS [Char] # readPrec :: ReadPrec Char # readListPrec :: ReadPrec [Char] #
Show Char	Since: base-2.1
Instance details Defined in GHC.Show Methods showsPrec :: Int -> Char -> ShowS # show :: Char -> String # showList :: [Char] -> ShowS #
Ix Char	Since: base-2.1
Instance details Defined in GHC.Arr Methods range :: (Char, Char) -> [Char] # index :: (Char, Char) -> Char -> Int # unsafeIndex :: (Char, Char) -> Char -> Int inRange :: (Char, Char) -> Char -> Bool # rangeSize :: (Char, Char) -> Int # unsafeRangeSize :: (Char, Char) -> Int
Storable Char	Since: base-2.1
Instance details Defined in Foreign.Storable Methods sizeOf :: Char -> Int # alignment :: Char -> Int # peekElemOff :: Ptr Char -> Int -> IO Char # pokeElemOff :: Ptr Char -> Int -> Char -> IO () # peekByteOff :: Ptr b -> Int -> IO Char # pokeByteOff :: Ptr b -> Int -> Char -> IO () # peek :: Ptr Char -> IO Char # poke :: Ptr Char -> Char -> IO () #
NFData Char
Instance details Defined in Control.DeepSeq Methods rnf :: Char -> () #
AEq Char
Instance details Defined in Data.AEq Methods (===) :: Char -> Char -> Bool # (~==) :: Char -> Char -> Bool #
Prim Char
Instance details Defined in Data.Primitive.Types Methods sizeOf# :: Char -> Int# # alignment# :: Char -> Int# # indexByteArray# :: ByteArray# -> Int# -> Char # readByteArray# :: MutableByteArray# s -> Int# -> State# s -> (#State# s, Char#) # writeByteArray# :: MutableByteArray# s -> Int# -> Char -> State# s -> State# s # setByteArray# :: MutableByteArray# s -> Int# -> Int# -> Char -> State# s -> State# s # indexOffAddr# :: Addr# -> Int# -> Char # readOffAddr# :: Addr# -> Int# -> State# s -> (#State# s, Char#) # writeOffAddr# :: Addr# -> Int# -> Char -> State# s -> State# s # setOffAddr# :: Addr# -> Int# -> Int# -> Char -> State# s -> State# s #
ErrorList Char
Instance details Defined in Control.Monad.Trans.Error Methods listMsg :: String -> [Char] #
Unbox Char
Instance details Defined in Data.Vector.Unboxed.Base
Vector Vector Char
Instance details Defined in Data.Vector.Unboxed.Base Methods basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) Char -> m (Vector Char) # basicUnsafeThaw :: PrimMonad m => Vector Char -> m (Mutable Vector (PrimState m) Char) # basicLength :: Vector Char -> Int # basicUnsafeSlice :: Int -> Int -> Vector Char -> Vector Char # basicUnsafeIndexM :: Monad m => Vector Char -> Int -> m Char # basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) Char -> Vector Char -> m () # elemseq :: Vector Char -> Char -> b -> b #
MVector MVector Char
Instance details Defined in Data.Vector.Unboxed.Base Methods basicLength :: MVector s Char -> Int # basicUnsafeSlice :: Int -> Int -> MVector s Char -> MVector s Char # basicOverlaps :: MVector s Char -> MVector s Char -> Bool # basicUnsafeNew :: PrimMonad m => Int -> m (MVector (PrimState m) Char) # basicInitialize :: PrimMonad m => MVector (PrimState m) Char -> m () # basicUnsafeReplicate :: PrimMonad m => Int -> Char -> m (MVector (PrimState m) Char) # basicUnsafeRead :: PrimMonad m => MVector (PrimState m) Char -> Int -> m Char # basicUnsafeWrite :: PrimMonad m => MVector (PrimState m) Char -> Int -> Char -> m () # basicClear :: PrimMonad m => MVector (PrimState m) Char -> m () # basicSet :: PrimMonad m => MVector (PrimState m) Char -> Char -> m () # basicUnsafeCopy :: PrimMonad m => MVector (PrimState m) Char -> MVector (PrimState m) Char -> m () # basicUnsafeMove :: PrimMonad m => MVector (PrimState m) Char -> MVector (PrimState m) Char -> m () # basicUnsafeGrow :: PrimMonad m => MVector (PrimState m) Char -> Int -> m (MVector (PrimState m) Char) #
Generic1 (URec Char :: k -> Type)
Instance details Defined in GHC.Generics Associated Types type Rep1 (URec Char) :: k -> Type # Methods from1 :: URec Char a -> Rep1 (URec Char) a # to1 :: Rep1 (URec Char) a -> URec Char a #
Functor (URec Char :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods fmap :: (a -> b) -> URec Char a -> URec Char b # (<$) :: a -> URec Char b -> URec Char a #
Foldable (URec Char :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Foldable Methods fold :: Monoid m => URec Char m -> m # foldMap :: Monoid m => (a -> m) -> URec Char a -> m # foldr :: (a -> b -> b) -> b -> URec Char a -> b # foldr' :: (a -> b -> b) -> b -> URec Char a -> b # foldl :: (b -> a -> b) -> b -> URec Char a -> b # foldl' :: (b -> a -> b) -> b -> URec Char a -> b # foldr1 :: (a -> a -> a) -> URec Char a -> a # foldl1 :: (a -> a -> a) -> URec Char a -> a # toList :: URec Char a -> [a] # null :: URec Char a -> Bool # length :: URec Char a -> Int # elem :: Eq a => a -> URec Char a -> Bool # maximum :: Ord a => URec Char a -> a # minimum :: Ord a => URec Char a -> a # sum :: Num a => URec Char a -> a # product :: Num a => URec Char a -> a #
Traversable (URec Char :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> URec Char a -> f (URec Char b) # sequenceA :: Applicative f => URec Char (f a) -> f (URec Char a) # mapM :: Monad m => (a -> m b) -> URec Char a -> m (URec Char b) # sequence :: Monad m => URec Char (m a) -> m (URec Char a) #
Eq (URec Char p)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods (==) :: URec Char p -> URec Char p -> Bool # (/=) :: URec Char p -> URec Char p -> Bool #
Ord (URec Char p)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods compare :: URec Char p -> URec Char p -> Ordering # (<) :: URec Char p -> URec Char p -> Bool # (<=) :: URec Char p -> URec Char p -> Bool # (>) :: URec Char p -> URec Char p -> Bool # (>=) :: URec Char p -> URec Char p -> Bool # max :: URec Char p -> URec Char p -> URec Char p # min :: URec Char p -> URec Char p -> URec Char p #
Show (URec Char p)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods showsPrec :: Int -> URec Char p -> ShowS # show :: URec Char p -> String # showList :: [URec Char p] -> ShowS #
Generic (URec Char p)
Instance details Defined in GHC.Generics Associated Types type Rep (URec Char p) :: Type -> Type # Methods from :: URec Char p -> Rep (URec Char p) x # to :: Rep (URec Char p) x -> URec Char p #
data Vector Char
Instance details Defined in Data.Vector.Unboxed.Base data Vector Char = V_Char (Vector Char)
data URec Char (p :: k)	Used for marking occurrences of `Char#` Since: base-4.9.0.0
Instance details Defined in GHC.Generics data URec Char (p :: k) = UChar { uChar# :: Char# }
data MVector s Char
Instance details Defined in Data.Vector.Unboxed.Base data MVector s Char = MV_Char (MVector s Char)
type Rep1 (URec Char :: k -> Type)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics type Rep1 (URec Char :: k -> Type) = D1 (MetaData "URec" "GHC.Generics" "base" False) (C1 (MetaCons "UChar" PrefixI True) (S1 (MetaSel (Just "uChar#") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (UChar :: k -> Type)))
type Rep (URec Char p)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics type Rep (URec Char p) = D1 (MetaData "URec" "GHC.Generics" "base" False) (C1 (MetaCons "UChar" PrefixI True) (S1 (MetaSel (Just "uChar#") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (UChar :: Type -> Type)))

data Double #

Double-precision floating point numbers. It is desirable that this type be at least equal in range and precision to the IEEE double-precision type.

Instances

Eq Double	Note that due to the presence of `NaN`, `Double`'s `Eq` instance does not satisfy reflexivity. `>>>` `0/0 == (0/0 :: Double)`False Also note that `Double`'s `Eq` instance does not satisfy substitutivity: `>>>` `0 == (-0 :: Double)`True `>>>` `recip 0 == recip (-0 :: Double)`False
Instance details Defined in GHC.Classes Methods (==) :: Double -> Double -> Bool # (/=) :: Double -> Double -> Bool #
Floating Double	Since: base-2.1
Instance details Defined in GHC.Float Methods pi :: Double # exp :: Double -> Double # log :: Double -> Double # sqrt :: Double -> Double # (**) :: Double -> Double -> Double # logBase :: Double -> Double -> Double # sin :: Double -> Double # cos :: Double -> Double # tan :: Double -> Double # asin :: Double -> Double # acos :: Double -> Double # atan :: Double -> Double # sinh :: Double -> Double # cosh :: Double -> Double # tanh :: Double -> Double # asinh :: Double -> Double # acosh :: Double -> Double # atanh :: Double -> Double # log1p :: Double -> Double # expm1 :: Double -> Double # log1pexp :: Double -> Double # log1mexp :: Double -> Double #
Data Double	Since: base-4.0.0.0
Instance details Defined in Data.Data Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Double -> c Double # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Double # toConstr :: Double -> Constr # dataTypeOf :: Double -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c Double) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Double) # gmapT :: (forall b. Data b => b -> b) -> Double -> Double # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Double -> r # gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Double -> r # gmapQ :: (forall d. Data d => d -> u) -> Double -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> Double -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Double -> m Double # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Double -> m Double # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Double -> m Double #
Ord Double	Note that due to the presence of `NaN`, `Double`'s `Ord` instance does not satisfy reflexivity. `>>>` `0/0 <= (0/0 :: Double)`False Also note that, due to the same, `Ord`'s operator interactions are not respected by `Double`'s instance: `>>>` `(0/0 :: Double) > 1`False `>>>` `compare (0/0 :: Double) 1`GT
Instance details Defined in GHC.Classes Methods compare :: Double -> Double -> Ordering # (<) :: Double -> Double -> Bool # (<=) :: Double -> Double -> Bool # (>) :: Double -> Double -> Bool # (>=) :: Double -> Double -> Bool # max :: Double -> Double -> Double # min :: Double -> Double -> Double #
Read Double	Since: base-2.1
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS Double # readList :: ReadS [Double] # readPrec :: ReadPrec Double # readListPrec :: ReadPrec [Double] #
RealFloat Double	Since: base-2.1
Instance details Defined in GHC.Float Methods floatRadix :: Double -> Integer # floatDigits :: Double -> Int # floatRange :: Double -> (Int, Int) # decodeFloat :: Double -> (Integer, Int) # encodeFloat :: Integer -> Int -> Double # exponent :: Double -> Int # significand :: Double -> Double # scaleFloat :: Int -> Double -> Double # isNaN :: Double -> Bool # isInfinite :: Double -> Bool # isDenormalized :: Double -> Bool # isNegativeZero :: Double -> Bool # isIEEE :: Double -> Bool # atan2 :: Double -> Double -> Double #
Storable Double	Since: base-2.1
Instance details Defined in Foreign.Storable Methods sizeOf :: Double -> Int # alignment :: Double -> Int # peekElemOff :: Ptr Double -> Int -> IO Double # pokeElemOff :: Ptr Double -> Int -> Double -> IO () # peekByteOff :: Ptr b -> Int -> IO Double # pokeByteOff :: Ptr b -> Int -> Double -> IO () # peek :: Ptr Double -> IO Double # poke :: Ptr Double -> Double -> IO () #
NFData Double
Instance details Defined in Control.DeepSeq Methods rnf :: Double -> () #
AEq Double
Instance details Defined in Data.AEq Methods (===) :: Double -> Double -> Bool # (~==) :: Double -> Double -> Bool #
IEEE Double
Instance details Defined in Numeric.IEEE Methods infinity :: Double # minDenormal :: Double # minNormal :: Double # maxFinite :: Double # epsilon :: Double # copySign :: Double -> Double -> Double # identicalIEEE :: Double -> Double -> Bool # succIEEE :: Double -> Double # predIEEE :: Double -> Double # bisectIEEE :: Double -> Double -> Double # sameSignificandBits :: Double -> Double -> Int # nan :: Double # nanWithPayload :: Word64 -> Double # maxNaNPayload :: Double -> Word64 # nanPayload :: Double -> Word64 #
Prim Double
Instance details Defined in Data.Primitive.Types Methods sizeOf# :: Double -> Int# # alignment# :: Double -> Int# # indexByteArray# :: ByteArray# -> Int# -> Double # readByteArray# :: MutableByteArray# s -> Int# -> State# s -> (#State# s, Double#) # writeByteArray# :: MutableByteArray# s -> Int# -> Double -> State# s -> State# s # setByteArray# :: MutableByteArray# s -> Int# -> Int# -> Double -> State# s -> State# s # indexOffAddr# :: Addr# -> Int# -> Double # readOffAddr# :: Addr# -> Int# -> State# s -> (#State# s, Double#) # writeOffAddr# :: Addr# -> Int# -> Double -> State# s -> State# s # setOffAddr# :: Addr# -> Int# -> Int# -> Double -> State# s -> State# s #
Unbox Double
Instance details Defined in Data.Vector.Unboxed.Base
Vector Vector Double
Instance details Defined in Data.Vector.Unboxed.Base Methods basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) Double -> m (Vector Double) # basicUnsafeThaw :: PrimMonad m => Vector Double -> m (Mutable Vector (PrimState m) Double) # basicLength :: Vector Double -> Int # basicUnsafeSlice :: Int -> Int -> Vector Double -> Vector Double # basicUnsafeIndexM :: Monad m => Vector Double -> Int -> m Double # basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) Double -> Vector Double -> m () # elemseq :: Vector Double -> Double -> b -> b #
MVector MVector Double
Instance details Defined in Data.Vector.Unboxed.Base Methods basicLength :: MVector s Double -> Int # basicUnsafeSlice :: Int -> Int -> MVector s Double -> MVector s Double # basicOverlaps :: MVector s Double -> MVector s Double -> Bool # basicUnsafeNew :: PrimMonad m => Int -> m (MVector (PrimState m) Double) # basicInitialize :: PrimMonad m => MVector (PrimState m) Double -> m () # basicUnsafeReplicate :: PrimMonad m => Int -> Double -> m (MVector (PrimState m) Double) # basicUnsafeRead :: PrimMonad m => MVector (PrimState m) Double -> Int -> m Double # basicUnsafeWrite :: PrimMonad m => MVector (PrimState m) Double -> Int -> Double -> m () # basicClear :: PrimMonad m => MVector (PrimState m) Double -> m () # basicSet :: PrimMonad m => MVector (PrimState m) Double -> Double -> m () # basicUnsafeCopy :: PrimMonad m => MVector (PrimState m) Double -> MVector (PrimState m) Double -> m () # basicUnsafeMove :: PrimMonad m => MVector (PrimState m) Double -> MVector (PrimState m) Double -> m () # basicUnsafeGrow :: PrimMonad m => MVector (PrimState m) Double -> Int -> m (MVector (PrimState m) Double) #
Generic1 (URec Double :: k -> Type)
Instance details Defined in GHC.Generics Associated Types type Rep1 (URec Double) :: k -> Type # Methods from1 :: URec Double a -> Rep1 (URec Double) a # to1 :: Rep1 (URec Double) a -> URec Double a #
AEq (Complex Double)
Instance details Defined in Data.AEq Methods (===) :: Complex Double -> Complex Double -> Bool # (~==) :: Complex Double -> Complex Double -> Bool #
Functor (URec Double :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods fmap :: (a -> b) -> URec Double a -> URec Double b # (<$) :: a -> URec Double b -> URec Double a #
Foldable (URec Double :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Foldable Methods fold :: Monoid m => URec Double m -> m # foldMap :: Monoid m => (a -> m) -> URec Double a -> m # foldr :: (a -> b -> b) -> b -> URec Double a -> b # foldr' :: (a -> b -> b) -> b -> URec Double a -> b # foldl :: (b -> a -> b) -> b -> URec Double a -> b # foldl' :: (b -> a -> b) -> b -> URec Double a -> b # foldr1 :: (a -> a -> a) -> URec Double a -> a # foldl1 :: (a -> a -> a) -> URec Double a -> a # toList :: URec Double a -> [a] # null :: URec Double a -> Bool # length :: URec Double a -> Int # elem :: Eq a => a -> URec Double a -> Bool # maximum :: Ord a => URec Double a -> a # minimum :: Ord a => URec Double a -> a # sum :: Num a => URec Double a -> a # product :: Num a => URec Double a -> a #
Traversable (URec Double :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> URec Double a -> f (URec Double b) # sequenceA :: Applicative f => URec Double (f a) -> f (URec Double a) # mapM :: Monad m => (a -> m b) -> URec Double a -> m (URec Double b) # sequence :: Monad m => URec Double (m a) -> m (URec Double a) #
Eq (URec Double p)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods (==) :: URec Double p -> URec Double p -> Bool # (/=) :: URec Double p -> URec Double p -> Bool #
Ord (URec Double p)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods compare :: URec Double p -> URec Double p -> Ordering # (<) :: URec Double p -> URec Double p -> Bool # (<=) :: URec Double p -> URec Double p -> Bool # (>) :: URec Double p -> URec Double p -> Bool # (>=) :: URec Double p -> URec Double p -> Bool # max :: URec Double p -> URec Double p -> URec Double p # min :: URec Double p -> URec Double p -> URec Double p #
Show (URec Double p)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods showsPrec :: Int -> URec Double p -> ShowS # show :: URec Double p -> String # showList :: [URec Double p] -> ShowS #
Generic (URec Double p)
Instance details Defined in GHC.Generics Associated Types type Rep (URec Double p) :: Type -> Type # Methods from :: URec Double p -> Rep (URec Double p) x # to :: Rep (URec Double p) x -> URec Double p #
data Vector Double
Instance details Defined in Data.Vector.Unboxed.Base data Vector Double = V_Double (Vector Double)
data URec Double (p :: k)	Used for marking occurrences of `Double#` Since: base-4.9.0.0
Instance details Defined in GHC.Generics data URec Double (p :: k) = UDouble { uDouble# :: Double# }
data MVector s Double
Instance details Defined in Data.Vector.Unboxed.Base data MVector s Double = MV_Double (MVector s Double)
type Rep1 (URec Double :: k -> Type)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics type Rep1 (URec Double :: k -> Type) = D1 (MetaData "URec" "GHC.Generics" "base" False) (C1 (MetaCons "UDouble" PrefixI True) (S1 (MetaSel (Just "uDouble#") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (UDouble :: k -> Type)))
type Rep (URec Double p)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics type Rep (URec Double p) = D1 (MetaData "URec" "GHC.Generics" "base" False) (C1 (MetaCons "UDouble" PrefixI True) (S1 (MetaSel (Just "uDouble#") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (UDouble :: Type -> Type)))

data Float #

Single-precision floating point numbers. It is desirable that this type be at least equal in range and precision to the IEEE single-precision type.

Instances

Eq Float	Note that due to the presence of `NaN`, `Float`'s `Eq` instance does not satisfy reflexivity. `>>>` `0/0 == (0/0 :: Float)`False Also note that `Float`'s `Eq` instance does not satisfy substitutivity: `>>>` `0 == (-0 :: Float)`True `>>>` `recip 0 == recip (-0 :: Float)`False
Instance details Defined in GHC.Classes Methods (==) :: Float -> Float -> Bool # (/=) :: Float -> Float -> Bool #
Floating Float	Since: base-2.1
Instance details Defined in GHC.Float Methods pi :: Float # exp :: Float -> Float # log :: Float -> Float # sqrt :: Float -> Float # (**) :: Float -> Float -> Float # logBase :: Float -> Float -> Float # sin :: Float -> Float # cos :: Float -> Float # tan :: Float -> Float # asin :: Float -> Float # acos :: Float -> Float # atan :: Float -> Float # sinh :: Float -> Float # cosh :: Float -> Float # tanh :: Float -> Float # asinh :: Float -> Float # acosh :: Float -> Float # atanh :: Float -> Float # log1p :: Float -> Float # expm1 :: Float -> Float # log1pexp :: Float -> Float # log1mexp :: Float -> Float #
Data Float	Since: base-4.0.0.0
Instance details Defined in Data.Data Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Float -> c Float # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Float # toConstr :: Float -> Constr # dataTypeOf :: Float -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c Float) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Float) # gmapT :: (forall b. Data b => b -> b) -> Float -> Float # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Float -> r # gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Float -> r # gmapQ :: (forall d. Data d => d -> u) -> Float -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> Float -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Float -> m Float # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Float -> m Float # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Float -> m Float #
Ord Float	Note that due to the presence of `NaN`, `Float`'s `Ord` instance does not satisfy reflexivity. `>>>` `0/0 <= (0/0 :: Float)`False Also note that, due to the same, `Ord`'s operator interactions are not respected by `Float`'s instance: `>>>` `(0/0 :: Float) > 1`False `>>>` `compare (0/0 :: Float) 1`GT
Instance details Defined in GHC.Classes Methods compare :: Float -> Float -> Ordering # (<) :: Float -> Float -> Bool # (<=) :: Float -> Float -> Bool # (>) :: Float -> Float -> Bool # (>=) :: Float -> Float -> Bool # max :: Float -> Float -> Float # min :: Float -> Float -> Float #
Read Float	Since: base-2.1
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS Float # readList :: ReadS [Float] # readPrec :: ReadPrec Float # readListPrec :: ReadPrec [Float] #
RealFloat Float	Since: base-2.1
Instance details Defined in GHC.Float Methods floatRadix :: Float -> Integer # floatDigits :: Float -> Int # floatRange :: Float -> (Int, Int) # decodeFloat :: Float -> (Integer, Int) # encodeFloat :: Integer -> Int -> Float # exponent :: Float -> Int # significand :: Float -> Float # scaleFloat :: Int -> Float -> Float # isNaN :: Float -> Bool # isInfinite :: Float -> Bool # isDenormalized :: Float -> Bool # isNegativeZero :: Float -> Bool # isIEEE :: Float -> Bool # atan2 :: Float -> Float -> Float #
Storable Float	Since: base-2.1
Instance details Defined in Foreign.Storable Methods sizeOf :: Float -> Int # alignment :: Float -> Int # peekElemOff :: Ptr Float -> Int -> IO Float # pokeElemOff :: Ptr Float -> Int -> Float -> IO () # peekByteOff :: Ptr b -> Int -> IO Float # pokeByteOff :: Ptr b -> Int -> Float -> IO () # peek :: Ptr Float -> IO Float # poke :: Ptr Float -> Float -> IO () #
NFData Float
Instance details Defined in Control.DeepSeq Methods rnf :: Float -> () #
AEq Float
Instance details Defined in Data.AEq Methods (===) :: Float -> Float -> Bool # (~==) :: Float -> Float -> Bool #
IEEE Float
Instance details Defined in Numeric.IEEE Methods infinity :: Float # minDenormal :: Float # minNormal :: Float # maxFinite :: Float # epsilon :: Float # copySign :: Float -> Float -> Float # identicalIEEE :: Float -> Float -> Bool # succIEEE :: Float -> Float # predIEEE :: Float -> Float # bisectIEEE :: Float -> Float -> Float # sameSignificandBits :: Float -> Float -> Int # nan :: Float # nanWithPayload :: Word64 -> Float # maxNaNPayload :: Float -> Word64 # nanPayload :: Float -> Word64 #
Prim Float
Instance details Defined in Data.Primitive.Types Methods sizeOf# :: Float -> Int# # alignment# :: Float -> Int# # indexByteArray# :: ByteArray# -> Int# -> Float # readByteArray# :: MutableByteArray# s -> Int# -> State# s -> (#State# s, Float#) # writeByteArray# :: MutableByteArray# s -> Int# -> Float -> State# s -> State# s # setByteArray# :: MutableByteArray# s -> Int# -> Int# -> Float -> State# s -> State# s # indexOffAddr# :: Addr# -> Int# -> Float # readOffAddr# :: Addr# -> Int# -> State# s -> (#State# s, Float#) # writeOffAddr# :: Addr# -> Int# -> Float -> State# s -> State# s # setOffAddr# :: Addr# -> Int# -> Int# -> Float -> State# s -> State# s #
Unbox Float
Instance details Defined in Data.Vector.Unboxed.Base
Vector Vector Float
Instance details Defined in Data.Vector.Unboxed.Base Methods basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) Float -> m (Vector Float) # basicUnsafeThaw :: PrimMonad m => Vector Float -> m (Mutable Vector (PrimState m) Float) # basicLength :: Vector Float -> Int # basicUnsafeSlice :: Int -> Int -> Vector Float -> Vector Float # basicUnsafeIndexM :: Monad m => Vector Float -> Int -> m Float # basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) Float -> Vector Float -> m () # elemseq :: Vector Float -> Float -> b -> b #
MVector MVector Float
Instance details Defined in Data.Vector.Unboxed.Base Methods basicLength :: MVector s Float -> Int # basicUnsafeSlice :: Int -> Int -> MVector s Float -> MVector s Float # basicOverlaps :: MVector s Float -> MVector s Float -> Bool # basicUnsafeNew :: PrimMonad m => Int -> m (MVector (PrimState m) Float) # basicInitialize :: PrimMonad m => MVector (PrimState m) Float -> m () # basicUnsafeReplicate :: PrimMonad m => Int -> Float -> m (MVector (PrimState m) Float) # basicUnsafeRead :: PrimMonad m => MVector (PrimState m) Float -> Int -> m Float # basicUnsafeWrite :: PrimMonad m => MVector (PrimState m) Float -> Int -> Float -> m () # basicClear :: PrimMonad m => MVector (PrimState m) Float -> m () # basicSet :: PrimMonad m => MVector (PrimState m) Float -> Float -> m () # basicUnsafeCopy :: PrimMonad m => MVector (PrimState m) Float -> MVector (PrimState m) Float -> m () # basicUnsafeMove :: PrimMonad m => MVector (PrimState m) Float -> MVector (PrimState m) Float -> m () # basicUnsafeGrow :: PrimMonad m => MVector (PrimState m) Float -> Int -> m (MVector (PrimState m) Float) #
Generic1 (URec Float :: k -> Type)
Instance details Defined in GHC.Generics Associated Types type Rep1 (URec Float) :: k -> Type # Methods from1 :: URec Float a -> Rep1 (URec Float) a # to1 :: Rep1 (URec Float) a -> URec Float a #
AEq (Complex Float)
Instance details Defined in Data.AEq Methods (===) :: Complex Float -> Complex Float -> Bool # (~==) :: Complex Float -> Complex Float -> Bool #
Functor (URec Float :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods fmap :: (a -> b) -> URec Float a -> URec Float b # (<$) :: a -> URec Float b -> URec Float a #
Foldable (URec Float :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Foldable Methods fold :: Monoid m => URec Float m -> m # foldMap :: Monoid m => (a -> m) -> URec Float a -> m # foldr :: (a -> b -> b) -> b -> URec Float a -> b # foldr' :: (a -> b -> b) -> b -> URec Float a -> b # foldl :: (b -> a -> b) -> b -> URec Float a -> b # foldl' :: (b -> a -> b) -> b -> URec Float a -> b # foldr1 :: (a -> a -> a) -> URec Float a -> a # foldl1 :: (a -> a -> a) -> URec Float a -> a # toList :: URec Float a -> [a] # null :: URec Float a -> Bool # length :: URec Float a -> Int # elem :: Eq a => a -> URec Float a -> Bool # maximum :: Ord a => URec Float a -> a # minimum :: Ord a => URec Float a -> a # sum :: Num a => URec Float a -> a # product :: Num a => URec Float a -> a #
Traversable (URec Float :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> URec Float a -> f (URec Float b) # sequenceA :: Applicative f => URec Float (f a) -> f (URec Float a) # mapM :: Monad m => (a -> m b) -> URec Float a -> m (URec Float b) # sequence :: Monad m => URec Float (m a) -> m (URec Float a) #
Eq (URec Float p)
Instance details Defined in GHC.Generics Methods (==) :: URec Float p -> URec Float p -> Bool # (/=) :: URec Float p -> URec Float p -> Bool #
Ord (URec Float p)
Instance details Defined in GHC.Generics Methods compare :: URec Float p -> URec Float p -> Ordering # (<) :: URec Float p -> URec Float p -> Bool # (<=) :: URec Float p -> URec Float p -> Bool # (>) :: URec Float p -> URec Float p -> Bool # (>=) :: URec Float p -> URec Float p -> Bool # max :: URec Float p -> URec Float p -> URec Float p # min :: URec Float p -> URec Float p -> URec Float p #
Show (URec Float p)
Instance details Defined in GHC.Generics Methods showsPrec :: Int -> URec Float p -> ShowS # show :: URec Float p -> String # showList :: [URec Float p] -> ShowS #
Generic (URec Float p)
Instance details Defined in GHC.Generics Associated Types type Rep (URec Float p) :: Type -> Type # Methods from :: URec Float p -> Rep (URec Float p) x # to :: Rep (URec Float p) x -> URec Float p #
data Vector Float
Instance details Defined in Data.Vector.Unboxed.Base data Vector Float = V_Float (Vector Float)
data URec Float (p :: k)	Used for marking occurrences of `Float#` Since: base-4.9.0.0
Instance details Defined in GHC.Generics data URec Float (p :: k) = UFloat { uFloat# :: Float# }
data MVector s Float
Instance details Defined in Data.Vector.Unboxed.Base data MVector s Float = MV_Float (MVector s Float)
type Rep1 (URec Float :: k -> Type)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics type Rep1 (URec Float :: k -> Type) = D1 (MetaData "URec" "GHC.Generics" "base" False) (C1 (MetaCons "UFloat" PrefixI True) (S1 (MetaSel (Just "uFloat#") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (UFloat :: k -> Type)))
type Rep (URec Float p)
Instance details Defined in GHC.Generics type Rep (URec Float p) = D1 (MetaData "URec" "GHC.Generics" "base" False) (C1 (MetaCons "UFloat" PrefixI True) (S1 (MetaSel (Just "uFloat#") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (UFloat :: Type -> Type)))

data Int #

A fixed-precision integer type with at least the range [-2^29 .. 2^29-1]. The exact range for a given implementation can be determined by using minBound and maxBound from the Bounded class.

Instances

Bounded Int	Since: base-2.1
Instance details Defined in GHC.Enum Methods minBound :: Int # maxBound :: Int #
Enum Int	Since: base-2.1
Instance details Defined in GHC.Enum Methods succ :: Int -> Int # pred :: Int -> Int # toEnum :: Int -> Int # fromEnum :: Int -> Int # enumFrom :: Int -> [Int] # enumFromThen :: Int -> Int -> [Int] # enumFromTo :: Int -> Int -> [Int] # enumFromThenTo :: Int -> Int -> Int -> [Int] #
Eq Int
Instance details Defined in GHC.Classes Methods (==) :: Int -> Int -> Bool # (/=) :: Int -> Int -> Bool #
Integral Int	Since: base-2.0.1
Instance details Defined in GHC.Real Methods quot :: Int -> Int -> Int # rem :: Int -> Int -> Int # div :: Int -> Int -> Int # mod :: Int -> Int -> Int # quotRem :: Int -> Int -> (Int, Int) # divMod :: Int -> Int -> (Int, Int) # toInteger :: Int -> Integer #
Data Int	Since: base-4.0.0.0
Instance details Defined in Data.Data Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Int -> c Int # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Int # toConstr :: Int -> Constr # dataTypeOf :: Int -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c Int) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Int) # gmapT :: (forall b. Data b => b -> b) -> Int -> Int # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Int -> r # gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Int -> r # gmapQ :: (forall d. Data d => d -> u) -> Int -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> Int -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Int -> m Int # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Int -> m Int # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Int -> m Int #
Num Int	Since: base-2.1
Instance details Defined in GHC.Num Methods (+) :: Int -> Int -> Int # (-) :: Int -> Int -> Int # (*) :: Int -> Int -> Int # negate :: Int -> Int # abs :: Int -> Int # signum :: Int -> Int # fromInteger :: Integer -> Int #
Ord Int
Instance details Defined in GHC.Classes Methods compare :: Int -> Int -> Ordering # (<) :: Int -> Int -> Bool # (<=) :: Int -> Int -> Bool # (>) :: Int -> Int -> Bool # (>=) :: Int -> Int -> Bool # max :: Int -> Int -> Int # min :: Int -> Int -> Int #
Read Int	Since: base-2.1
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS Int # readList :: ReadS [Int] # readPrec :: ReadPrec Int # readListPrec :: ReadPrec [Int] #
Real Int	Since: base-2.0.1
Instance details Defined in GHC.Real Methods toRational :: Int -> Rational #
Show Int	Since: base-2.1
Instance details Defined in GHC.Show Methods showsPrec :: Int -> Int -> ShowS # show :: Int -> String # showList :: [Int] -> ShowS #
Ix Int	Since: base-2.1
Instance details Defined in GHC.Arr Methods range :: (Int, Int) -> [Int] # index :: (Int, Int) -> Int -> Int # unsafeIndex :: (Int, Int) -> Int -> Int inRange :: (Int, Int) -> Int -> Bool # rangeSize :: (Int, Int) -> Int # unsafeRangeSize :: (Int, Int) -> Int
Storable Int	Since: base-2.1
Instance details Defined in Foreign.Storable Methods sizeOf :: Int -> Int # alignment :: Int -> Int # peekElemOff :: Ptr Int -> Int -> IO Int # pokeElemOff :: Ptr Int -> Int -> Int -> IO () # peekByteOff :: Ptr b -> Int -> IO Int # pokeByteOff :: Ptr b -> Int -> Int -> IO () # peek :: Ptr Int -> IO Int # poke :: Ptr Int -> Int -> IO () #
Bits Int	Since: base-2.1
Instance details Defined in Data.Bits Methods (.&.) :: Int -> Int -> Int # (.\|.) :: Int -> Int -> Int # xor :: Int -> Int -> Int # complement :: Int -> Int # shift :: Int -> Int -> Int # rotate :: Int -> Int -> Int # zeroBits :: Int # bit :: Int -> Int # setBit :: Int -> Int -> Int # clearBit :: Int -> Int -> Int # complementBit :: Int -> Int -> Int # testBit :: Int -> Int -> Bool # bitSizeMaybe :: Int -> Maybe Int # bitSize :: Int -> Int # isSigned :: Int -> Bool # shiftL :: Int -> Int -> Int # unsafeShiftL :: Int -> Int -> Int # shiftR :: Int -> Int -> Int # unsafeShiftR :: Int -> Int -> Int # rotateL :: Int -> Int -> Int # rotateR :: Int -> Int -> Int # popCount :: Int -> Int #
FiniteBits Int	Since: base-4.6.0.0
Instance details Defined in Data.Bits Methods finiteBitSize :: Int -> Int # countLeadingZeros :: Int -> Int # countTrailingZeros :: Int -> Int #
NFData Int
Instance details Defined in Control.DeepSeq Methods rnf :: Int -> () #
AEq Int
Instance details Defined in Data.AEq Methods (===) :: Int -> Int -> Bool # (~==) :: Int -> Int -> Bool #
Prim Int
Instance details Defined in Data.Primitive.Types Methods sizeOf# :: Int -> Int# # alignment# :: Int -> Int# # indexByteArray# :: ByteArray# -> Int# -> Int # readByteArray# :: MutableByteArray# s -> Int# -> State# s -> (#State# s, Int#) # writeByteArray# :: MutableByteArray# s -> Int# -> Int -> State# s -> State# s # setByteArray# :: MutableByteArray# s -> Int# -> Int# -> Int -> State# s -> State# s # indexOffAddr# :: Addr# -> Int# -> Int # readOffAddr# :: Addr# -> Int# -> State# s -> (#State# s, Int#) # writeOffAddr# :: Addr# -> Int# -> Int -> State# s -> State# s # setOffAddr# :: Addr# -> Int# -> Int# -> Int -> State# s -> State# s #
Unbox Int
Instance details Defined in Data.Vector.Unboxed.Base
Vector Vector Int
Instance details Defined in Data.Vector.Unboxed.Base Methods basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) Int -> m (Vector Int) # basicUnsafeThaw :: PrimMonad m => Vector Int -> m (Mutable Vector (PrimState m) Int) # basicLength :: Vector Int -> Int # basicUnsafeSlice :: Int -> Int -> Vector Int -> Vector Int # basicUnsafeIndexM :: Monad m => Vector Int -> Int -> m Int # basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) Int -> Vector Int -> m () # elemseq :: Vector Int -> Int -> b -> b #
MVector MVector Int
Instance details Defined in Data.Vector.Unboxed.Base Methods basicLength :: MVector s Int -> Int # basicUnsafeSlice :: Int -> Int -> MVector s Int -> MVector s Int # basicOverlaps :: MVector s Int -> MVector s Int -> Bool # basicUnsafeNew :: PrimMonad m => Int -> m (MVector (PrimState m) Int) # basicInitialize :: PrimMonad m => MVector (PrimState m) Int -> m () # basicUnsafeReplicate :: PrimMonad m => Int -> Int -> m (MVector (PrimState m) Int) # basicUnsafeRead :: PrimMonad m => MVector (PrimState m) Int -> Int -> m Int # basicUnsafeWrite :: PrimMonad m => MVector (PrimState m) Int -> Int -> Int -> m () # basicClear :: PrimMonad m => MVector (PrimState m) Int -> m () # basicSet :: PrimMonad m => MVector (PrimState m) Int -> Int -> m () # basicUnsafeCopy :: PrimMonad m => MVector (PrimState m) Int -> MVector (PrimState m) Int -> m () # basicUnsafeMove :: PrimMonad m => MVector (PrimState m) Int -> MVector (PrimState m) Int -> m () # basicUnsafeGrow :: PrimMonad m => MVector (PrimState m) Int -> Int -> m (MVector (PrimState m) Int) #
Generic1 (URec Int :: k -> Type)
Instance details Defined in GHC.Generics Associated Types type Rep1 (URec Int) :: k -> Type # Methods from1 :: URec Int a -> Rep1 (URec Int) a # to1 :: Rep1 (URec Int) a -> URec Int a #
Functor (URec Int :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods fmap :: (a -> b) -> URec Int a -> URec Int b # (<$) :: a -> URec Int b -> URec Int a #
Foldable (URec Int :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Foldable Methods fold :: Monoid m => URec Int m -> m # foldMap :: Monoid m => (a -> m) -> URec Int a -> m # foldr :: (a -> b -> b) -> b -> URec Int a -> b # foldr' :: (a -> b -> b) -> b -> URec Int a -> b # foldl :: (b -> a -> b) -> b -> URec Int a -> b # foldl' :: (b -> a -> b) -> b -> URec Int a -> b # foldr1 :: (a -> a -> a) -> URec Int a -> a # foldl1 :: (a -> a -> a) -> URec Int a -> a # toList :: URec Int a -> [a] # null :: URec Int a -> Bool # length :: URec Int a -> Int # elem :: Eq a => a -> URec Int a -> Bool # maximum :: Ord a => URec Int a -> a # minimum :: Ord a => URec Int a -> a # sum :: Num a => URec Int a -> a # product :: Num a => URec Int a -> a #
Traversable (URec Int :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> URec Int a -> f (URec Int b) # sequenceA :: Applicative f => URec Int (f a) -> f (URec Int a) # mapM :: Monad m => (a -> m b) -> URec Int a -> m (URec Int b) # sequence :: Monad m => URec Int (m a) -> m (URec Int a) #
Eq (URec Int p)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods (==) :: URec Int p -> URec Int p -> Bool # (/=) :: URec Int p -> URec Int p -> Bool #
Ord (URec Int p)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods compare :: URec Int p -> URec Int p -> Ordering # (<) :: URec Int p -> URec Int p -> Bool # (<=) :: URec Int p -> URec Int p -> Bool # (>) :: URec Int p -> URec Int p -> Bool # (>=) :: URec Int p -> URec Int p -> Bool # max :: URec Int p -> URec Int p -> URec Int p # min :: URec Int p -> URec Int p -> URec Int p #
Show (URec Int p)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods showsPrec :: Int -> URec Int p -> ShowS # show :: URec Int p -> String # showList :: [URec Int p] -> ShowS #
Generic (URec Int p)
Instance details Defined in GHC.Generics Associated Types type Rep (URec Int p) :: Type -> Type # Methods from :: URec Int p -> Rep (URec Int p) x # to :: Rep (URec Int p) x -> URec Int p #
data Vector Int
Instance details Defined in Data.Vector.Unboxed.Base data Vector Int = V_Int (Vector Int)
data URec Int (p :: k)	Used for marking occurrences of `Int#` Since: base-4.9.0.0
Instance details Defined in GHC.Generics data URec Int (p :: k) = UInt { uInt# :: Int# }
data MVector s Int
Instance details Defined in Data.Vector.Unboxed.Base data MVector s Int = MV_Int (MVector s Int)
type Rep1 (URec Int :: k -> Type)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics type Rep1 (URec Int :: k -> Type) = D1 (MetaData "URec" "GHC.Generics" "base" False) (C1 (MetaCons "UInt" PrefixI True) (S1 (MetaSel (Just "uInt#") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (UInt :: k -> Type)))
type Rep (URec Int p)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics type Rep (URec Int p) = D1 (MetaData "URec" "GHC.Generics" "base" False) (C1 (MetaCons "UInt" PrefixI True) (S1 (MetaSel (Just "uInt#") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (UInt :: Type -> Type)))

data Integer #

Invariant: Jn# and Jp# are used iff value doesn't fit in S#

Useful properties resulting from the invariants:

```
abs (S# _) <= abs (Jp# _)
```
```
abs (S# _) <  abs (Jn# _)
```

Instances

Enum Integer	Since: base-2.1
Instance details Defined in GHC.Enum Methods succ :: Integer -> Integer # pred :: Integer -> Integer # toEnum :: Int -> Integer # fromEnum :: Integer -> Int # enumFrom :: Integer -> [Integer] # enumFromThen :: Integer -> Integer -> [Integer] # enumFromTo :: Integer -> Integer -> [Integer] # enumFromThenTo :: Integer -> Integer -> Integer -> [Integer] #
Eq Integer
Instance details Defined in GHC.Integer.Type Methods (==) :: Integer -> Integer -> Bool # (/=) :: Integer -> Integer -> Bool #
Integral Integer	Since: base-2.0.1
Instance details Defined in GHC.Real Methods quot :: Integer -> Integer -> Integer # rem :: Integer -> Integer -> Integer # div :: Integer -> Integer -> Integer # mod :: Integer -> Integer -> Integer # quotRem :: Integer -> Integer -> (Integer, Integer) # divMod :: Integer -> Integer -> (Integer, Integer) # toInteger :: Integer -> Integer #
Data Integer	Since: base-4.0.0.0
Instance details Defined in Data.Data Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Integer -> c Integer # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Integer # toConstr :: Integer -> Constr # dataTypeOf :: Integer -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c Integer) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Integer) # gmapT :: (forall b. Data b => b -> b) -> Integer -> Integer # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Integer -> r # gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Integer -> r # gmapQ :: (forall d. Data d => d -> u) -> Integer -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> Integer -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Integer -> m Integer # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Integer -> m Integer # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Integer -> m Integer #
Num Integer	Since: base-2.1
Instance details Defined in GHC.Num Methods (+) :: Integer -> Integer -> Integer # (-) :: Integer -> Integer -> Integer # (*) :: Integer -> Integer -> Integer # negate :: Integer -> Integer # abs :: Integer -> Integer # signum :: Integer -> Integer # fromInteger :: Integer -> Integer #
Ord Integer
Instance details Defined in GHC.Integer.Type Methods compare :: Integer -> Integer -> Ordering # (<) :: Integer -> Integer -> Bool # (<=) :: Integer -> Integer -> Bool # (>) :: Integer -> Integer -> Bool # (>=) :: Integer -> Integer -> Bool # max :: Integer -> Integer -> Integer # min :: Integer -> Integer -> Integer #
Read Integer	Since: base-2.1
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS Integer # readList :: ReadS [Integer] # readPrec :: ReadPrec Integer # readListPrec :: ReadPrec [Integer] #
Real Integer	Since: base-2.0.1
Instance details Defined in GHC.Real Methods toRational :: Integer -> Rational #
Show Integer	Since: base-2.1
Instance details Defined in GHC.Show Methods showsPrec :: Int -> Integer -> ShowS # show :: Integer -> String # showList :: [Integer] -> ShowS #
Ix Integer	Since: base-2.1
Instance details Defined in GHC.Arr Methods range :: (Integer, Integer) -> [Integer] # index :: (Integer, Integer) -> Integer -> Int # unsafeIndex :: (Integer, Integer) -> Integer -> Int inRange :: (Integer, Integer) -> Integer -> Bool # rangeSize :: (Integer, Integer) -> Int # unsafeRangeSize :: (Integer, Integer) -> Int
Bits Integer	Since: base-2.1
Instance details Defined in Data.Bits Methods (.&.) :: Integer -> Integer -> Integer # (.\|.) :: Integer -> Integer -> Integer # xor :: Integer -> Integer -> Integer # complement :: Integer -> Integer # shift :: Integer -> Int -> Integer # rotate :: Integer -> Int -> Integer # zeroBits :: Integer # bit :: Int -> Integer # setBit :: Integer -> Int -> Integer # clearBit :: Integer -> Int -> Integer # complementBit :: Integer -> Int -> Integer # testBit :: Integer -> Int -> Bool # bitSizeMaybe :: Integer -> Maybe Int # bitSize :: Integer -> Int # isSigned :: Integer -> Bool # shiftL :: Integer -> Int -> Integer # unsafeShiftL :: Integer -> Int -> Integer # shiftR :: Integer -> Int -> Integer # unsafeShiftR :: Integer -> Int -> Integer # rotateL :: Integer -> Int -> Integer # rotateR :: Integer -> Int -> Integer # popCount :: Integer -> Int #
NFData Integer
Instance details Defined in Control.DeepSeq Methods rnf :: Integer -> () #
AEq Integer
Instance details Defined in Data.AEq Methods (===) :: Integer -> Integer -> Bool # (~==) :: Integer -> Integer -> Bool #

data Maybe a #

The Maybe type encapsulates an optional value. A value of type Maybe a either contains a value of type a (represented as Just a), or it is empty (represented as Nothing). Using Maybe is a good way to deal with errors or exceptional cases without resorting to drastic measures such as error.

The Maybe type is also a monad. It is a simple kind of error monad, where all errors are represented by Nothing. A richer error monad can be built using the Either type.

Constructors

Nothing
Just a

Instances

Monad Maybe	Since: base-2.1
Instance details Defined in GHC.Base Methods (>>=) :: Maybe a -> (a -> Maybe b) -> Maybe b # (>>) :: Maybe a -> Maybe b -> Maybe b # return :: a -> Maybe a # fail :: String -> Maybe a #
Functor Maybe	Since: base-2.1
Instance details Defined in GHC.Base Methods fmap :: (a -> b) -> Maybe a -> Maybe b # (<$) :: a -> Maybe b -> Maybe a #
Applicative Maybe	Since: base-2.1
Instance details Defined in GHC.Base Methods pure :: a -> Maybe a # (<>) :: Maybe (a -> b) -> Maybe a -> Maybe b # liftA2 :: (a -> b -> c) -> Maybe a -> Maybe b -> Maybe c # (>) :: Maybe a -> Maybe b -> Maybe b # (<*) :: Maybe a -> Maybe b -> Maybe a #
Foldable Maybe	Since: base-2.1
Instance details Defined in Data.Foldable Methods fold :: Monoid m => Maybe m -> m # foldMap :: Monoid m => (a -> m) -> Maybe a -> m # foldr :: (a -> b -> b) -> b -> Maybe a -> b # foldr' :: (a -> b -> b) -> b -> Maybe a -> b # foldl :: (b -> a -> b) -> b -> Maybe a -> b # foldl' :: (b -> a -> b) -> b -> Maybe a -> b # foldr1 :: (a -> a -> a) -> Maybe a -> a # foldl1 :: (a -> a -> a) -> Maybe a -> a # toList :: Maybe a -> [a] # null :: Maybe a -> Bool # length :: Maybe a -> Int # elem :: Eq a => a -> Maybe a -> Bool # maximum :: Ord a => Maybe a -> a # minimum :: Ord a => Maybe a -> a # sum :: Num a => Maybe a -> a # product :: Num a => Maybe a -> a #
Traversable Maybe	Since: base-2.1
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> Maybe a -> f (Maybe b) # sequenceA :: Applicative f => Maybe (f a) -> f (Maybe a) # mapM :: Monad m => (a -> m b) -> Maybe a -> m (Maybe b) # sequence :: Monad m => Maybe (m a) -> m (Maybe a) #
Eq1 Maybe	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Classes Methods liftEq :: (a -> b -> Bool) -> Maybe a -> Maybe b -> Bool #
Ord1 Maybe	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Classes Methods liftCompare :: (a -> b -> Ordering) -> Maybe a -> Maybe b -> Ordering #
Read1 Maybe	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Classes Methods liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (Maybe a) # liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [Maybe a] # liftReadPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec (Maybe a) # liftReadListPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec [Maybe a] #
Show1 Maybe	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Classes Methods liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> Maybe a -> ShowS # liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [Maybe a] -> ShowS #
Alternative Maybe	Since: base-2.1
Instance details Defined in GHC.Base Methods empty :: Maybe a # (<\|>) :: Maybe a -> Maybe a -> Maybe a # some :: Maybe a -> Maybe [a] # many :: Maybe a -> Maybe [a] #
MonadPlus Maybe	Since: base-2.1
Instance details Defined in GHC.Base Methods mzero :: Maybe a # mplus :: Maybe a -> Maybe a -> Maybe a #
NFData1 Maybe	Since: deepseq-1.4.3.0
Instance details Defined in Control.DeepSeq Methods liftRnf :: (a -> ()) -> Maybe a -> () #
Eq a => Eq (Maybe a)	Since: base-2.1
Instance details Defined in GHC.Maybe Methods (==) :: Maybe a -> Maybe a -> Bool # (/=) :: Maybe a -> Maybe a -> Bool #
Data a => Data (Maybe a)	Since: base-4.0.0.0
Instance details Defined in Data.Data Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Maybe a -> c (Maybe a) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Maybe a) # toConstr :: Maybe a -> Constr # dataTypeOf :: Maybe a -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Maybe a)) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Maybe a)) # gmapT :: (forall b. Data b => b -> b) -> Maybe a -> Maybe a # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Maybe a -> r # gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Maybe a -> r # gmapQ :: (forall d. Data d => d -> u) -> Maybe a -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> Maybe a -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Maybe a -> m (Maybe a) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Maybe a -> m (Maybe a) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Maybe a -> m (Maybe a) #
Ord a => Ord (Maybe a)	Since: base-2.1
Instance details Defined in GHC.Maybe Methods compare :: Maybe a -> Maybe a -> Ordering # (<) :: Maybe a -> Maybe a -> Bool # (<=) :: Maybe a -> Maybe a -> Bool # (>) :: Maybe a -> Maybe a -> Bool # (>=) :: Maybe a -> Maybe a -> Bool # max :: Maybe a -> Maybe a -> Maybe a # min :: Maybe a -> Maybe a -> Maybe a #
Read a => Read (Maybe a)	Since: base-2.1
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS (Maybe a) # readList :: ReadS [Maybe a] # readPrec :: ReadPrec (Maybe a) # readListPrec :: ReadPrec [Maybe a] #
Show a => Show (Maybe a)	Since: base-2.1
Instance details Defined in GHC.Show Methods showsPrec :: Int -> Maybe a -> ShowS # show :: Maybe a -> String # showList :: [Maybe a] -> ShowS #
Generic (Maybe a)
Instance details Defined in GHC.Generics Associated Types type Rep (Maybe a) :: Type -> Type # Methods from :: Maybe a -> Rep (Maybe a) x # to :: Rep (Maybe a) x -> Maybe a #
Semigroup a => Semigroup (Maybe a)	Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods (<>) :: Maybe a -> Maybe a -> Maybe a # sconcat :: NonEmpty (Maybe a) -> Maybe a # stimes :: Integral b => b -> Maybe a -> Maybe a #
Semigroup a => Monoid (Maybe a)	Lift a semigroup into `Maybe` forming a `Monoid` according to http://en.wikipedia.org/wiki/Monoid: "Any semigroup `S` may be turned into a monoid simply by adjoining an element `e` not in `S` and defining `ee = e` and `es = s = se` for all `s ∈ S`." Since 4.11.0: constraint on inner `a` value generalised from `Monoid` to `Semigroup`. Since: base-2.1*
Instance details Defined in GHC.Base Methods mempty :: Maybe a # mappend :: Maybe a -> Maybe a -> Maybe a # mconcat :: [Maybe a] -> Maybe a #
SingKind a => SingKind (Maybe a)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Associated Types type DemoteRep (Maybe a) :: Type Methods fromSing :: Sing a0 -> DemoteRep (Maybe a)
NFData a => NFData (Maybe a)
Instance details Defined in Control.DeepSeq Methods rnf :: Maybe a -> () #
AEq a => AEq (Maybe a)
Instance details Defined in Data.AEq Methods (===) :: Maybe a -> Maybe a -> Bool # (~==) :: Maybe a -> Maybe a -> Bool #
Generic1 Maybe
Instance details Defined in GHC.Generics Associated Types type Rep1 Maybe :: k -> Type # Methods from1 :: Maybe a -> Rep1 Maybe a # to1 :: Rep1 Maybe a -> Maybe a #
SingI (Nothing :: Maybe a)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods sing :: Sing Nothing
SingI a2 => SingI (Just a2 :: Maybe a1)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods sing :: Sing (Just a2)
type Rep (Maybe a)	Since: base-4.6.0.0
Instance details Defined in GHC.Generics type Rep (Maybe a) = D1 (MetaData "Maybe" "GHC.Maybe" "base" False) (C1 (MetaCons "Nothing" PrefixI False) (U1 :: Type -> Type) :+: C1 (MetaCons "Just" PrefixI False) (S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a)))
data Sing (b :: Maybe a)
Instance details Defined in GHC.Generics data Sing (b :: Maybe a) where SNothing :: forall a (b :: Maybe a). Sing (Nothing :: Maybe a) SJust :: forall a (b :: Maybe a) (a1 :: a). Sing a1 -> Sing (Just a1)
type DemoteRep (Maybe a)
Instance details Defined in GHC.Generics type DemoteRep (Maybe a) = Maybe (DemoteRep a)
type Rep1 Maybe	Since: base-4.6.0.0
Instance details Defined in GHC.Generics type Rep1 Maybe = D1 (MetaData "Maybe" "GHC.Maybe" "base" False) (C1 (MetaCons "Nothing" PrefixI False) (U1 :: Type -> Type) :+: C1 (MetaCons "Just" PrefixI False) (S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) Par1))

data Ordering #

Constructors

LT
EQ
GT

Instances

Bounded Ordering	Since: base-2.1
Instance details Defined in GHC.Enum Methods minBound :: Ordering # maxBound :: Ordering #
Enum Ordering	Since: base-2.1
Instance details Defined in GHC.Enum Methods succ :: Ordering -> Ordering # pred :: Ordering -> Ordering # toEnum :: Int -> Ordering # fromEnum :: Ordering -> Int # enumFrom :: Ordering -> [Ordering] # enumFromThen :: Ordering -> Ordering -> [Ordering] # enumFromTo :: Ordering -> Ordering -> [Ordering] # enumFromThenTo :: Ordering -> Ordering -> Ordering -> [Ordering] #
Eq Ordering
Instance details Defined in GHC.Classes Methods (==) :: Ordering -> Ordering -> Bool # (/=) :: Ordering -> Ordering -> Bool #
Data Ordering	Since: base-4.0.0.0
Instance details Defined in Data.Data Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Ordering -> c Ordering # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Ordering # toConstr :: Ordering -> Constr # dataTypeOf :: Ordering -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c Ordering) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Ordering) # gmapT :: (forall b. Data b => b -> b) -> Ordering -> Ordering # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Ordering -> r # gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Ordering -> r # gmapQ :: (forall d. Data d => d -> u) -> Ordering -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> Ordering -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Ordering -> m Ordering # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Ordering -> m Ordering # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Ordering -> m Ordering #
Ord Ordering
Instance details Defined in GHC.Classes Methods compare :: Ordering -> Ordering -> Ordering # (<) :: Ordering -> Ordering -> Bool # (<=) :: Ordering -> Ordering -> Bool # (>) :: Ordering -> Ordering -> Bool # (>=) :: Ordering -> Ordering -> Bool # max :: Ordering -> Ordering -> Ordering # min :: Ordering -> Ordering -> Ordering #
Read Ordering	Since: base-2.1
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS Ordering # readList :: ReadS [Ordering] # readPrec :: ReadPrec Ordering # readListPrec :: ReadPrec [Ordering] #
Show Ordering	Since: base-2.1
Instance details Defined in GHC.Show Methods showsPrec :: Int -> Ordering -> ShowS # show :: Ordering -> String # showList :: [Ordering] -> ShowS #
Ix Ordering	Since: base-2.1
Instance details Defined in GHC.Arr Methods range :: (Ordering, Ordering) -> [Ordering] # index :: (Ordering, Ordering) -> Ordering -> Int # unsafeIndex :: (Ordering, Ordering) -> Ordering -> Int inRange :: (Ordering, Ordering) -> Ordering -> Bool # rangeSize :: (Ordering, Ordering) -> Int # unsafeRangeSize :: (Ordering, Ordering) -> Int
Generic Ordering
Instance details Defined in GHC.Generics Associated Types type Rep Ordering :: Type -> Type # Methods from :: Ordering -> Rep Ordering x # to :: Rep Ordering x -> Ordering #
Semigroup Ordering	Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods (<>) :: Ordering -> Ordering -> Ordering # sconcat :: NonEmpty Ordering -> Ordering # stimes :: Integral b => b -> Ordering -> Ordering #
Monoid Ordering	Since: base-2.1
Instance details Defined in GHC.Base Methods mempty :: Ordering # mappend :: Ordering -> Ordering -> Ordering # mconcat :: [Ordering] -> Ordering #
NFData Ordering
Instance details Defined in Control.DeepSeq Methods rnf :: Ordering -> () #
AEq Ordering
Instance details Defined in Data.AEq Methods (===) :: Ordering -> Ordering -> Bool # (~==) :: Ordering -> Ordering -> Bool #
type Rep Ordering	Since: base-4.6.0.0
Instance details Defined in GHC.Generics type Rep Ordering = D1 (MetaData "Ordering" "GHC.Types" "ghc-prim" False) (C1 (MetaCons "LT" PrefixI False) (U1 :: Type -> Type) :+: (C1 (MetaCons "EQ" PrefixI False) (U1 :: Type -> Type) :+: C1 (MetaCons "GT" PrefixI False) (U1 :: Type -> Type)))

type Rational = Ratio Integer #

Arbitrary-precision rational numbers, represented as a ratio of two Integer values. A rational number may be constructed using the % operator.

data IO a #

A value of type IO a is a computation which, when performed, does some I/O before returning a value of type a.

There is really only one way to "perform" an I/O action: bind it to Main.main in your program. When your program is run, the I/O will be performed. It isn't possible to perform I/O from an arbitrary function, unless that function is itself in the IO monad and called at some point, directly or indirectly, from Main.main.

IO is a monad, so IO actions can be combined using either the do-notation or the >> and >>= operations from the Monad class.

Instances

Monad IO	Since: base-2.1
Instance details Defined in GHC.Base Methods (>>=) :: IO a -> (a -> IO b) -> IO b # (>>) :: IO a -> IO b -> IO b # return :: a -> IO a # fail :: String -> IO a #
Functor IO	Since: base-2.1
Instance details Defined in GHC.Base Methods fmap :: (a -> b) -> IO a -> IO b # (<$) :: a -> IO b -> IO a #
Applicative IO	Since: base-2.1
Instance details Defined in GHC.Base Methods pure :: a -> IO a # (<>) :: IO (a -> b) -> IO a -> IO b # liftA2 :: (a -> b -> c) -> IO a -> IO b -> IO c # (>) :: IO a -> IO b -> IO b # (<*) :: IO a -> IO b -> IO a #
Alternative IO	Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods empty :: IO a # (<\|>) :: IO a -> IO a -> IO a # some :: IO a -> IO [a] # many :: IO a -> IO [a] #
MonadPlus IO	Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods mzero :: IO a # mplus :: IO a -> IO a -> IO a #
PrimMonad IO
Instance details Defined in Control.Monad.Primitive Associated Types type PrimState IO :: Type # Methods primitive :: (State# (PrimState IO) -> (#State# (PrimState IO), a#)) -> IO a #
PrimBase IO
Instance details Defined in Control.Monad.Primitive Methods internal :: IO a -> State# (PrimState IO) -> (#State# (PrimState IO), a#) #
Semigroup a => Semigroup (IO a)	Since: base-4.10.0.0
Instance details Defined in GHC.Base Methods (<>) :: IO a -> IO a -> IO a # sconcat :: NonEmpty (IO a) -> IO a # stimes :: Integral b => b -> IO a -> IO a #
Monoid a => Monoid (IO a)	Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods mempty :: IO a # mappend :: IO a -> IO a -> IO a # mconcat :: [IO a] -> IO a #
type PrimState IO
Instance details Defined in Control.Monad.Primitive type PrimState IO = RealWorld

data Word #

A Word is an unsigned integral type, with the same size as Int.

Instances

Bounded Word	Since: base-2.1
Instance details Defined in GHC.Enum Methods minBound :: Word # maxBound :: Word #
Enum Word	Since: base-2.1
Instance details Defined in GHC.Enum Methods succ :: Word -> Word # pred :: Word -> Word # toEnum :: Int -> Word # fromEnum :: Word -> Int # enumFrom :: Word -> [Word] # enumFromThen :: Word -> Word -> [Word] # enumFromTo :: Word -> Word -> [Word] # enumFromThenTo :: Word -> Word -> Word -> [Word] #
Eq Word
Instance details Defined in GHC.Classes Methods (==) :: Word -> Word -> Bool # (/=) :: Word -> Word -> Bool #
Integral Word	Since: base-2.1
Instance details Defined in GHC.Real Methods quot :: Word -> Word -> Word # rem :: Word -> Word -> Word # div :: Word -> Word -> Word # mod :: Word -> Word -> Word # quotRem :: Word -> Word -> (Word, Word) # divMod :: Word -> Word -> (Word, Word) # toInteger :: Word -> Integer #
Data Word	Since: base-4.0.0.0
Instance details Defined in Data.Data Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Word -> c Word # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Word # toConstr :: Word -> Constr # dataTypeOf :: Word -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c Word) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Word) # gmapT :: (forall b. Data b => b -> b) -> Word -> Word # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Word -> r # gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Word -> r # gmapQ :: (forall d. Data d => d -> u) -> Word -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> Word -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Word -> m Word # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Word -> m Word # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Word -> m Word #
Num Word	Since: base-2.1
Instance details Defined in GHC.Num Methods (+) :: Word -> Word -> Word # (-) :: Word -> Word -> Word # (*) :: Word -> Word -> Word # negate :: Word -> Word # abs :: Word -> Word # signum :: Word -> Word # fromInteger :: Integer -> Word #
Ord Word
Instance details Defined in GHC.Classes Methods compare :: Word -> Word -> Ordering # (<) :: Word -> Word -> Bool # (<=) :: Word -> Word -> Bool # (>) :: Word -> Word -> Bool # (>=) :: Word -> Word -> Bool # max :: Word -> Word -> Word # min :: Word -> Word -> Word #
Read Word	Since: base-4.5.0.0
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS Word # readList :: ReadS [Word] # readPrec :: ReadPrec Word # readListPrec :: ReadPrec [Word] #
Real Word	Since: base-2.1
Instance details Defined in GHC.Real Methods toRational :: Word -> Rational #
Show Word	Since: base-2.1
Instance details Defined in GHC.Show Methods showsPrec :: Int -> Word -> ShowS # show :: Word -> String # showList :: [Word] -> ShowS #
Ix Word	Since: base-4.6.0.0
Instance details Defined in GHC.Arr Methods range :: (Word, Word) -> [Word] # index :: (Word, Word) -> Word -> Int # unsafeIndex :: (Word, Word) -> Word -> Int inRange :: (Word, Word) -> Word -> Bool # rangeSize :: (Word, Word) -> Int # unsafeRangeSize :: (Word, Word) -> Int
Storable Word	Since: base-2.1
Instance details Defined in Foreign.Storable Methods sizeOf :: Word -> Int # alignment :: Word -> Int # peekElemOff :: Ptr Word -> Int -> IO Word # pokeElemOff :: Ptr Word -> Int -> Word -> IO () # peekByteOff :: Ptr b -> Int -> IO Word # pokeByteOff :: Ptr b -> Int -> Word -> IO () # peek :: Ptr Word -> IO Word # poke :: Ptr Word -> Word -> IO () #
Bits Word	Since: base-2.1
Instance details Defined in Data.Bits Methods (.&.) :: Word -> Word -> Word # (.\|.) :: Word -> Word -> Word # xor :: Word -> Word -> Word # complement :: Word -> Word # shift :: Word -> Int -> Word # rotate :: Word -> Int -> Word # zeroBits :: Word # bit :: Int -> Word # setBit :: Word -> Int -> Word # clearBit :: Word -> Int -> Word # complementBit :: Word -> Int -> Word # testBit :: Word -> Int -> Bool # bitSizeMaybe :: Word -> Maybe Int # bitSize :: Word -> Int # isSigned :: Word -> Bool # shiftL :: Word -> Int -> Word # unsafeShiftL :: Word -> Int -> Word # shiftR :: Word -> Int -> Word # unsafeShiftR :: Word -> Int -> Word # rotateL :: Word -> Int -> Word # rotateR :: Word -> Int -> Word # popCount :: Word -> Int #
FiniteBits Word	Since: base-4.6.0.0
Instance details Defined in Data.Bits Methods finiteBitSize :: Word -> Int # countLeadingZeros :: Word -> Int # countTrailingZeros :: Word -> Int #
NFData Word
Instance details Defined in Control.DeepSeq Methods rnf :: Word -> () #
AEq Word
Instance details Defined in Data.AEq Methods (===) :: Word -> Word -> Bool # (~==) :: Word -> Word -> Bool #
Prim Word
Instance details Defined in Data.Primitive.Types Methods sizeOf# :: Word -> Int# # alignment# :: Word -> Int# # indexByteArray# :: ByteArray# -> Int# -> Word # readByteArray# :: MutableByteArray# s -> Int# -> State# s -> (#State# s, Word#) # writeByteArray# :: MutableByteArray# s -> Int# -> Word -> State# s -> State# s # setByteArray# :: MutableByteArray# s -> Int# -> Int# -> Word -> State# s -> State# s # indexOffAddr# :: Addr# -> Int# -> Word # readOffAddr# :: Addr# -> Int# -> State# s -> (#State# s, Word#) # writeOffAddr# :: Addr# -> Int# -> Word -> State# s -> State# s # setOffAddr# :: Addr# -> Int# -> Int# -> Word -> State# s -> State# s #
Unbox Word
Instance details Defined in Data.Vector.Unboxed.Base
Vector Vector Word
Instance details Defined in Data.Vector.Unboxed.Base Methods basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) Word -> m (Vector Word) # basicUnsafeThaw :: PrimMonad m => Vector Word -> m (Mutable Vector (PrimState m) Word) # basicLength :: Vector Word -> Int # basicUnsafeSlice :: Int -> Int -> Vector Word -> Vector Word # basicUnsafeIndexM :: Monad m => Vector Word -> Int -> m Word # basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) Word -> Vector Word -> m () # elemseq :: Vector Word -> Word -> b -> b #
MVector MVector Word
Instance details Defined in Data.Vector.Unboxed.Base Methods basicLength :: MVector s Word -> Int # basicUnsafeSlice :: Int -> Int -> MVector s Word -> MVector s Word # basicOverlaps :: MVector s Word -> MVector s Word -> Bool # basicUnsafeNew :: PrimMonad m => Int -> m (MVector (PrimState m) Word) # basicInitialize :: PrimMonad m => MVector (PrimState m) Word -> m () # basicUnsafeReplicate :: PrimMonad m => Int -> Word -> m (MVector (PrimState m) Word) # basicUnsafeRead :: PrimMonad m => MVector (PrimState m) Word -> Int -> m Word # basicUnsafeWrite :: PrimMonad m => MVector (PrimState m) Word -> Int -> Word -> m () # basicClear :: PrimMonad m => MVector (PrimState m) Word -> m () # basicSet :: PrimMonad m => MVector (PrimState m) Word -> Word -> m () # basicUnsafeCopy :: PrimMonad m => MVector (PrimState m) Word -> MVector (PrimState m) Word -> m () # basicUnsafeMove :: PrimMonad m => MVector (PrimState m) Word -> MVector (PrimState m) Word -> m () # basicUnsafeGrow :: PrimMonad m => MVector (PrimState m) Word -> Int -> m (MVector (PrimState m) Word) #
Generic1 (URec Word :: k -> Type)
Instance details Defined in GHC.Generics Associated Types type Rep1 (URec Word) :: k -> Type # Methods from1 :: URec Word a -> Rep1 (URec Word) a # to1 :: Rep1 (URec Word) a -> URec Word a #
Functor (URec Word :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods fmap :: (a -> b) -> URec Word a -> URec Word b # (<$) :: a -> URec Word b -> URec Word a #
Foldable (URec Word :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Foldable Methods fold :: Monoid m => URec Word m -> m # foldMap :: Monoid m => (a -> m) -> URec Word a -> m # foldr :: (a -> b -> b) -> b -> URec Word a -> b # foldr' :: (a -> b -> b) -> b -> URec Word a -> b # foldl :: (b -> a -> b) -> b -> URec Word a -> b # foldl' :: (b -> a -> b) -> b -> URec Word a -> b # foldr1 :: (a -> a -> a) -> URec Word a -> a # foldl1 :: (a -> a -> a) -> URec Word a -> a # toList :: URec Word a -> [a] # null :: URec Word a -> Bool # length :: URec Word a -> Int # elem :: Eq a => a -> URec Word a -> Bool # maximum :: Ord a => URec Word a -> a # minimum :: Ord a => URec Word a -> a # sum :: Num a => URec Word a -> a # product :: Num a => URec Word a -> a #
Traversable (URec Word :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> URec Word a -> f (URec Word b) # sequenceA :: Applicative f => URec Word (f a) -> f (URec Word a) # mapM :: Monad m => (a -> m b) -> URec Word a -> m (URec Word b) # sequence :: Monad m => URec Word (m a) -> m (URec Word a) #
Eq (URec Word p)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods (==) :: URec Word p -> URec Word p -> Bool # (/=) :: URec Word p -> URec Word p -> Bool #
Ord (URec Word p)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods compare :: URec Word p -> URec Word p -> Ordering # (<) :: URec Word p -> URec Word p -> Bool # (<=) :: URec Word p -> URec Word p -> Bool # (>) :: URec Word p -> URec Word p -> Bool # (>=) :: URec Word p -> URec Word p -> Bool # max :: URec Word p -> URec Word p -> URec Word p # min :: URec Word p -> URec Word p -> URec Word p #
Show (URec Word p)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods showsPrec :: Int -> URec Word p -> ShowS # show :: URec Word p -> String # showList :: [URec Word p] -> ShowS #
Generic (URec Word p)
Instance details Defined in GHC.Generics Associated Types type Rep (URec Word p) :: Type -> Type # Methods from :: URec Word p -> Rep (URec Word p) x # to :: Rep (URec Word p) x -> URec Word p #
data Vector Word
Instance details Defined in Data.Vector.Unboxed.Base data Vector Word = V_Word (Vector Word)
data URec Word (p :: k)	Used for marking occurrences of `Word#` Since: base-4.9.0.0
Instance details Defined in GHC.Generics data URec Word (p :: k) = UWord { uWord# :: Word# }
data MVector s Word
Instance details Defined in Data.Vector.Unboxed.Base data MVector s Word = MV_Word (MVector s Word)
type Rep1 (URec Word :: k -> Type)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics type Rep1 (URec Word :: k -> Type) = D1 (MetaData "URec" "GHC.Generics" "base" False) (C1 (MetaCons "UWord" PrefixI True) (S1 (MetaSel (Just "uWord#") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (UWord :: k -> Type)))
type Rep (URec Word p)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics type Rep (URec Word p) = D1 (MetaData "URec" "GHC.Generics" "base" False) (C1 (MetaCons "UWord" PrefixI True) (S1 (MetaSel (Just "uWord#") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (UWord :: Type -> Type)))

data Either a b #

The Either type represents values with two possibilities: a value of type Either a b is either Left a or Right b.

The Either type is sometimes used to represent a value which is either correct or an error; by convention, the Left constructor is used to hold an error value and the Right constructor is used to hold a correct value (mnemonic: "right" also means "correct").

Examples

Expand

The type Either String Int is the type of values which can be either a String or an Int. The Left constructor can be used only on Strings, and the Right constructor can be used only on Ints:

>>> let s = Left "foo" :: Either String Int
>>> s
Left "foo"
>>> let n = Right 3 :: Either String Int
>>> n
Right 3
>>> :type s
s :: Either String Int
>>> :type n
n :: Either String Int

The fmap from our Functor instance will ignore Left values, but will apply the supplied function to values contained in a Right:

>>> let s = Left "foo" :: Either String Int
>>> let n = Right 3 :: Either String Int
>>> fmap (*2) s
Left "foo"
>>> fmap (*2) n
Right 6

The Monad instance for Either allows us to chain together multiple actions which may fail, and fail overall if any of the individual steps failed. First we'll write a function that can either parse an Int from a Char, or fail.

>>> import Data.Char ( digitToInt, isDigit )
>>> :{
    let parseEither :: Char -> Either String Int
        parseEither c
          | isDigit c = Right (digitToInt c)
          | otherwise = Left "parse error"
>>> :}

The following should work, since both '1' and '2' can be parsed as Ints.

>>> :{
    let parseMultiple :: Either String Int
        parseMultiple = do
          x <- parseEither '1'
          y <- parseEither '2'
          return (x + y)
>>> :}

>>> parseMultiple
Right 3

But the following should fail overall, since the first operation where we attempt to parse 'm' as an Int will fail:

>>> :{
    let parseMultiple :: Either String Int
        parseMultiple = do
          x <- parseEither 'm'
          y <- parseEither '2'
          return (x + y)
>>> :}

>>> parseMultiple
Left "parse error"

Constructors

Left a
Right b

Instances

Eq2 Either	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Classes Methods liftEq2 :: (a -> b -> Bool) -> (c -> d -> Bool) -> Either a c -> Either b d -> Bool #
Ord2 Either	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Classes Methods liftCompare2 :: (a -> b -> Ordering) -> (c -> d -> Ordering) -> Either a c -> Either b d -> Ordering #
Read2 Either	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Classes Methods liftReadsPrec2 :: (Int -> ReadS a) -> ReadS [a] -> (Int -> ReadS b) -> ReadS [b] -> Int -> ReadS (Either a b) # liftReadList2 :: (Int -> ReadS a) -> ReadS [a] -> (Int -> ReadS b) -> ReadS [b] -> ReadS [Either a b] # liftReadPrec2 :: ReadPrec a -> ReadPrec [a] -> ReadPrec b -> ReadPrec [b] -> ReadPrec (Either a b) # liftReadListPrec2 :: ReadPrec a -> ReadPrec [a] -> ReadPrec b -> ReadPrec [b] -> ReadPrec [Either a b] #
Show2 Either	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Classes Methods liftShowsPrec2 :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> (Int -> b -> ShowS) -> ([b] -> ShowS) -> Int -> Either a b -> ShowS # liftShowList2 :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> (Int -> b -> ShowS) -> ([b] -> ShowS) -> [Either a b] -> ShowS #
NFData2 Either	Since: deepseq-1.4.3.0
Instance details Defined in Control.DeepSeq Methods liftRnf2 :: (a -> ()) -> (b -> ()) -> Either a b -> () #
Monad (Either e)	Since: base-4.4.0.0
Instance details Defined in Data.Either Methods (>>=) :: Either e a -> (a -> Either e b) -> Either e b # (>>) :: Either e a -> Either e b -> Either e b # return :: a -> Either e a # fail :: String -> Either e a #
Functor (Either a)	Since: base-3.0
Instance details Defined in Data.Either Methods fmap :: (a0 -> b) -> Either a a0 -> Either a b # (<$) :: a0 -> Either a b -> Either a a0 #
Applicative (Either e)	Since: base-3.0
Instance details Defined in Data.Either Methods pure :: a -> Either e a # (<>) :: Either e (a -> b) -> Either e a -> Either e b # liftA2 :: (a -> b -> c) -> Either e a -> Either e b -> Either e c # (>) :: Either e a -> Either e b -> Either e b # (<*) :: Either e a -> Either e b -> Either e a #
Foldable (Either a)	Since: base-4.7.0.0
Instance details Defined in Data.Foldable Methods fold :: Monoid m => Either a m -> m # foldMap :: Monoid m => (a0 -> m) -> Either a a0 -> m # foldr :: (a0 -> b -> b) -> b -> Either a a0 -> b # foldr' :: (a0 -> b -> b) -> b -> Either a a0 -> b # foldl :: (b -> a0 -> b) -> b -> Either a a0 -> b # foldl' :: (b -> a0 -> b) -> b -> Either a a0 -> b # foldr1 :: (a0 -> a0 -> a0) -> Either a a0 -> a0 # foldl1 :: (a0 -> a0 -> a0) -> Either a a0 -> a0 # toList :: Either a a0 -> [a0] # null :: Either a a0 -> Bool # length :: Either a a0 -> Int # elem :: Eq a0 => a0 -> Either a a0 -> Bool # maximum :: Ord a0 => Either a a0 -> a0 # minimum :: Ord a0 => Either a a0 -> a0 # sum :: Num a0 => Either a a0 -> a0 # product :: Num a0 => Either a a0 -> a0 #
Traversable (Either a)	Since: base-4.7.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a0 -> f b) -> Either a a0 -> f (Either a b) # sequenceA :: Applicative f => Either a (f a0) -> f (Either a a0) # mapM :: Monad m => (a0 -> m b) -> Either a a0 -> m (Either a b) # sequence :: Monad m => Either a (m a0) -> m (Either a a0) #
Eq a => Eq1 (Either a)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Classes Methods liftEq :: (a0 -> b -> Bool) -> Either a a0 -> Either a b -> Bool #
Ord a => Ord1 (Either a)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Classes Methods liftCompare :: (a0 -> b -> Ordering) -> Either a a0 -> Either a b -> Ordering #
Read a => Read1 (Either a)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Classes Methods liftReadsPrec :: (Int -> ReadS a0) -> ReadS [a0] -> Int -> ReadS (Either a a0) # liftReadList :: (Int -> ReadS a0) -> ReadS [a0] -> ReadS [Either a a0] # liftReadPrec :: ReadPrec a0 -> ReadPrec [a0] -> ReadPrec (Either a a0) # liftReadListPrec :: ReadPrec a0 -> ReadPrec [a0] -> ReadPrec [Either a a0] #
Show a => Show1 (Either a)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Classes Methods liftShowsPrec :: (Int -> a0 -> ShowS) -> ([a0] -> ShowS) -> Int -> Either a a0 -> ShowS # liftShowList :: (Int -> a0 -> ShowS) -> ([a0] -> ShowS) -> [Either a a0] -> ShowS #
NFData a => NFData1 (Either a)	Since: deepseq-1.4.3.0
Instance details Defined in Control.DeepSeq Methods liftRnf :: (a0 -> ()) -> Either a a0 -> () #
Generic1 (Either a :: Type -> Type)
Instance details Defined in GHC.Generics Associated Types type Rep1 (Either a) :: k -> Type # Methods from1 :: Either a a0 -> Rep1 (Either a) a0 # to1 :: Rep1 (Either a) a0 -> Either a a0 #
(Eq a, Eq b) => Eq (Either a b)	Since: base-2.1
Instance details Defined in Data.Either Methods (==) :: Either a b -> Either a b -> Bool # (/=) :: Either a b -> Either a b -> Bool #
(Data a, Data b) => Data (Either a b)	Since: base-4.0.0.0
Instance details Defined in Data.Data Methods gfoldl :: (forall d b0. Data d => c (d -> b0) -> d -> c b0) -> (forall g. g -> c g) -> Either a b -> c (Either a b) # gunfold :: (forall b0 r. Data b0 => c (b0 -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Either a b) # toConstr :: Either a b -> Constr # dataTypeOf :: Either a b -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Either a b)) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Either a b)) # gmapT :: (forall b0. Data b0 => b0 -> b0) -> Either a b -> Either a b # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Either a b -> r # gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Either a b -> r # gmapQ :: (forall d. Data d => d -> u) -> Either a b -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> Either a b -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Either a b -> m (Either a b) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Either a b -> m (Either a b) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Either a b -> m (Either a b) #
(Ord a, Ord b) => Ord (Either a b)	Since: base-2.1
Instance details Defined in Data.Either Methods compare :: Either a b -> Either a b -> Ordering # (<) :: Either a b -> Either a b -> Bool # (<=) :: Either a b -> Either a b -> Bool # (>) :: Either a b -> Either a b -> Bool # (>=) :: Either a b -> Either a b -> Bool # max :: Either a b -> Either a b -> Either a b # min :: Either a b -> Either a b -> Either a b #
(Read a, Read b) => Read (Either a b)	Since: base-3.0
Instance details Defined in Data.Either Methods readsPrec :: Int -> ReadS (Either a b) # readList :: ReadS [Either a b] # readPrec :: ReadPrec (Either a b) # readListPrec :: ReadPrec [Either a b] #
(Show a, Show b) => Show (Either a b)	Since: base-3.0
Instance details Defined in Data.Either Methods showsPrec :: Int -> Either a b -> ShowS # show :: Either a b -> String # showList :: [Either a b] -> ShowS #
Generic (Either a b)
Instance details Defined in GHC.Generics Associated Types type Rep (Either a b) :: Type -> Type # Methods from :: Either a b -> Rep (Either a b) x # to :: Rep (Either a b) x -> Either a b #
Semigroup (Either a b)	Since: base-4.9.0.0
Instance details Defined in Data.Either Methods (<>) :: Either a b -> Either a b -> Either a b # sconcat :: NonEmpty (Either a b) -> Either a b # stimes :: Integral b0 => b0 -> Either a b -> Either a b #
(NFData a, NFData b) => NFData (Either a b)
Instance details Defined in Control.DeepSeq Methods rnf :: Either a b -> () #
(AEq a, AEq b) => AEq (Either a b)
Instance details Defined in Data.AEq Methods (===) :: Either a b -> Either a b -> Bool # (~==) :: Either a b -> Either a b -> Bool #
type Rep1 (Either a :: Type -> Type)	Since: base-4.6.0.0
Instance details Defined in GHC.Generics type Rep1 (Either a :: Type -> Type) = D1 (MetaData "Either" "Data.Either" "base" False) (C1 (MetaCons "Left" PrefixI False) (S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a)) :+: C1 (MetaCons "Right" PrefixI False) (S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) Par1))
type Rep (Either a b)	Since: base-4.6.0.0
Instance details Defined in GHC.Generics type Rep (Either a b) = D1 (MetaData "Either" "Data.Either" "base" False) (C1 (MetaCons "Left" PrefixI False) (S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a)) :+: C1 (MetaCons "Right" PrefixI False) (S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 b)))

readIO :: Read a => String -> IO a #

The readIO function is similar to read except that it signals parse failure to the IO monad instead of terminating the program.

readLn :: Read a => IO a #

The readLn function combines getLine and readIO.

appendFile :: FilePath -> String -> IO () #

The computation appendFile file str function appends the string str, to the file file.

Note that writeFile and appendFile write a literal string to a file. To write a value of any printable type, as with print, use the show function to convert the value to a string first.

main = appendFile "squares" (show [(x,x*x) | x <- [0,0.1..2]])

writeFile :: FilePath -> String -> IO () #

The computation writeFile file str function writes the string str, to the file file.

readFile :: FilePath -> IO String #

The readFile function reads a file and returns the contents of the file as a string. The file is read lazily, on demand, as with getContents.

interact :: (String -> String) -> IO () #

The interact function takes a function of type String->String as its argument. The entire input from the standard input device is passed to this function as its argument, and the resulting string is output on the standard output device.

getContents :: IO String #

The getContents operation returns all user input as a single string, which is read lazily as it is needed (same as hGetContents stdin).

getLine :: IO String #

Read a line from the standard input device (same as hGetLine stdin).

getChar :: IO Char #

Read a character from the standard input device (same as hGetChar stdin).

putStrLn :: String -> IO () #

The same as putStr, but adds a newline character.

putStr :: String -> IO () #

Write a string to the standard output device (same as hPutStr stdout).

putChar :: Char -> IO () #

Write a character to the standard output device (same as hPutChar stdout).

ioError :: IOError -> IO a #

Raise an IOException in the IO monad.

type FilePath = String #

File and directory names are values of type String, whose precise meaning is operating system dependent. Files can be opened, yielding a handle which can then be used to operate on the contents of that file.

userError :: String -> IOError #

Construct an IOException value with a string describing the error. The fail method of the IO instance of the Monad class raises a userError, thus:

instance Monad IO where
  ...
  fail s = ioError (userError s)

type IOError = IOException #

The Haskell 2010 type for exceptions in the IO monad. Any I/O operation may raise an IOException instead of returning a result. For a more general type of exception, including also those that arise in pure code, see Exception.

In Haskell 2010, this is an opaque type.

notElem :: (Foldable t, Eq a) => a -> t a -> Bool infix 4 #

notElem is the negation of elem.

all :: Foldable t => (a -> Bool) -> t a -> Bool #

Determines whether all elements of the structure satisfy the predicate.

any :: Foldable t => (a -> Bool) -> t a -> Bool #

Determines whether any element of the structure satisfies the predicate.

or :: Foldable t => t Bool -> Bool #

or returns the disjunction of a container of Bools. For the result to be False, the container must be finite; True, however, results from a True value finitely far from the left end.

and :: Foldable t => t Bool -> Bool #

and returns the conjunction of a container of Bools. For the result to be True, the container must be finite; False, however, results from a False value finitely far from the left end.

concatMap :: Foldable t => (a -> [b]) -> t a -> [b] #

Map a function over all the elements of a container and concatenate the resulting lists.

concat :: Foldable t => t [a] -> [a] #

The concatenation of all the elements of a container of lists.

sequence_ :: (Foldable t, Monad m) => t (m a) -> m () #

Evaluate each monadic action in the structure from left to right, and ignore the results. For a version that doesn't ignore the results see sequence.

As of base 4.8.0.0, sequence_ is just sequenceA_, specialized to Monad.

mapM_ :: (Foldable t, Monad m) => (a -> m b) -> t a -> m () #

Map each element of a structure to a monadic action, evaluate these actions from left to right, and ignore the results. For a version that doesn't ignore the results see mapM.

As of base 4.8.0.0, mapM_ is just traverse_, specialized to Monad.

unwords :: [String] -> String #

unwords is an inverse operation to words. It joins words with separating spaces.

>>> unwords ["Lorem", "ipsum", "dolor"]
"Lorem ipsum dolor"

words :: String -> [String] #

words breaks a string up into a list of words, which were delimited by white space.

>>> words "Lorem ipsum\ndolor"
["Lorem","ipsum","dolor"]

unlines :: [String] -> String #

unlines is an inverse operation to lines. It joins lines, after appending a terminating newline to each.

>>> unlines ["Hello", "World", "!"]
"Hello\nWorld\n!\n"

lines :: String -> [String] #

lines breaks a string up into a list of strings at newline characters. The resulting strings do not contain newlines.

Note that after splitting the string at newline characters, the last part of the string is considered a line even if it doesn't end with a newline. For example,

>>> lines ""
[]

>>> lines "\n"
[""]

>>> lines "one"
["one"]

>>> lines "one\n"
["one"]

>>> lines "one\n\n"
["one",""]

>>> lines "one\ntwo"
["one","two"]

>>> lines "one\ntwo\n"
["one","two"]

Thus lines s contains at least as many elements as newlines in s.

read :: Read a => String -> a #

The read function reads input from a string, which must be completely consumed by the input process. read fails with an error if the parse is unsuccessful, and it is therefore discouraged from being used in real applications. Use readMaybe or readEither for safe alternatives.

>>> read "123" :: Int
123

>>> read "hello" :: Int
*** Exception: Prelude.read: no parse

reads :: Read a => ReadS a #

equivalent to readsPrec with a precedence of 0.

either :: (a -> c) -> (b -> c) -> Either a b -> c #

Case analysis for the Either type. If the value is Left a, apply the first function to a; if it is Right b, apply the second function to b.

Examples

Expand

We create two values of type Either String Int, one using the Left constructor and another using the Right constructor. Then we apply "either" the length function (if we have a String) or the "times-two" function (if we have an Int):

>>> let s = Left "foo" :: Either String Int
>>> let n = Right 3 :: Either String Int
>>> either length (*2) s
3
>>> either length (*2) n
6

lex :: ReadS String #

The lex function reads a single lexeme from the input, discarding initial white space, and returning the characters that constitute the lexeme. If the input string contains only white space, lex returns a single successful `lexeme' consisting of the empty string. (Thus lex "" = [("","")].) If there is no legal lexeme at the beginning of the input string, lex fails (i.e. returns []).

This lexer is not completely faithful to the Haskell lexical syntax in the following respects:

Qualified names are not handled properly
Octal and hexadecimal numerics are not recognized as a single token
Comments are not treated properly

readParen :: Bool -> ReadS a -> ReadS a #

readParen True p parses what p parses, but surrounded with parentheses.

readParen False p parses what p parses, but optionally surrounded with parentheses.

type ReadS a = String -> [(a, String)] #

A parser for a type a, represented as a function that takes a String and returns a list of possible parses as (a,String) pairs.

Note that this kind of backtracking parser is very inefficient; reading a large structure may be quite slow (cf ReadP).

(<$>) :: Functor f => (a -> b) -> f a -> f b infixl 4 #

An infix synonym for fmap.

The name of this operator is an allusion to $. Note the similarities between their types:

 ($)  ::              (a -> b) ->   a ->   b
(<$>) :: Functor f => (a -> b) -> f a -> f b

Whereas $ is function application, <$> is function application lifted over a Functor.

Examples

Expand

Convert from a Maybe Int to a Maybe String using show:

>>> show <$> Nothing
Nothing
>>> show <$> Just 3
Just "3"

Convert from an Either Int Int to an Either Int String using show:

>>> show <$> Left 17
Left 17
>>> show <$> Right 17
Right "17"

Double each element of a list:

>>> (*2) <$> [1,2,3]
[2,4,6]

Apply even to the second element of a pair:

>>> even <$> (2,2)
(2,True)

lcm :: Integral a => a -> a -> a #

lcm x y is the smallest positive integer that both x and y divide.

gcd :: Integral a => a -> a -> a #

gcd x y is the non-negative factor of both x and y of which every common factor of x and y is also a factor; for example gcd 4 2 = 2, gcd (-4) 6 = 2, gcd 0 4 = 4. gcd 0 0 = 0. (That is, the common divisor that is "greatest" in the divisibility preordering.)

Note: Since for signed fixed-width integer types, abs minBound < 0, the result may be negative if one of the arguments is minBound (and necessarily is if the other is 0 or minBound) for such types.

(^^) :: (Fractional a, Integral b) => a -> b -> a infixr 8 #

raise a number to an integral power

odd :: Integral a => a -> Bool #

even :: Integral a => a -> Bool #

showParen :: Bool -> ShowS -> ShowS #

utility function that surrounds the inner show function with parentheses when the Bool parameter is True.

showString :: String -> ShowS #

utility function converting a String to a show function that simply prepends the string unchanged.

showChar :: Char -> ShowS #

utility function converting a Char to a show function that simply prepends the character unchanged.

shows :: Show a => a -> ShowS #

equivalent to showsPrec with a precedence of 0.

type ShowS = String -> String #

The shows functions return a function that prepends the output String to an existing String. This allows constant-time concatenation of results using function composition.

unzip3 :: [(a, b, c)] -> ([a], [b], [c]) #

The unzip3 function takes a list of triples and returns three lists, analogous to unzip.

unzip :: [(a, b)] -> ([a], [b]) #

unzip transforms a list of pairs into a list of first components and a list of second components.

zipWith3 :: (a -> b -> c -> d) -> [a] -> [b] -> [c] -> [d] #

The zipWith3 function takes a function which combines three elements, as well as three lists and returns a list of their point-wise combination, analogous to zipWith.

zipWith :: (a -> b -> c) -> [a] -> [b] -> [c] #

zipWith generalises zip by zipping with the function given as the first argument, instead of a tupling function. For example, zipWith (+) is applied to two lists to produce the list of corresponding sums.

zipWith is right-lazy:

zipWith f [] _|_ = []

zip3 :: [a] -> [b] -> [c] -> [(a, b, c)] #

zip3 takes three lists and returns a list of triples, analogous to zip.

(!!) :: [a] -> Int -> a infixl 9 #

List index (subscript) operator, starting from 0. It is an instance of the more general genericIndex, which takes an index of any integral type.

lookup :: Eq a => a -> [(a, b)] -> Maybe b #

lookup key assocs looks up a key in an association list.

reverse :: [a] -> [a] #

reverse xs returns the elements of xs in reverse order. xs must be finite.

break :: (a -> Bool) -> [a] -> ([a], [a]) #

break, applied to a predicate p and a list xs, returns a tuple where first element is longest prefix (possibly empty) of xs of elements that do not satisfy p and second element is the remainder of the list:

break (> 3) [1,2,3,4,1,2,3,4] == ([1,2,3],[4,1,2,3,4])
break (< 9) [1,2,3] == ([],[1,2,3])
break (> 9) [1,2,3] == ([1,2,3],[])

break p is equivalent to span (not . p).

span :: (a -> Bool) -> [a] -> ([a], [a]) #

span, applied to a predicate p and a list xs, returns a tuple where first element is longest prefix (possibly empty) of xs of elements that satisfy p and second element is the remainder of the list:

span (< 3) [1,2,3,4,1,2,3,4] == ([1,2],[3,4,1,2,3,4])
span (< 9) [1,2,3] == ([1,2,3],[])
span (< 0) [1,2,3] == ([],[1,2,3])

span p xs is equivalent to (takeWhile p xs, dropWhile p xs)

splitAt :: Int -> [a] -> ([a], [a]) #

splitAt n xs returns a tuple where first element is xs prefix of length n and second element is the remainder of the list:

splitAt 6 "Hello World!" == ("Hello ","World!")
splitAt 3 [1,2,3,4,5] == ([1,2,3],[4,5])
splitAt 1 [1,2,3] == ([1],[2,3])
splitAt 3 [1,2,3] == ([1,2,3],[])
splitAt 4 [1,2,3] == ([1,2,3],[])
splitAt 0 [1,2,3] == ([],[1,2,3])
splitAt (-1) [1,2,3] == ([],[1,2,3])

It is equivalent to (take n xs, drop n xs) when n is not _|_ (splitAt _|_ xs = _|_). splitAt is an instance of the more general genericSplitAt, in which n may be of any integral type.

drop :: Int -> [a] -> [a] #

drop n xs returns the suffix of xs after the first n elements, or [] if n > length xs:

drop 6 "Hello World!" == "World!"
drop 3 [1,2,3,4,5] == [4,5]
drop 3 [1,2] == []
drop 3 [] == []
drop (-1) [1,2] == [1,2]
drop 0 [1,2] == [1,2]

It is an instance of the more general genericDrop, in which n may be of any integral type.

take :: Int -> [a] -> [a] #

take n, applied to a list xs, returns the prefix of xs of length n, or xs itself if n > length xs:

take 5 "Hello World!" == "Hello"
take 3 [1,2,3,4,5] == [1,2,3]
take 3 [1,2] == [1,2]
take 3 [] == []
take (-1) [1,2] == []
take 0 [1,2] == []

It is an instance of the more general genericTake, in which n may be of any integral type.

dropWhile :: (a -> Bool) -> [a] -> [a] #

dropWhile p xs returns the suffix remaining after takeWhile p xs:

dropWhile (< 3) [1,2,3,4,5,1,2,3] == [3,4,5,1,2,3]
dropWhile (< 9) [1,2,3] == []
dropWhile (< 0) [1,2,3] == [1,2,3]

takeWhile :: (a -> Bool) -> [a] -> [a] #

takeWhile, applied to a predicate p and a list xs, returns the longest prefix (possibly empty) of xs of elements that satisfy p:

takeWhile (< 3) [1,2,3,4,1,2,3,4] == [1,2]
takeWhile (< 9) [1,2,3] == [1,2,3]
takeWhile (< 0) [1,2,3] == []

cycle :: [a] -> [a] #

cycle ties a finite list into a circular one, or equivalently, the infinite repetition of the original list. It is the identity on infinite lists.

replicate :: Int -> a -> [a] #

replicate n x is a list of length n with x the value of every element. It is an instance of the more general genericReplicate, in which n may be of any integral type.

repeat :: a -> [a] #

repeat x is an infinite list, with x the value of every element.

iterate :: (a -> a) -> a -> [a] #

iterate f x returns an infinite list of repeated applications of f to x:

iterate f x == [x, f x, f (f x), ...]

Note that iterate is lazy, potentially leading to thunk build-up if the consumer doesn't force each iterate. See 'iterate\'' for a strict variant of this function.

scanr1 :: (a -> a -> a) -> [a] -> [a] #

scanr1 is a variant of scanr that has no starting value argument.

scanr :: (a -> b -> b) -> b -> [a] -> [b] #

scanr is the right-to-left dual of scanl. Note that

head (scanr f z xs) == foldr f z xs.

scanl1 :: (a -> a -> a) -> [a] -> [a] #

scanl1 is a variant of scanl that has no starting value argument:

scanl1 f [x1, x2, ...] == [x1, x1 `f` x2, ...]

scanl :: (b -> a -> b) -> b -> [a] -> [b] #

scanl is similar to foldl, but returns a list of successive reduced values from the left:

scanl f z [x1, x2, ...] == [z, z `f` x1, (z `f` x1) `f` x2, ...]

Note that

last (scanl f z xs) == foldl f z xs.

init :: [a] -> [a] #

Return all the elements of a list except the last one. The list must be non-empty.

last :: [a] -> a #

Extract the last element of a list, which must be finite and non-empty.

tail :: [a] -> [a] #

Extract the elements after the head of a list, which must be non-empty.

head :: [a] -> a #

Extract the first element of a list, which must be non-empty.

maybe :: b -> (a -> b) -> Maybe a -> b #

The maybe function takes a default value, a function, and a Maybe value. If the Maybe value is Nothing, the function returns the default value. Otherwise, it applies the function to the value inside the Just and returns the result.

Examples

Expand

Basic usage:

>>> maybe False odd (Just 3)
True

>>> maybe False odd Nothing
False

Read an integer from a string using readMaybe. If we succeed, return twice the integer; that is, apply (*2) to it. If instead we fail to parse an integer, return 0 by default:

>>> import Text.Read ( readMaybe )
>>> maybe 0 (*2) (readMaybe "5")
10
>>> maybe 0 (*2) (readMaybe "")
0

Apply show to a Maybe Int. If we have Just n, we want to show the underlying Int n. But if we have Nothing, we return the empty string instead of (for example) "Nothing":

>>> maybe "" show (Just 5)
"5"
>>> maybe "" show Nothing
""

uncurry :: (a -> b -> c) -> (a, b) -> c #

uncurry converts a curried function to a function on pairs.

Examples

Expand

>>> uncurry (+) (1,2)
3

>>> uncurry ($) (show, 1)
"1"

>>> map (uncurry max) [(1,2), (3,4), (6,8)]
[2,4,8]

curry :: ((a, b) -> c) -> a -> b -> c #

curry converts an uncurried function to a curried function.

Examples

Expand

>>> curry fst 1 2
1

subtract :: Num a => a -> a -> a #

the same as flip (-).

Because - is treated specially in the Haskell grammar, (- e) is not a section, but an application of prefix negation. However, (subtract exp) is equivalent to the disallowed section.

asTypeOf :: a -> a -> a #

asTypeOf is a type-restricted version of const. It is usually used as an infix operator, and its typing forces its first argument (which is usually overloaded) to have the same type as the second.

until :: (a -> Bool) -> (a -> a) -> a -> a #

until p f yields the result of applying f until p holds.

($!) :: (a -> b) -> a -> b infixr 0 #

Strict (call-by-value) application operator. It takes a function and an argument, evaluates the argument to weak head normal form (WHNF), then calls the function with that value.

flip :: (a -> b -> c) -> b -> a -> c #

flip f takes its (first) two arguments in the reverse order of f.

>>> flip (++) "hello" "world"
"worldhello"

const :: a -> b -> a #

const x is a unary function which evaluates to x for all inputs.

>>> const 42 "hello"
42

>>> map (const 42) [0..3]
[42,42,42,42]

(=<<) :: Monad m => (a -> m b) -> m a -> m b infixr 1 #

Same as >>=, but with the arguments interchanged.

type String = [Char] #

A String is a list of characters. String constants in Haskell are values of type String.

undefined :: HasCallStack => a #

A special case of error. It is expected that compilers will recognize this and insert error messages which are more appropriate to the context in which undefined appears.

errorWithoutStackTrace :: [Char] -> a #

A variant of error that does not produce a stack trace.

Since: base-4.9.0.0

error :: HasCallStack => [Char] -> a #

error stops execution and displays an error message.

(&&) :: Bool -> Bool -> Bool infixr 3 #

Boolean "and"

(||) :: Bool -> Bool -> Bool infixr 2 #

Boolean "or"

not :: Bool -> Bool #

Boolean "not"