Copyright | (c) 2013-2023 Brendan Hay |
---|---|
License | Mozilla Public License, v. 2.0. |
Maintainer | Brendan Hay <brendan.g.hay+amazonka@gmail.com> |
Stability | provisional |
Portability | non-portable (GHC extensions) |
Safe Haskell | Safe-Inferred |
Language | Haskell2010 |
Amazonka.Prelude
Description
An intentionally limited set of prelude exports to control backward compatibility and simplify code generation.
Please consider long and hard before adding any addtional types exports to this module - they should either be in pervasive use throughout the project or have zero ambiguity. If you ever are forced to disambiguate at any point, it's a bad export.
Try and avoid any value, operator, or symbol exports, if possible. Most of the ones here exist to ease legacy code-migration.
Synopsis
- (++) :: [a] -> [a] -> [a]
- seq :: forall {r :: RuntimeRep} a (b :: TYPE r). 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]
- ($) :: forall (r :: RuntimeRep) a (b :: TYPE r). (a -> b) -> a -> b
- coerce :: forall {k :: RuntimeRep} (a :: TYPE k) (b :: TYPE k). Coercible a b => a -> b
- fromIntegral :: (Integral a, Num b) => a -> b
- realToFrac :: (Real a, Fractional b) => a -> b
- guard :: Alternative f => Bool -> f ()
- class IsList l where
- join :: Monad m => m (m a) -> m a
- class Bounded a where
- 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
- class Fractional a => Floating a where
- class Num a => Fractional a where
- (/) :: a -> a -> a
- recip :: a -> a
- fromRational :: Rational -> a
- class (Real a, Enum a) => Integral a where
- class Applicative m => Monad (m :: Type -> Type) where
- class Functor (f :: Type -> Type) where
- class Num a where
- class Eq a => Ord a where
- class Read a where
- 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
- atan2 :: a -> a -> a
- class (Real a, Fractional a) => RealFrac a where
- class Show a where
- class Monad m => MonadFail (m :: Type -> Type) where
- class IsString a where
- fromString :: String -> a
- class Functor f => Applicative (f :: Type -> Type) where
- class Foldable (t :: TYPE LiftedRep -> 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
- maximum :: Ord a => t a -> a
- minimum :: Ord a => t a -> a
- sum :: Num a => t a -> a
- product :: Num a => t a -> a
- 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 Generic a
- class KnownNat (n :: Nat)
- class KnownSymbol (n :: Symbol)
- class Semigroup a where
- (<>) :: a -> a -> a
- class Semigroup a => Monoid a where
- data Bool
- type String = [Char]
- data Char
- data Double
- data Float
- data Int
- data Int8
- data Int16
- data Int32
- data Int64
- data Integer
- data Natural
- data Maybe a
- data Ordering
- type Rational = Ratio Integer
- data IO a
- data Word
- data Word8
- data Word16
- data Word32
- data Word64
- data Either a b
- data NonEmpty a = a :| [a]
- type Type = TYPE LiftedRep
- class a ~R# b => Coercible (a :: k) (b :: k)
- data Symbol
- liftM :: Monad m => (a1 -> r) -> m a1 -> m r
- id :: a -> a
- either :: (a -> c) -> (b -> c) -> Either a b -> c
- data Scientific
- class Eq a => Hashable a where
- hashWithSalt :: Int -> a -> Int
- hash :: a -> Int
- (<$>) :: Functor f => (a -> b) -> f a -> f b
- const :: a -> b -> a
- (.) :: (b -> c) -> (a -> b) -> a -> c
- data UTCTime
- data ByteString
- data Text
- data HashMap k v
- class Bifunctor (p :: Type -> Type -> Type) where
- forM_ :: (Foldable t, Monad m) => t a -> (a -> m b) -> m ()
- mapM_ :: (Foldable t, Monad m) => (a -> m b) -> t a -> m ()
- read :: Read a => String -> a
- class Applicative f => Alternative (f :: Type -> Type) where
- (<|>) :: f a -> f a -> f a
- class (Alternative m, Monad m) => MonadPlus (m :: Type -> Type) where
- data Void
- type family Item l
- class (Bifunctor t, Bifoldable t) => Bitraversable (t :: Type -> Type -> Type) where
- bitraverse :: Applicative f => (a -> f c) -> (b -> f d) -> t a b -> f (t c d)
- bisequenceA :: (Bitraversable t, Applicative f) => t (f a) (f b) -> f (t a b)
- bisequence :: (Bitraversable t, Applicative f) => t (f a) (f b) -> f (t a b)
- bimapM :: (Bitraversable t, Applicative f) => (a -> f c) -> (b -> f d) -> t a b -> f (t c d)
- bimapDefault :: Bitraversable t => (a -> b) -> (c -> d) -> t a c -> t b d
- bimapAccumR :: Bitraversable t => (a -> b -> (a, c)) -> (a -> d -> (a, e)) -> a -> t b d -> (a, t c e)
- bimapAccumL :: Bitraversable t => (a -> b -> (a, c)) -> (a -> d -> (a, e)) -> a -> t b d -> (a, t c e)
- biforM :: (Bitraversable t, Applicative f) => t a b -> (a -> f c) -> (b -> f d) -> f (t c d)
- bifor :: (Bitraversable t, Applicative f) => t a b -> (a -> f c) -> (b -> f d) -> f (t c d)
- bifoldMapDefault :: (Bitraversable t, Monoid m) => (a -> m) -> (b -> m) -> t a b -> m
- class Bifoldable (p :: TYPE LiftedRep -> TYPE LiftedRep -> Type) where
- bitraverse_ :: (Bifoldable t, Applicative f) => (a -> f c) -> (b -> f d) -> t a b -> f ()
- bisum :: (Bifoldable t, Num a) => t a a -> a
- bisequence_ :: (Bifoldable t, Applicative f) => t (f a) (f b) -> f ()
- bisequenceA_ :: (Bifoldable t, Applicative f) => t (f a) (f b) -> f ()
- biproduct :: (Bifoldable t, Num a) => t a a -> a
- bior :: Bifoldable t => t Bool Bool -> Bool
- binull :: Bifoldable t => t a b -> Bool
- binotElem :: (Bifoldable t, Eq a) => a -> t a a -> Bool
- bimsum :: (Bifoldable t, Alternative f) => t (f a) (f a) -> f a
- biminimumBy :: Bifoldable t => (a -> a -> Ordering) -> t a a -> a
- biminimum :: (Bifoldable t, Ord a) => t a a -> a
- bimaximumBy :: Bifoldable t => (a -> a -> Ordering) -> t a a -> a
- bimaximum :: (Bifoldable t, Ord a) => t a a -> a
- bimapM_ :: (Bifoldable t, Applicative f) => (a -> f c) -> (b -> f d) -> t a b -> f ()
- bilength :: Bifoldable t => t a b -> Int
- bifor_ :: (Bifoldable t, Applicative f) => t a b -> (a -> f c) -> (b -> f d) -> f ()
- biforM_ :: (Bifoldable t, Applicative f) => t a b -> (a -> f c) -> (b -> f d) -> f ()
- bifoldrM :: (Bifoldable t, Monad m) => (a -> c -> m c) -> (b -> c -> m c) -> c -> t a b -> m c
- bifoldr1 :: Bifoldable t => (a -> a -> a) -> t a a -> a
- bifoldr' :: Bifoldable t => (a -> c -> c) -> (b -> c -> c) -> c -> t a b -> c
- bifoldlM :: (Bifoldable t, Monad m) => (a -> b -> m a) -> (a -> c -> m a) -> a -> t b c -> m a
- bifoldl1 :: Bifoldable t => (a -> a -> a) -> t a a -> a
- bifoldl' :: Bifoldable t => (a -> b -> a) -> (a -> c -> a) -> a -> t b c -> a
- bifind :: Bifoldable t => (a -> Bool) -> t a a -> Maybe a
- bielem :: (Bifoldable t, Eq a) => a -> t a a -> Bool
- biconcatMap :: Bifoldable t => (a -> [c]) -> (b -> [c]) -> t a b -> [c]
- biconcat :: Bifoldable t => t [a] [a] -> [a]
- biasum :: (Bifoldable t, Alternative f) => t (f a) (f a) -> f a
- biany :: Bifoldable t => (a -> Bool) -> (b -> Bool) -> t a b -> Bool
- biand :: Bifoldable t => t Bool Bool -> Bool
- biall :: Bifoldable t => (a -> Bool) -> (b -> Bool) -> t a b -> Bool
- biList :: Bifoldable t => t a a -> [a]
- class Monad m => MonadIO (m :: Type -> Type) where
- zipWithM_ :: Applicative m => (a -> b -> m c) -> [a] -> [b] -> m ()
- zipWithM :: Applicative m => (a -> b -> m c) -> [a] -> [b] -> m [c]
- unless :: Applicative f => Bool -> f () -> f ()
- replicateM_ :: Applicative m => Int -> m a -> m ()
- replicateM :: Applicative m => Int -> m a -> m [a]
- mfilter :: MonadPlus m => (a -> Bool) -> m a -> m a
- mapAndUnzipM :: Applicative m => (a -> m (b, c)) -> [a] -> m ([b], [c])
- forever :: Applicative f => f a -> f b
- foldM_ :: (Foldable t, Monad m) => (b -> a -> m b) -> b -> t a -> m ()
- foldM :: (Foldable t, Monad m) => (b -> a -> m b) -> b -> t a -> m b
- filterM :: Applicative m => (a -> m Bool) -> [a] -> m [a]
- (>=>) :: Monad m => (a -> m b) -> (b -> m c) -> a -> m c
- (<=<) :: Monad m => (b -> m c) -> (a -> m b) -> a -> m c
- (<$!>) :: Monad m => (a -> b) -> m a -> m b
- forM :: (Traversable t, Monad m) => t a -> (a -> m b) -> m (t b)
- newtype Identity a = Identity {
- runIdentity :: a
- writeFile :: FilePath -> String -> IO ()
- readLn :: Read a => IO a
- readIO :: Read a => String -> IO a
- readFile :: FilePath -> IO String
- putStrLn :: String -> IO ()
- putStr :: String -> IO ()
- putChar :: Char -> IO ()
- interact :: (String -> String) -> IO ()
- getLine :: IO String
- getContents :: IO String
- getChar :: IO Char
- appendFile :: FilePath -> String -> IO ()
- ioError :: IOError -> IO a
- type FilePath = String
- type IOError = IOException
- userError :: String -> IOError
- class (Typeable e, Show e) => Exception e
- sequence_ :: (Foldable t, Monad m) => t (m a) -> m ()
- or :: Foldable t => t Bool -> Bool
- notElem :: (Foldable t, Eq a) => a -> t a -> Bool
- msum :: (Foldable t, MonadPlus m) => t (m a) -> m a
- concatMap :: Foldable t => (a -> [b]) -> t a -> [b]
- concat :: Foldable t => t [a] -> [a]
- any :: Foldable t => (a -> Bool) -> t a -> Bool
- and :: Foldable t => t Bool -> Bool
- all :: Foldable t => (a -> Bool) -> t a -> Bool
- words :: String -> [String]
- unwords :: [String] -> String
- unlines :: [String] -> String
- lines :: String -> [String]
- data First a
- type Nat = Natural
- reads :: Read a => ReadS a
- data Proxy (t :: k) = Proxy
- readParen :: Bool -> ReadS a -> ReadS a
- lex :: ReadS String
- type ReadS a = String -> [(a, String)]
- odd :: Integral a => a -> Bool
- lcm :: Integral a => a -> a -> a
- gcd :: Integral a => a -> a -> a
- even :: Integral a => a -> Bool
- (^^) :: (Fractional a, Integral b) => a -> b -> a
- (^) :: (Num a, Integral b) => a -> b -> a
- type ShowS = String -> String
- shows :: Show a => a -> ShowS
- showString :: String -> ShowS
- showParen :: Bool -> ShowS -> ShowS
- showChar :: Char -> ShowS
- zipWith3 :: (a -> b -> c -> d) -> [a] -> [b] -> [c] -> [d]
- zipWith :: (a -> b -> c) -> [a] -> [b] -> [c]
- zip3 :: [a] -> [b] -> [c] -> [(a, b, c)]
- unzip3 :: [(a, b, c)] -> ([a], [b], [c])
- unzip :: [(a, b)] -> ([a], [b])
- takeWhile :: (a -> Bool) -> [a] -> [a]
- take :: Int -> [a] -> [a]
- tail :: [a] -> [a]
- splitAt :: Int -> [a] -> ([a], [a])
- span :: (a -> Bool) -> [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]
- reverse :: [a] -> [a]
- replicate :: Int -> a -> [a]
- repeat :: a -> [a]
- lookup :: Eq a => a -> [(a, b)] -> Maybe b
- last :: [a] -> a
- iterate :: (a -> a) -> a -> [a]
- init :: [a] -> [a]
- head :: [a] -> a
- dropWhile :: (a -> Bool) -> [a] -> [a]
- drop :: Int -> [a] -> [a]
- cycle :: [a] -> [a]
- break :: (a -> Bool) -> [a] -> ([a], [a])
- (!!) :: [a] -> Int -> a
- maybeToList :: Maybe a -> [a]
- maybe :: b -> (a -> b) -> Maybe a -> b
- mapMaybe :: (a -> Maybe b) -> [a] -> [b]
- listToMaybe :: [a] -> Maybe a
- isNothing :: Maybe a -> Bool
- isJust :: Maybe a -> Bool
- fromMaybe :: a -> Maybe a -> a
- fromJust :: HasCallStack => Maybe a -> a
- catMaybes :: [Maybe a] -> [a]
- (&) :: a -> (a -> b) -> b
- void :: Functor f => f a -> f ()
- (<&>) :: Functor f => f a -> (a -> b) -> f b
- uncurry :: (a -> b -> c) -> (a, b) -> c
- curry :: ((a, b) -> c) -> a -> b -> c
- subtract :: Num a => a -> a -> a
- when :: Applicative f => Bool -> f () -> f ()
- until :: (a -> Bool) -> (a -> a) -> a -> a
- liftM5 :: Monad m => (a1 -> a2 -> a3 -> a4 -> a5 -> r) -> m a1 -> m a2 -> m a3 -> m a4 -> m a5 -> m r
- liftM4 :: Monad m => (a1 -> a2 -> a3 -> a4 -> r) -> m a1 -> m a2 -> m a3 -> m a4 -> m r
- liftM3 :: Monad m => (a1 -> a2 -> a3 -> r) -> m a1 -> m a2 -> m a3 -> m r
- liftM2 :: Monad m => (a1 -> a2 -> r) -> m a1 -> m a2 -> m r
- flip :: (a -> b -> c) -> b -> a -> c
- asTypeOf :: a -> a -> a
- ap :: Monad m => m (a -> b) -> m a -> m b
- (=<<) :: Monad m => (a -> m b) -> m a -> m b
- ($!) :: forall (r :: RuntimeRep) a (b :: TYPE r). (a -> b) -> a -> b
- undefined :: forall (r :: RuntimeRep) (a :: TYPE r). HasCallStack => a
- errorWithoutStackTrace :: forall (r :: RuntimeRep) (a :: TYPE r). [Char] -> a
- error :: forall (r :: RuntimeRep) (a :: TYPE r). HasCallStack => [Char] -> a
- data SomeException
- (&&) :: Bool -> Bool -> Bool
- not :: Bool -> Bool
- (||) :: Bool -> Bool -> Bool
- data CI s
- class MonadIO m => MonadResource (m :: Type -> Type)
- class MonadTrans (t :: (Type -> Type) -> Type -> Type) where
- data DiffTime
- class NFData a where
- rnf :: a -> ()
- data HashSet a
- type Lens' s a = Lens s s a a
- type Traversal' s a = Traversal s s a a
- type Setter' s a = Setter s s a a
- type Iso' s a = Iso s s a a
- type Prism' s a = Prism s s a a
- data NominalDiffTime
- data Day
- type TextLazy = Text
- type TextBuilder = Builder
- type ByteStringLazy = ByteString
- type ByteStringBuilder = Builder
Documentation
(++) :: [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 :: forall {r :: RuntimeRep} a (b :: TYPE r). a -> b -> b infixr 0 #
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] #
\(\mathcal{O}(n)\). 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]
>>>
filter odd [1, 2, 3]
[1,3]
zip :: [a] -> [b] -> [(a, b)] #
\(\mathcal{O}(\min(m,n))\). 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 shorter than the other, excess elements of the longer list are discarded, even if one of the lists is infinite:
>>>
zip [1] ['a', 'b']
[(1,'a')]>>>
zip [1, 2] ['a']
[(1,'a')]>>>
zip [] [1..]
[]>>>
zip [1..] []
[]
zip
is right-lazy:
>>>
zip [] undefined
[]>>>
zip undefined []
*** Exception: Prelude.undefined ...
zip
is capable of list fusion, but it is restricted to its
first list argument and its resulting list.
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]])
map :: (a -> b) -> [a] -> [b] #
\(\mathcal{O}(n)\). 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, ...]
>>>
map (+1) [1, 2, 3]
[2,3,4]
($) :: forall (r :: RuntimeRep) a (b :: TYPE r). (a -> b) -> a -> b infixr 0 #
Application operator. This operator is redundant, since ordinary
application (f x)
means the same as (f
. However, $
x)$
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
,
or map
($
0) xs
.zipWith
($
) fs xs
Note that (
is levity-polymorphic in its result type, so that
$
)foo
where $
Truefoo :: Bool -> Int#
is well-typed.
coerce :: forall {k :: RuntimeRep} (a :: TYPE k) (b :: TYPE k). Coercible a b => a -> b #
The function coerce
allows you to safely convert between values of
types that have the same representation with no run-time overhead. In the
simplest case you can use it instead of a newtype constructor, to go from
the newtype's concrete type to the abstract type. But it also works in
more complicated settings, e.g. converting a list of newtypes to a list of
concrete types.
This function is runtime-representation polymorphic, but the
RuntimeRep
type argument is marked as Inferred
, meaning
that it is not available for visible type application. This means
the typechecker will accept coerce @Int @Age 42
.
fromIntegral :: (Integral a, Num b) => a -> b #
general coercion from integral types
realToFrac :: (Real a, Fractional b) => a -> b #
general coercion to fractional types
guard :: Alternative f => Bool -> f () #
Conditional failure of Alternative
computations. Defined by
guard True =pure
() guard False =empty
Examples
Common uses of guard
include conditionally signaling an error in
an error monad and conditionally rejecting the current choice in an
Alternative
-based parser.
As an example of signaling an error in the error monad Maybe
,
consider a safe division function safeDiv x y
that returns
Nothing
when the denominator y
is zero and
otherwise. For example:Just
(x `div`
y)
>>>
safeDiv 4 0
Nothing
>>>
safeDiv 4 2
Just 2
A definition of safeDiv
using guards, but not guard
:
safeDiv :: Int -> Int -> Maybe Int safeDiv x y | y /= 0 = Just (x `div` y) | otherwise = Nothing
A definition of safeDiv
using guard
and Monad
do
-notation:
safeDiv :: Int -> Int -> Maybe Int safeDiv x y = do guard (y /= 0) return (x `div` y)
The IsList
class and its methods are intended to be used in
conjunction with the OverloadedLists extension.
Since: base-4.7.0.0
Methods
The fromList
function constructs the structure l
from the given
list of Item l
fromListN :: Int -> [Item l] -> l #
The fromListN
function takes the input list's length and potentially
uses it to construct the structure l
more efficiently compared to
fromList
. If the given number does not equal to the input list's length
the behaviour of fromListN
is not specified.
fromListN (length xs) xs == fromList xs
The toList
function extracts a list of Item l
from the structure l
.
It should satisfy fromList . toList = id.
Instances
IsList Version | Since: base-4.8.0.0 |
IsList CallStack | Be aware that 'fromList . toList = id' only for unfrozen Since: base-4.9.0.0 |
IsList String | |
IsList ByteString | Since: bytestring-0.10.12.0 |
Defined in Data.ByteString.Internal Associated Types type Item ByteString # Methods fromList :: [Item ByteString] -> ByteString # fromListN :: Int -> [Item ByteString] -> ByteString # toList :: ByteString -> [Item ByteString] # | |
IsList ByteString | Since: bytestring-0.10.12.0 |
Defined in Data.ByteString.Lazy.Internal Associated Types type Item ByteString # Methods fromList :: [Item ByteString] -> ByteString # fromListN :: Int -> [Item ByteString] -> ByteString # toList :: ByteString -> [Item ByteString] # | |
IsList ShortByteString | Since: bytestring-0.10.12.0 |
Defined in Data.ByteString.Short.Internal Associated Types type Item ShortByteString # Methods fromList :: [Item ShortByteString] -> ShortByteString # fromListN :: Int -> [Item ShortByteString] -> ShortByteString # toList :: ShortByteString -> [Item ShortByteString] # | |
IsList IntSet | Since: containers-0.5.6.2 |
IsList ByteArray | |
IsList ShortText | Note: Surrogate pairs ( Since: text-short-0.1.2 |
IsList (KeyMap v) | Since: aeson-2.0.2.0 |
IsList a => IsList (Sensitive a) Source # | |
IsList (ZipList a) | Since: base-4.15.0.0 |
PrimType ty => IsList (Block ty) | |
IsList c => IsList (NonEmpty c) | |
PrimType ty => IsList (UArray ty) | |
IsList (IntMap a) | Since: containers-0.5.6.2 |
IsList (Seq a) | |
Ord a => IsList (Set a) | Since: containers-0.5.6.2 |
IsList (DNonEmpty a) | |
IsList (DList a) | |
IsList (Array a) | |
Prim a => IsList (PrimArray a) | Since: primitive-0.6.4.0 |
IsList (SmallArray a) | |
Defined in Data.Primitive.SmallArray Associated Types type Item (SmallArray a) # Methods fromList :: [Item (SmallArray a)] -> SmallArray a # fromListN :: Int -> [Item (SmallArray a)] -> SmallArray a # toList :: SmallArray a -> [Item (SmallArray a)] # | |
(Eq a, Hashable a) => IsList (HashSet a) | |
IsList (Vector a) | |
Prim a => IsList (Vector a) | |
Storable a => IsList (Vector a) | |
IsList (NonEmpty a) | Since: base-4.9.0.0 |
IsList [a] | Since: base-4.7.0.0 |
Ord k => IsList (Map k v) | Since: containers-0.5.6.2 |
(Eq k, Hashable k) => IsList (HashMap k v) | |
join :: Monad m => m (m a) -> m a #
The join
function is the conventional monad join operator. It
is used to remove one level of monadic structure, projecting its
bound argument into the outer level.
'
' can be understood as the join
bssdo
expression
do bs <- bss bs
Examples
A common use of join
is to run an IO
computation returned from
an STM
transaction, since STM
transactions
can't perform IO
directly. Recall that
atomically
:: STM a -> IO a
is used to run STM
transactions atomically. So, by
specializing the types of atomically
and join
to
atomically
:: STM (IO b) -> IO (IO b)join
:: IO (IO b) -> IO b
we can compose them as
join
.atomically
:: STM (IO b) -> IO b
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
.
Instances
Bounded All | Since: base-2.1 |
Bounded Any | Since: base-2.1 |
Bounded CBool | |
Bounded CChar | |
Bounded CInt | |
Bounded CIntMax | |
Bounded CIntPtr | |
Bounded CLLong | |
Bounded CLong | |
Bounded CPtrdiff | |
Bounded CSChar | |
Bounded CShort | |
Bounded CSigAtomic | |
Defined in Foreign.C.Types | |
Bounded CSize | |
Bounded CUChar | |
Bounded CUInt | |
Bounded CUIntMax | |
Bounded CUIntPtr | |
Bounded CULLong | |
Bounded CULong | |
Bounded CUShort | |
Bounded CWchar | |
Bounded IntPtr | |
Bounded WordPtr | |
Bounded Associativity | Since: base-4.9.0.0 |
Defined in GHC.Generics | |
Bounded DecidedStrictness | Since: base-4.9.0.0 |
Defined in GHC.Generics | |
Bounded SourceStrictness | Since: base-4.9.0.0 |
Defined in GHC.Generics | |
Bounded SourceUnpackedness | Since: base-4.9.0.0 |
Defined in GHC.Generics | |
Bounded Int16 | Since: base-2.1 |
Bounded Int32 | Since: base-2.1 |
Bounded Int64 | Since: base-2.1 |
Bounded Int8 | Since: base-2.1 |
Bounded GeneralCategory | Since: base-2.1 |
Defined in GHC.Unicode | |
Bounded Word16 | Since: base-2.1 |
Bounded Word32 | Since: base-2.1 |
Bounded Word64 | Since: base-2.1 |
Bounded Word8 | Since: base-2.1 |
Bounded Encoding | |
Bounded UTF32_Invalid | |
Defined in Basement.String.Encoding.UTF32 | |
Bounded Extension | |
Bounded Ordering | Since: base-2.1 |
Bounded StdMethod | |
Bounded Status | |
Bounded IPv4 | |
Bounded IPv6 | |
Bounded PortNumber | |
Defined in Network.Socket.Types | |
Bounded QuarterOfYear | |
Defined in Data.Time.Calendar.Quarter | |
Bounded CompressionStrategy | |
Defined in Codec.Compression.Zlib.Stream | |
Bounded Format | |
Bounded Method | |
Bounded () | Since: base-2.1 |
Bounded Bool | Since: base-2.1 |
Bounded Char | Since: base-2.1 |
Bounded Int | Since: base-2.1 |
Bounded Levity | Since: base-4.16.0.0 |
Bounded VecCount | Since: base-4.10.0.0 |
Bounded VecElem | Since: base-4.10.0.0 |
Bounded Word | Since: base-2.1 |
Bounded a => Bounded (Identity a) | Since: base-4.9.0.0 |
Bounded a => Bounded (Down a) | Swaps Since: base-4.14.0.0 |
Bounded a => Bounded (First a) | Since: base-4.9.0.0 |
Bounded a => Bounded (Last a) | Since: base-4.9.0.0 |
Bounded a => Bounded (Max a) | Since: base-4.9.0.0 |
Bounded a => Bounded (Min a) | Since: base-4.9.0.0 |
Bounded m => Bounded (WrappedMonoid m) | Since: base-4.9.0.0 |
Defined in Data.Semigroup | |
Bounded a => Bounded (Dual a) | Since: base-2.1 |
Bounded a => Bounded (Product a) | Since: base-2.1 |
Bounded a => Bounded (Sum a) | Since: base-2.1 |
SizeValid n => Bounded (Bits n) | |
Bounded a => Bounded (a) | |
Bounded (Proxy t) | Since: base-4.7.0.0 |
(Bounded a, Bounded b) => Bounded (Pair a b) | |
(Bounded a, Bounded b) => Bounded (a, b) | Since: base-2.1 |
Bounded a => Bounded (Const a b) | Since: base-4.9.0.0 |
(Applicative f, Bounded a) => Bounded (Ap f a) | Since: base-4.12.0.0 |
a ~ b => Bounded (a :~: b) | Since: base-4.7.0.0 |
Bounded b => Bounded (Tagged s b) | |
(Bounded a, Bounded b, Bounded c) => Bounded (a, b, c) | Since: base-2.1 |
a ~~ b => Bounded (a :~~: b) | Since: base-4.10.0.0 |
(Bounded a, Bounded b, Bounded c, Bounded d) => Bounded (a, b, c, d) | Since: base-2.1 |
(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e) => Bounded (a, b, c, d, e) | Since: base-2.1 |
(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f) => Bounded (a, b, c, d, e, f) | Since: base-2.1 |
(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 |
(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 |
(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 |
(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 |
(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 |
(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 |
(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 |
(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 |
(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 |
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
andsucc
maxBound
should result in a runtime error.pred
minBound
fromEnum
andtoEnum
should give a runtime error if the result value is not representable in the result type. For example,
is an error.toEnum
7 ::Bool
enumFrom
andenumFromThen
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
Methods
the successor of a value. For numeric types, succ
adds 1.
the predecessor of a value. For numeric types, pred
subtracts 1.
Convert from an 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
.
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
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, instances are
encouraged to follow these properties:
Instances
Eq Key | |
Eq DotNetTime | |
Defined in Data.Aeson.Types.Internal | |
Eq JSONPathElement | |
Defined in Data.Aeson.Types.Internal Methods (==) :: JSONPathElement -> JSONPathElement -> Bool # (/=) :: JSONPathElement -> JSONPathElement -> Bool # | |
Eq SumEncoding | |
Defined in Data.Aeson.Types.Internal | |
Eq Value | |
Eq Base64 Source # | |
Eq ChunkSize Source # | |
Eq TwiceEscapedPath Source # | |
Defined in Amazonka.Data.Path Methods (==) :: TwiceEscapedPath -> TwiceEscapedPath -> Bool # (/=) :: TwiceEscapedPath -> TwiceEscapedPath -> Bool # | |
Eq QueryString Source # | |
Defined in Amazonka.Data.Query | |
Eq Format Source # | |
Eq Abbrev Source # | |
Eq AccessKey Source # | |
Eq AuthEnv Source # | |
Eq Endpoint Source # | |
Eq ErrorCode Source # | |
Eq ErrorMessage Source # | |
Defined in Amazonka.Types | |
Eq Region Source # | |
Eq RequestId Source # | |
Eq S3AddressingStyle Source # | |
Defined in Amazonka.Types Methods (==) :: S3AddressingStyle -> S3AddressingStyle -> Bool # (/=) :: S3AddressingStyle -> S3AddressingStyle -> Bool # | |
Eq Seconds Source # | |
Eq SecretKey Source # | |
Eq SerializeError Source # | |
Defined in Amazonka.Types Methods (==) :: SerializeError -> SerializeError -> Bool # (/=) :: SerializeError -> SerializeError -> Bool # | |
Eq ServiceError Source # | |
Defined in Amazonka.Types | |
Eq SessionToken Source # | |
Defined in Amazonka.Types | |
Eq Accept Source # | |
Eq More | |
Eq Pos | |
Eq Number | |
Eq All | Since: base-2.1 |
Eq Any | Since: base-2.1 |
Eq SomeTypeRep | |
Defined in Data.Typeable.Internal | |
Eq Unique | |
Eq Version | Since: base-2.1 |
Eq Void | Since: base-4.8.0.0 |
Eq CBool | |
Eq CChar | |
Eq CClock | |
Eq CDouble | |
Eq CFloat | |
Eq CInt | |
Eq CIntMax | |
Eq CIntPtr | |
Eq CLLong | |
Eq CLong | |
Eq CPtrdiff | |
Eq CSChar | |
Eq CSUSeconds | |
Defined in Foreign.C.Types | |
Eq CShort | |
Eq CSigAtomic | |
Defined in Foreign.C.Types | |
Eq CSize | |
Eq CTime | |
Eq CUChar | |
Eq CUInt | |
Eq CUIntMax | |
Eq CUIntPtr | |
Eq CULLong | |
Eq CULong | |
Eq CUSeconds | |
Eq CUShort | |
Eq CWchar | |
Eq IntPtr | |
Eq WordPtr | |
Eq BlockReason | Since: base-4.3.0.0 |
Defined in GHC.Conc.Sync | |
Eq ThreadId | Since: base-4.2.0.0 |
Eq ThreadStatus | Since: base-4.3.0.0 |
Defined in GHC.Conc.Sync | |
Eq ArithException | Since: base-3.0 |
Defined in GHC.Exception.Type Methods (==) :: ArithException -> ArithException -> Bool # (/=) :: ArithException -> ArithException -> Bool # | |
Eq SpecConstrAnnotation | Since: base-4.3.0.0 |
Defined in GHC.Exts Methods (==) :: SpecConstrAnnotation -> SpecConstrAnnotation -> Bool # (/=) :: SpecConstrAnnotation -> SpecConstrAnnotation -> Bool # | |
Eq Fingerprint | Since: base-4.4.0.0 |
Defined in GHC.Fingerprint.Type | |
Eq Associativity | Since: base-4.6.0.0 |
Defined in GHC.Generics Methods (==) :: Associativity -> Associativity -> Bool # (/=) :: Associativity -> Associativity -> Bool # | |
Eq DecidedStrictness | Since: base-4.9.0.0 |
Defined in GHC.Generics Methods (==) :: DecidedStrictness -> DecidedStrictness -> Bool # (/=) :: DecidedStrictness -> DecidedStrictness -> Bool # | |
Eq Fixity | Since: base-4.6.0.0 |
Eq SourceStrictness | Since: base-4.9.0.0 |
Defined in GHC.Generics Methods (==) :: SourceStrictness -> SourceStrictness -> Bool # (/=) :: SourceStrictness -> SourceStrictness -> Bool # | |
Eq SourceUnpackedness | Since: base-4.9.0.0 |
Defined in GHC.Generics Methods (==) :: SourceUnpackedness -> SourceUnpackedness -> Bool # (/=) :: SourceUnpackedness -> SourceUnpackedness -> Bool # | |
Eq MaskingState | Since: base-4.3.0.0 |
Defined in GHC.IO | |
Eq IODeviceType | Since: base-4.2.0.0 |
Defined in GHC.IO.Device | |
Eq SeekMode | Since: base-4.2.0.0 |
Eq ArrayException | Since: base-4.2.0.0 |
Defined in GHC.IO.Exception Methods (==) :: ArrayException -> ArrayException -> Bool # (/=) :: ArrayException -> ArrayException -> Bool # | |
Eq AsyncException | Since: base-4.2.0.0 |
Defined in GHC.IO.Exception Methods (==) :: AsyncException -> AsyncException -> Bool # (/=) :: AsyncException -> AsyncException -> Bool # | |
Eq ExitCode | |
Eq IOErrorType | Since: base-4.1.0.0 |
Defined in GHC.IO.Exception | |
Eq IOException | Since: base-4.1.0.0 |
Defined in GHC.IO.Exception | |
Eq HandlePosn | Since: base-4.1.0.0 |
Defined in GHC.IO.Handle | |
Eq BufferMode | Since: base-4.2.0.0 |
Defined in GHC.IO.Handle.Types | |
Eq Handle | Since: base-4.1.0.0 |
Eq Newline | Since: base-4.2.0.0 |
Eq NewlineMode | Since: base-4.2.0.0 |
Defined in GHC.IO.Handle.Types | |
Eq IOMode | Since: base-4.2.0.0 |
Eq Int16 | Since: base-2.1 |
Eq Int32 | Since: base-2.1 |
Eq Int64 | Since: base-2.1 |
Eq Int8 | Since: base-2.1 |
Eq IoSubSystem | |
Defined in GHC.RTS.Flags | |
Eq SrcLoc | Since: base-4.9.0.0 |
Eq SomeChar | |
Eq SomeSymbol | Since: base-4.7.0.0 |
Defined in GHC.TypeLits | |
Eq SomeNat | Since: base-4.7.0.0 |
Eq GeneralCategory | Since: base-2.1 |
Defined in GHC.Unicode Methods (==) :: GeneralCategory -> GeneralCategory -> Bool # (/=) :: GeneralCategory -> GeneralCategory -> Bool # | |
Eq Word16 | Since: base-2.1 |
Eq Word32 | Since: base-2.1 |
Eq Word64 | Since: base-2.1 |
Eq Word8 | Since: base-2.1 |
Eq Lexeme | Since: base-2.1 |
Eq Number | Since: base-4.6.0.0 |
Eq Encoding | |
Eq ASCII7_Invalid | |
Eq ISO_8859_1_Invalid | |
Eq UTF16_Invalid | |
Eq UTF32_Invalid | |
Eq FileSize | |
Eq String | |
Eq ByteString | |
Defined in Data.ByteString.Internal | |
Eq ByteString | |
Defined in Data.ByteString.Lazy.Internal | |
Eq ShortByteString | |
Defined in Data.ByteString.Short.Internal Methods (==) :: ShortByteString -> ShortByteString -> Bool # (/=) :: ShortByteString -> ShortByteString -> Bool # | |
Eq IntSet | |
Eq SharedSecret | |
Defined in Crypto.ECC | |
Eq CryptoError | |
Defined in Crypto.Error.Types | |
Eq ByteArray | |
Eq BigNat | |
Eq ForeignSrcLang | |
Defined in GHC.ForeignSrcLang.Type Methods (==) :: ForeignSrcLang -> ForeignSrcLang -> Bool # (/=) :: ForeignSrcLang -> ForeignSrcLang -> Bool # | |
Eq Extension | |
Eq Module | |
Eq Ordering | |
Eq TrName | |
Eq TyCon | |
Eq ConnHost | |
Eq ConnKey | |
Eq Proxy | |
Eq ProxySecureMode | |
Defined in Network.HTTP.Client.Types Methods (==) :: ProxySecureMode -> ProxySecureMode -> Bool # (/=) :: ProxySecureMode -> ProxySecureMode -> Bool # | |
Eq ResponseTimeout | |
Defined in Network.HTTP.Client.Types Methods (==) :: ResponseTimeout -> ResponseTimeout -> Bool # (/=) :: ResponseTimeout -> ResponseTimeout -> Bool # | |
Eq StatusHeaders | |
Defined in Network.HTTP.Client.Types Methods (==) :: StatusHeaders -> StatusHeaders -> Bool # (/=) :: StatusHeaders -> StatusHeaders -> Bool # | |
Eq StreamFileStatus | |
Defined in Network.HTTP.Client.Types Methods (==) :: StreamFileStatus -> StreamFileStatus -> Bool # (/=) :: StreamFileStatus -> StreamFileStatus -> Bool # | |
Eq ByteRange | |
Eq StdMethod | |
Eq Status | |
Eq EscapeItem | |
Defined in Network.HTTP.Types.URI | |
Eq HttpVersion | |
Defined in Network.HTTP.Types.Version | |
Eq IP | Equality over IP addresses. Correctly compare IPv4 and IPv4-embedded-in-IPv6 addresses.
|
Eq IPv4 | |
Eq IPv6 | |
Eq IPRange | |
Eq Base | |
Eq AddrInfo | |
Eq AddrInfoFlag | |
Defined in Network.Socket.Info | |
Eq NameInfoFlag | |
Defined in Network.Socket.Info | |
Eq Family | |
Eq PortNumber | |
Defined in Network.Socket.Types | |
Eq SockAddr | |
Eq Socket | |
Eq SocketType | |
Defined in Network.Socket.Types | |
Eq URI | |
Eq URIAuth | |
Eq Mode | |
Eq Style | |
Eq TextDetails | |
Defined in Text.PrettyPrint.Annotated.HughesPJ | |
Eq Doc | |
Eq StdGen | |
Eq CompOption | |
Defined in Text.Regex.Posix.Wrap | |
Eq ExecOption | |
Defined in Text.Regex.Posix.Wrap | |
Eq ReturnCode | |
Defined in Text.Regex.Posix.Wrap | |
Eq Scientific | Scientific numbers can be safely compared for equality. No magnitude |
Defined in Data.Scientific | |
Eq AnnLookup | |
Eq AnnTarget | |
Eq Bang | |
Eq Body | |
Eq Bytes | |
Eq Callconv | |
Eq Clause | |
Eq Con | |
Eq Dec | |
Eq DecidedStrictness | |
Defined in Language.Haskell.TH.Syntax Methods (==) :: DecidedStrictness -> DecidedStrictness -> Bool # (/=) :: DecidedStrictness -> DecidedStrictness -> Bool # | |
Eq DerivClause | |
Defined in Language.Haskell.TH.Syntax | |
Eq DerivStrategy | |
Defined in Language.Haskell.TH.Syntax Methods (==) :: DerivStrategy -> DerivStrategy -> Bool # (/=) :: DerivStrategy -> DerivStrategy -> Bool # | |
Eq DocLoc | |
Eq Exp | |
Eq FamilyResultSig | |
Defined in Language.Haskell.TH.Syntax Methods (==) :: FamilyResultSig -> FamilyResultSig -> Bool # (/=) :: FamilyResultSig -> FamilyResultSig -> Bool # | |
Eq Fixity | |
Eq FixityDirection | |
Defined in Language.Haskell.TH.Syntax Methods (==) :: FixityDirection -> FixityDirection -> Bool # (/=) :: FixityDirection -> FixityDirection -> Bool # | |
Eq Foreign | |
Eq FunDep | |
Eq Guard | |
Eq Info | |
Eq InjectivityAnn | |
Defined in Language.Haskell.TH.Syntax Methods (==) :: InjectivityAnn -> InjectivityAnn -> Bool # (/=) :: InjectivityAnn -> InjectivityAnn -> Bool # | |
Eq Inline | |
Eq Lit | |
Eq Loc | |
Eq Match | |
Eq ModName | |
Eq Module | |
Eq ModuleInfo | |
Defined in Language.Haskell.TH.Syntax | |
Eq Name | |
Eq NameFlavour | |
Defined in Language.Haskell.TH.Syntax | |
Eq NameSpace | |
Eq OccName | |
Eq Overlap | |
Eq Pat | |
Eq PatSynArgs | |
Defined in Language.Haskell.TH.Syntax | |
Eq PatSynDir | |
Eq Phases | |
Eq PkgName | |
Eq Pragma | |
Eq Range | |
Eq Role | |
Eq RuleBndr | |
Eq RuleMatch | |
Eq Safety | |
Eq SourceStrictness | |
Defined in Language.Haskell.TH.Syntax Methods (==) :: SourceStrictness -> SourceStrictness -> Bool # (/=) :: SourceStrictness -> SourceStrictness -> Bool # | |
Eq SourceUnpackedness | |
Defined in Language.Haskell.TH.Syntax Methods (==) :: SourceUnpackedness -> SourceUnpackedness -> Bool # (/=) :: SourceUnpackedness -> SourceUnpackedness -> Bool # | |
Eq Specificity | |
Defined in Language.Haskell.TH.Syntax | |
Eq Stmt | |
Eq TyLit | |
Eq TySynEqn | |
Eq Type | |
Eq TypeFamilyHead | |
Defined in Language.Haskell.TH.Syntax Methods (==) :: TypeFamilyHead -> TypeFamilyHead -> Bool # (/=) :: TypeFamilyHead -> TypeFamilyHead -> Bool # | |
Eq CodePoint | |
Eq DecoderState | |
Eq Builder | |
Eq B | |
Eq ShortText | |
Eq ConstructorInfo | |
Defined in Language.Haskell.TH.Datatype Methods (==) :: ConstructorInfo -> ConstructorInfo -> Bool # (/=) :: ConstructorInfo -> ConstructorInfo -> Bool # | |
Eq ConstructorVariant | |
Defined in Language.Haskell.TH.Datatype Methods (==) :: ConstructorVariant -> ConstructorVariant -> Bool # (/=) :: ConstructorVariant -> ConstructorVariant -> Bool # | |
Eq DatatypeInfo | |
Defined in Language.Haskell.TH.Datatype | |
Eq DatatypeVariant | |
Defined in Language.Haskell.TH.Datatype Methods (==) :: DatatypeVariant -> DatatypeVariant -> Bool # (/=) :: DatatypeVariant -> DatatypeVariant -> Bool # | |
Eq FieldStrictness | |
Defined in Language.Haskell.TH.Datatype Methods (==) :: FieldStrictness -> FieldStrictness -> Bool # (/=) :: FieldStrictness -> FieldStrictness -> Bool # | |
Eq Strictness | |
Defined in Language.Haskell.TH.Datatype | |
Eq Unpackedness | |
Defined in Language.Haskell.TH.Datatype | |
Eq CalendarDiffDays | |
Defined in Data.Time.Calendar.CalendarDiffDays Methods (==) :: CalendarDiffDays -> CalendarDiffDays -> Bool # (/=) :: CalendarDiffDays -> CalendarDiffDays -> Bool # | |
Eq Day | |
Eq Month | |
Eq Quarter | |
Eq QuarterOfYear | |
Defined in Data.Time.Calendar.Quarter Methods (==) :: QuarterOfYear -> QuarterOfYear -> Bool # (/=) :: QuarterOfYear -> QuarterOfYear -> Bool # | |
Eq DayOfWeek | |
Eq AbsoluteTime | |
Defined in Data.Time.Clock.Internal.AbsoluteTime | |
Eq DiffTime | |
Eq NominalDiffTime | |
Defined in Data.Time.Clock.Internal.NominalDiffTime Methods (==) :: NominalDiffTime -> NominalDiffTime -> Bool # (/=) :: NominalDiffTime -> NominalDiffTime -> Bool # | |
Eq SystemTime | |
Defined in Data.Time.Clock.Internal.SystemTime | |
Eq UTCTime | |
Eq UniversalTime | |
Defined in Data.Time.Clock.Internal.UniversalTime Methods (==) :: UniversalTime -> UniversalTime -> Bool # (/=) :: UniversalTime -> UniversalTime -> Bool # | |
Eq TimeLocale | |
Defined in Data.Time.Format.Locale | |
Eq CalendarDiffTime | |
Defined in Data.Time.LocalTime.Internal.CalendarDiffTime Methods (==) :: CalendarDiffTime -> CalendarDiffTime -> Bool # (/=) :: CalendarDiffTime -> CalendarDiffTime -> Bool # | |
Eq LocalTime | |
Eq TimeOfDay | |
Eq TimeZone | |
Eq UnixDiffTime | |
Defined in Data.UnixTime.Types | |
Eq UnixTime | |
Eq UUID | |
Eq UnpackedUUID | |
Eq Document | |
Eq Element | |
Eq Node | |
Eq Content | |
Eq Doctype | |
Eq Document | |
Eq Element | |
Eq Event | |
Eq ExternalID | |
Defined in Data.XML.Types | |
Eq Instruction | |
Defined in Data.XML.Types | |
Eq Miscellaneous | |
Defined in Data.XML.Types Methods (==) :: Miscellaneous -> Miscellaneous -> Bool # (/=) :: Miscellaneous -> Miscellaneous -> Bool # | |
Eq Name | |
Eq Node | |
Eq Prologue | |
Eq CompressionLevel | |
Defined in Codec.Compression.Zlib.Stream Methods (==) :: CompressionLevel -> CompressionLevel -> Bool # (/=) :: CompressionLevel -> CompressionLevel -> Bool # | |
Eq CompressionStrategy | |
Defined in Codec.Compression.Zlib.Stream Methods (==) :: CompressionStrategy -> CompressionStrategy -> Bool # (/=) :: CompressionStrategy -> CompressionStrategy -> Bool # | |
Eq DictionaryHash | |
Eq Format | |
Eq MemoryLevel | |
Defined in Codec.Compression.Zlib.Stream | |
Eq Method | |
Eq WindowBits | |
Defined in Codec.Compression.Zlib.Stream | |
Eq Integer | |
Eq Natural | |
Eq () | |
Eq Bool | |
Eq Char | |
Eq Double | Note that due to the presence of
Also note that
|
Eq Float | Note that due to the presence of
Also note that
|
Eq Int | |
Eq Word | |
Eq (Encoding' a) | |
Eq v => Eq (KeyMap v) | |
Eq a => Eq (IResult a) | |
Eq a => Eq (Result a) | |
Eq (Path a) Source # | |
Eq a => Eq (Sensitive a) Source # | |
Eq (Time a) Source # | |
Eq a => Eq (ZipList a) | Since: base-4.7.0.0 |
Eq a => Eq (Complex a) | Since: base-2.1 |
Eq a => Eq (Identity a) | Since: base-4.8.0.0 |
Eq a => Eq (First a) | Since: base-2.1 |
Eq a => Eq (Last a) | Since: base-2.1 |
Eq a => Eq (Down a) | Since: base-4.6.0.0 |
Eq a => Eq (First a) | Since: base-4.9.0.0 |
Eq a => Eq (Last a) | Since: base-4.9.0.0 |
Eq a => Eq (Max a) | Since: base-4.9.0.0 |
Eq a => Eq (Min a) | Since: base-4.9.0.0 |
Eq m => Eq (WrappedMonoid m) | Since: base-4.9.0.0 |
Defined in Data.Semigroup Methods (==) :: WrappedMonoid m -> WrappedMonoid m -> Bool # (/=) :: WrappedMonoid m -> WrappedMonoid m -> Bool # | |
Eq a => Eq (Dual a) | Since: base-2.1 |
Eq a => Eq (Product a) | Since: base-2.1 |
Eq a => Eq (Sum a) | Since: base-2.1 |
Eq (TVar a) | Since: base-4.8.0.0 |
Eq p => Eq (Par1 p) | Since: base-4.7.0.0 |
Eq (IORef a) | Pointer equality. Since: base-4.0.0.0 |
Eq (MVar a) | Since: base-4.1.0.0 |
Eq (FunPtr a) | |
Eq (Ptr a) | Since: base-2.1 |
Eq a => Eq (Ratio a) | Since: base-2.1 |
Eq (StableName a) | Since: base-2.1 |
Defined in GHC.StableName | |
Eq (Bits n) | |
(PrimType ty, Eq ty) => Eq (Block ty) | |
Eq (Zn n) | |
Eq (Zn64 n) | |
Eq a => Eq (NonEmpty a) | |
Eq (CountOf ty) | |
Eq (Offset ty) | |
(PrimType ty, Eq ty) => Eq (UArray ty) | |
Eq s => Eq (CI s) | |
Eq a => Eq (Flush a) | |
Eq a => Eq (IntMap a) | |
Eq a => Eq (Seq a) | |
Eq a => Eq (ViewL a) | |
Eq a => Eq (ViewR a) | |
Eq a => Eq (Set a) | |
Eq a => Eq (Tree a) | |
Eq a => Eq (CryptoFailable a) | |
Defined in Crypto.Error.Types Methods (==) :: CryptoFailable a -> CryptoFailable a -> Bool # (/=) :: CryptoFailable a -> CryptoFailable a -> Bool # | |
Eq (Digest a) | |
Eq (HMAC a) | |
Eq (MutableByteArray s) | |
Defined in Data.Array.Byte Methods (==) :: MutableByteArray s -> MutableByteArray s -> Bool # (/=) :: MutableByteArray s -> MutableByteArray s -> Bool # | |
Eq1 f => Eq (Fix f) | |
(Functor f, Eq1 f) => Eq (Mu f) | |
(Functor f, Eq1 f) => Eq (Nu f) | |
Eq a => Eq (DNonEmpty a) | |
Eq a => Eq (DList a) | |
Eq a => Eq (Hashed a) | Uses precomputed hash to detect inequality faster |
Eq a => Eq (AddrRange a) | |
Eq mono => Eq (NonNull mono) | |
Eq a => Eq (AnnotDetails a) | |
Defined in Text.PrettyPrint.Annotated.HughesPJ Methods (==) :: AnnotDetails a -> AnnotDetails a -> Bool # (/=) :: AnnotDetails a -> AnnotDetails a -> Bool # | |
Eq (Doc a) | |
Eq a => Eq (Span a) | |
Eq a => Eq (Array a) | |
(Eq a, Prim a) => Eq (PrimArray a) | Since: primitive-0.6.4.0 |
Eq a => Eq (SmallArray a) | |
Defined in Data.Primitive.SmallArray | |
Eq g => Eq (StateGen g) | |
Eq g => Eq (AtomicGen g) | |
Eq g => Eq (IOGen g) | |
Eq g => Eq (STGen g) | |
Eq g => Eq (TGen g) | |
Eq a => Eq (Maybe a) | |
Eq flag => Eq (TyVarBndr flag) | |
Eq a => Eq (HashSet a) | Note that, in the presence of hash collisions, equal
In general, the lack of substitutivity can be observed with any function that depends on the key ordering, such as folds and traversals. |
Eq a => Eq (Vector a) | |
(Prim a, Eq a) => Eq (Vector a) | |
(Storable a, Eq a) => Eq (Vector a) | |
Eq a => Eq (NonEmpty a) | Since: base-4.9.0.0 |
Eq a => Eq (Maybe a) | Since: base-2.1 |
Eq a => Eq (a) | |
Eq a => Eq [a] | |
(Eq a, Eq b) => Eq (Either a b) | Since: base-2.1 |
Eq (Fixed a) | Since: base-2.1 |
Eq (Proxy s) | Since: base-4.7.0.0 |
Eq a => Eq (Arg a b) | Since: base-4.9.0.0 |
Eq (TypeRep a) | Since: base-2.1 |
(Ix i, Eq e) => Eq (Array i e) | Since: base-2.1 |
Eq (U1 p) | Since: base-4.9.0.0 |
Eq (V1 p) | Since: base-4.9.0.0 |
Eq (STRef s a) | Pointer equality. Since: base-2.1 |
PrimType a => Eq (BlockN n a) | |
(Eq k, Eq a) => Eq (Map k a) | |
(Eq1 f, Eq a) => Eq (Cofree f a) | |
(Eq1 f, Eq a) => Eq (Free f a) | |
(Eq1 f, Eq a) => Eq (Yoneda f a) | |
Eq (MutableArray s a) | |
Defined in Data.Primitive.Array Methods (==) :: MutableArray s a -> MutableArray s a -> Bool # (/=) :: MutableArray s a -> MutableArray s a -> Bool # | |
Eq (MutablePrimArray s a) | |
Defined in Data.Primitive.PrimArray Methods (==) :: MutablePrimArray s a -> MutablePrimArray s a -> Bool # (/=) :: MutablePrimArray s a -> MutablePrimArray s a -> Bool # | |
Eq (SmallMutableArray s a) | |
Defined in Data.Primitive.SmallArray Methods (==) :: SmallMutableArray s a -> SmallMutableArray s a -> Bool # (/=) :: SmallMutableArray s a -> SmallMutableArray s a -> Bool # | |
(Eq a, Eq b) => Eq (Either a b) | |
(Eq a, Eq b) => Eq (These a b) | |
(Eq a, Eq b) => Eq (Pair a b) | |
(Eq a, Eq b) => Eq (These a b) | |
(Eq k, Eq v) => Eq (HashMap k v) | Note that, in the presence of hash collisions, equal
In general, the lack of substitutivity can be observed with any function that depends on the key ordering, such as folds and traversals. |
(Eq k, Eq v) => Eq (Leaf k v) | |
(Eq a, Eq b) => Eq (a, b) | |
Eq a => Eq (Const a b) | Since: base-4.9.0.0 |
Eq (f a) => Eq (Ap f a) | Since: base-4.12.0.0 |
Eq (f a) => Eq (Alt f a) | Since: base-4.8.0.0 |
Eq (a :~: b) | Since: base-4.7.0.0 |
Eq (OrderingI a b) | |
Eq (STArray s i e) | Since: base-2.1 |
Eq (f p) => Eq (Rec1 f p) | Since: base-4.7.0.0 |
Eq (URec (Ptr ()) p) | Since: base-4.9.0.0 |
Eq (URec Char p) | Since: base-4.9.0.0 |
Eq (URec Double p) | Since: base-4.9.0.0 |
Eq (URec Float p) | |
Eq (URec Int p) | Since: base-4.9.0.0 |
Eq (URec Word p) | Since: base-4.9.0.0 |
Eq (p (Fix p a) a) => Eq (Fix p a) | |
Eq (p a a) => Eq (Join p a) | |
(Eq a, Eq (f b)) => Eq (CofreeF f a b) | |
Eq (w (CofreeF f a (CofreeT f w a))) => Eq (CofreeT f w a) | |
(Eq a, Eq (f b)) => Eq (FreeF f a b) | |
(Eq1 f, Eq1 m, Eq a) => Eq (FreeT f m a) | |
(Generic1 f, Eq (Rep1 f a)) => Eq (Generically1 f a) | |
Defined in GHC.Generics.Generically Methods (==) :: Generically1 f a -> Generically1 f a -> Bool # (/=) :: Generically1 f a -> Generically1 f a -> Bool # | |
Eq b => Eq (Tagged s b) | |
(Eq (f a), Eq (g a), Eq a) => Eq (These1 f g a) | |
(Eq e, Eq1 m, Eq a) => Eq (ErrorT e m a) | |
(Eq e, Eq1 m, Eq a) => Eq (ExceptT e m a) | |
(Eq a, Eq b, Eq c) => Eq (a, b, c) | |
(Eq1 f, Eq1 g, Eq a) => Eq (Product f g a) | Since: base-4.9.0.0 |
(Eq1 f, Eq1 g, Eq a) => Eq (Sum f g a) | Since: base-4.9.0.0 |
Eq (a :~~: b) | Since: base-4.10.0.0 |
(Eq (f p), Eq (g p)) => Eq ((f :*: g) p) | Since: base-4.7.0.0 |
(Eq (f p), Eq (g p)) => Eq ((f :+: g) p) | Since: base-4.7.0.0 |
Eq c => Eq (K1 i c p) | Since: base-4.7.0.0 |
(Eq a, Eq b, Eq c, Eq d) => Eq (a, b, c, d) | |
(Eq1 f, Eq1 g, Eq a) => Eq (Compose f g a) | Since: base-4.9.0.0 |
Eq (f (g p)) => Eq ((f :.: g) p) | Since: base-4.7.0.0 |
Eq (f p) => Eq (M1 i c f p) | Since: base-4.7.0.0 |
Eq (f a) => Eq (Clown f a b) | |
Eq (p b a) => Eq (Flip p a b) | |
Eq (g b) => Eq (Joker g a b) | |
Eq (p a b) => Eq (WrappedBifunctor p a b) | |
Defined in Data.Bifunctor.Wrapped Methods (==) :: WrappedBifunctor p a b -> WrappedBifunctor p a b -> Bool # (/=) :: WrappedBifunctor p a b -> WrappedBifunctor p a b -> Bool # | |
(Eq a, Eq b, Eq c, Eq d, Eq e) => Eq (a, b, c, d, e) | |
(Eq (f a b), Eq (g a b)) => Eq (Product f g a b) | |
(Eq (p a b), Eq (q a b)) => Eq (Sum p q a b) | |
(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f) => Eq (a, b, c, d, e, f) | |
Eq (f (p a b)) => Eq (Tannen f p a b) | |
(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g) => Eq (a, b, c, d, e, f, g) | |
(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) | |
Eq (p (f a) (g b)) => Eq (Biff p f g a b) | |
(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) | |
(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) | |
(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) | |
(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) | |
(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) | |
(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) | |
(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) | |
class Fractional a => Floating a where #
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
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 inversex * 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.
Minimal complete definition
fromRational, (recip | (/))
Methods
Fractional division.
Reciprocal fraction.
fromRational :: Rational -> a #
Conversion from a Rational
(that is
).
A floating literal stands for an application of Ratio
Integer
fromRational
to a value of type Rational
, so such literals have type
(
.Fractional
a) => a
Instances
Fractional Number | |
Fractional CDouble | |
Fractional CFloat | |
Fractional Scientific | WARNING: These methods also compute
|
Defined in Data.Scientific Methods (/) :: Scientific -> Scientific -> Scientific # recip :: Scientific -> Scientific # fromRational :: Rational -> Scientific # | |
Fractional DiffTime | |
Fractional NominalDiffTime | |
Defined in Data.Time.Clock.Internal.NominalDiffTime Methods (/) :: NominalDiffTime -> NominalDiffTime -> NominalDiffTime # recip :: NominalDiffTime -> NominalDiffTime # fromRational :: Rational -> NominalDiffTime # | |
RealFloat a => Fractional (Complex a) | Since: base-2.1 |
Fractional a => Fractional (Identity a) | Since: base-4.9.0.0 |
Fractional a => Fractional (Down a) | Since: base-4.14.0.0 |
Integral a => Fractional (Ratio a) | Since: base-2.0.1 |
HasResolution a => Fractional (Fixed a) | Since: base-2.1 |
Fractional a => Fractional (Op a b) | |
Fractional a => Fractional (Const a b) | Since: base-4.9.0.0 |
Fractional a => Fractional (Tagged s a) | |
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
withrem x y
=fromInteger 0
org (rem x y)
<g y
x
=y * div x y + mod x y
withmod x y
=fromInteger 0
orf (mod x y)
<f y
An example of a suitable Euclidean function, for Integer
's instance, is
abs
.
Methods
quot :: a -> a -> a infixl 7 #
integer division truncated toward zero
integer remainder, satisfying
(x `quot` y)*y + (x `rem` y) == x
integer division truncated toward negative infinity
integer modulus, satisfying
(x `div` y)*y + (x `mod` y) == x
conversion to Integer
Instances
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:
- Left identity
return
a>>=
k = k a- Right identity
m
>>=
return
= m- Associativity
m
>>=
(\x -> k x>>=
h) = (m>>=
k)>>=
h
Furthermore, the Monad
and Applicative
operations should relate as follows:
The above laws imply:
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.
'as
' can be understood as the >>=
bsdo
expression
do a <- as bs a
(>>) :: 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.
'as
' can be understood as the >>
bsdo
expression
do as bs
Inject a value into the monadic type.
Instances
Monad IResult | |
Monad Parser | |
Monad Result | |
Monad Complex | Since: base-4.9.0.0 |
Monad Identity | Since: base-4.8.0.0 |
Monad First | Since: base-4.8.0.0 |
Monad Last | Since: base-4.8.0.0 |
Monad Down | Since: base-4.11.0.0 |
Monad First | Since: base-4.9.0.0 |
Monad Last | Since: base-4.9.0.0 |
Monad Max | Since: base-4.9.0.0 |
Monad Min | Since: base-4.9.0.0 |
Monad Dual | Since: base-4.8.0.0 |
Monad Product | Since: base-4.8.0.0 |
Monad Sum | Since: base-4.8.0.0 |
Monad STM | Since: base-4.3.0.0 |
Monad Par1 | Since: base-4.9.0.0 |
Monad P | Since: base-2.1 |
Monad ReadP | Since: base-2.1 |
Monad ReadPrec | Since: base-2.1 |
Monad Put | |
Monad Seq | |
Monad Tree | |
Monad CryptoFailable | |
Defined in Crypto.Error.Types Methods (>>=) :: CryptoFailable a -> (a -> CryptoFailable b) -> CryptoFailable b # (>>) :: CryptoFailable a -> CryptoFailable b -> CryptoFailable b # return :: a -> CryptoFailable a # | |
Monad DNonEmpty | |
Monad DList | |
Monad IO | Since: base-2.1 |
Monad Array | |
Monad SmallArray | |
Defined in Data.Primitive.SmallArray Methods (>>=) :: SmallArray a -> (a -> SmallArray b) -> SmallArray b # (>>) :: SmallArray a -> SmallArray b -> SmallArray b # return :: a -> SmallArray a # | |
Monad Q | |
Monad Vector | |
Monad Id | |
Monad AttrParser | |
Defined in Text.XML.Stream.Parse Methods (>>=) :: AttrParser a -> (a -> AttrParser b) -> AttrParser b # (>>) :: AttrParser a -> AttrParser b -> AttrParser b # return :: a -> AttrParser a # | |
Monad Stream | |
Monad NonEmpty | Since: base-4.9.0.0 |
Monad Maybe | Since: base-2.1 |
Monad Solo | Since: base-4.15 |
Monad [] | Since: base-2.1 |
Representable f => Monad (Co f) | |
Monad (Parser i) | |
Monad m => Monad (WrappedMonad m) | Since: base-4.7.0.0 |
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 # | |
ArrowApply a => Monad (ArrowMonad a) | Since: base-2.1 |
Defined in Control.Arrow Methods (>>=) :: ArrowMonad a a0 -> (a0 -> ArrowMonad a b) -> ArrowMonad a b # (>>) :: ArrowMonad a a0 -> ArrowMonad a b -> ArrowMonad a b # return :: a0 -> ArrowMonad a a0 # | |
Monad (Either e) | Since: base-4.4.0.0 |
Monad (Proxy :: Type -> Type) | Since: base-4.7.0.0 |
Monad (U1 :: Type -> Type) | Since: base-4.9.0.0 |
Alternative f => Monad (Cofree f) | |
Functor f => Monad (Free f) | |
Monad m => Monad (Yoneda m) | |
Monad (ReifiedFold s) | |
Defined in Control.Lens.Reified Methods (>>=) :: ReifiedFold s a -> (a -> ReifiedFold s b) -> ReifiedFold s b # (>>) :: ReifiedFold s a -> ReifiedFold s b -> ReifiedFold s b # return :: a -> ReifiedFold s a # | |
Monad (ReifiedGetter s) | |
Defined in Control.Lens.Reified Methods (>>=) :: ReifiedGetter s a -> (a -> ReifiedGetter s b) -> ReifiedGetter s b # (>>) :: ReifiedGetter s a -> ReifiedGetter s b -> ReifiedGetter s b # return :: a -> ReifiedGetter s a # | |
Monad f => Monad (WrappedPoly f) | |
Defined in Data.MonoTraversable Methods (>>=) :: WrappedPoly f a -> (a -> WrappedPoly f b) -> WrappedPoly f b # (>>) :: WrappedPoly f a -> WrappedPoly f b -> WrappedPoly f b # return :: a -> WrappedPoly f a # | |
Monad m => Monad (ResourceT m) | |
Semigroup a => Monad (These a) | |
Semigroup a => Monad (These a) | |
Monoid a => Monad ((,) a) | Since: base-4.9.0.0 |
Monad m => Monad (Kleisli m a) | Since: base-4.14.0.0 |
Monad f => Monad (Ap f) | Since: base-4.12.0.0 |
Monad f => Monad (Alt f) | Since: base-4.8.0.0 |
Monad f => Monad (Rec1 f) | Since: base-4.9.0.0 |
(Applicative f, Monad f) => Monad (WhenMissing f x) | Equivalent to Since: containers-0.5.9 |
Defined in Data.IntMap.Internal Methods (>>=) :: WhenMissing f x a -> (a -> WhenMissing f x b) -> WhenMissing f x b # (>>) :: WhenMissing f x a -> WhenMissing f x b -> WhenMissing f x b # return :: a -> WhenMissing f x a # | |
(Alternative f, Monad w) => Monad (CofreeT f w) | |
(Functor f, Monad m) => Monad (FreeT f m) | |
Monad (Indexed i a) | |
(Monad (Rep p), Representable p) => Monad (Prep p) | |
Monad (Tagged s) | |
(Monad m, Error e) => Monad (ErrorT e m) | |
Monad m => Monad (ExceptT e m) | |
(Monoid a, Monoid b) => Monad ((,,) a b) | Since: base-4.14.0.0 |
(Monad f, Monad g) => Monad (Product f g) | Since: base-4.9.0.0 |
(Monad f, Monad g) => Monad (f :*: g) | Since: base-4.9.0.0 |
Monad (ConduitT i o m) | |
(Monad f, Applicative f) => Monad (WhenMatched f x y) | Equivalent to Since: containers-0.5.9 |
Defined in Data.IntMap.Internal Methods (>>=) :: WhenMatched f x y a -> (a -> WhenMatched f x y b) -> WhenMatched f x y b # (>>) :: WhenMatched f x y a -> WhenMatched f x y b -> WhenMatched f x y b # return :: a -> WhenMatched f x y a # | |
(Applicative f, Monad f) => Monad (WhenMissing f k x) | Equivalent to Since: containers-0.5.9 |
Defined in Data.Map.Internal Methods (>>=) :: WhenMissing f k x a -> (a -> WhenMissing f k x b) -> WhenMissing f k x b # (>>) :: WhenMissing f k x a -> WhenMissing f k x b -> WhenMissing f k x b # return :: a -> WhenMissing f k x a # | |
(Monoid a, Monoid b, Monoid c) => Monad ((,,,) a b c) | Since: base-4.14.0.0 |
Monad ((->) r) | Since: base-2.1 |
Monad f => Monad (M1 i c f) | Since: base-4.9.0.0 |
(Monad f, Applicative f) => Monad (WhenMatched f k x y) | Equivalent to Since: containers-0.5.9 |
Defined in Data.Map.Internal Methods (>>=) :: WhenMatched f k x y a -> (a -> WhenMatched f k x y b) -> WhenMatched f k x y b # (>>) :: WhenMatched f k x y a -> WhenMatched f k x y b -> WhenMatched f k x y b # return :: a -> WhenMatched f k x y a # | |
Monad state => Monad (Builder collection mutCollection step state err) | |
Defined in Basement.MutableBuilder Methods (>>=) :: Builder collection mutCollection step state err a -> (a -> Builder collection mutCollection step state err b) -> Builder collection mutCollection step state err b # (>>) :: Builder collection mutCollection step state err a -> Builder collection mutCollection step state err b -> Builder collection mutCollection step state err b # return :: a -> Builder collection mutCollection step state err a # | |
Monad m => Monad (Pipe l i o u m) | |
class Functor (f :: Type -> Type) where #
A type f
is a Functor if it provides a function fmap
which, given any types a
and b
lets you apply any function from (a -> b)
to turn an f a
into an f b
, preserving the
structure of f
. Furthermore f
needs to adhere to the following:
Note, that the second law follows from the free theorem of the type fmap
and
the first law, so you need only check that the former condition holds.
Minimal complete definition
Methods
fmap :: (a -> b) -> f a -> f b #
fmap
is used to apply a function of type (a -> b)
to a value of type f a
,
where f is a functor, to produce a value of type f b
.
Note that for any type constructor with more than one parameter (e.g., Either
),
only the last type parameter can be modified with fmap
(e.g., b
in `Either a b`).
Some type constructors with two parameters or more have a
instance that allows
both the last and the penultimate parameters to be mapped over.Bifunctor
Examples
Convert from a
to a Maybe
IntMaybe String
using show
:
>>>
fmap show Nothing
Nothing>>>
fmap show (Just 3)
Just "3"
Convert from an
to an
Either
Int IntEither Int String
using show
:
>>>
fmap show (Left 17)
Left 17>>>
fmap show (Right 17)
Right "17"
Double each element of a list:
>>>
fmap (*2) [1,2,3]
[2,4,6]
Apply even
to the second element of a pair:
>>>
fmap even (2,2)
(2,True)
It may seem surprising that the function is only applied to the last element of the tuple
compared to the list example above which applies it to every element in the list.
To understand, remember that tuples are type constructors with multiple type parameters:
a tuple of 3 elements (a,b,c)
can also be written (,,) a b c
and its Functor
instance
is defined for Functor ((,,) a b)
(i.e., only the third parameter is free to be mapped over
with fmap
).
It explains why fmap
can be used with tuples containing values of different types as in the
following example:
>>>
fmap even ("hello", 1.0, 4)
("hello",1.0,True)
Instances
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
is the additive identityfromInteger
0x + fromInteger 0
=x
negate
gives the additive inversex + negate x
=fromInteger 0
- Associativity of
(
*
) (x * y) * z
=x * (y * z)
is the multiplicative identityfromInteger
1x * fromInteger 1
=x
andfromInteger 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.
Methods
Unary negation.
Absolute value.
Sign of a number.
The functions abs
and signum
should satisfy the law:
abs x * signum x == x
For real numbers, the signum
is either -1
(negative), 0
(zero)
or 1
(positive).
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 ChunkSize Source # | |
Defined in Amazonka.Data.Body | |
Num Seconds Source # | |
Num Pos | |
Num Number | |
Num CBool | |
Num CChar | |
Num CClock | |
Num CDouble | |
Num CFloat | |
Num CInt | |
Num CIntMax | |
Num CIntPtr | |
Num CLLong | |
Num CLong | |
Num CPtrdiff | |
Num CSChar | |
Num CSUSeconds | |
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 CShort | |
Num CSigAtomic | |
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 CSize | |
Num CTime | |
Num CUChar | |
Num CUInt | |
Num CUIntMax | |
Num CUIntPtr | |
Num CULLong | |
Num CULong | |
Num CUSeconds | |
Defined in Foreign.C.Types | |
Num CUShort | |
Num CWchar | |
Num IntPtr | |
Num WordPtr | |
Num Int16 | Since: base-2.1 |
Num Int32 | Since: base-2.1 |
Num Int64 | Since: base-2.1 |
Num Int8 | Since: base-2.1 |
Num Word16 | Since: base-2.1 |
Num Word32 | Since: base-2.1 |
Num Word64 | Since: base-2.1 |
Num Word8 | Since: base-2.1 |
Num PortNumber | |
Defined in Network.Socket.Types Methods (+) :: PortNumber -> PortNumber -> PortNumber # (-) :: PortNumber -> PortNumber -> PortNumber # (*) :: PortNumber -> PortNumber -> PortNumber # negate :: PortNumber -> PortNumber # abs :: PortNumber -> PortNumber # signum :: PortNumber -> PortNumber # fromInteger :: Integer -> PortNumber # | |
Num CompOption | |
Defined in Text.Regex.Posix.Wrap Methods (+) :: CompOption -> CompOption -> CompOption # (-) :: CompOption -> CompOption -> CompOption # (*) :: CompOption -> CompOption -> CompOption # negate :: CompOption -> CompOption # abs :: CompOption -> CompOption # signum :: CompOption -> CompOption # fromInteger :: Integer -> CompOption # | |
Num ExecOption | |
Defined in Text.Regex.Posix.Wrap Methods (+) :: ExecOption -> ExecOption -> ExecOption # (-) :: ExecOption -> ExecOption -> ExecOption # (*) :: ExecOption -> ExecOption -> ExecOption # negate :: ExecOption -> ExecOption # abs :: ExecOption -> ExecOption # signum :: ExecOption -> ExecOption # fromInteger :: Integer -> ExecOption # | |
Num Scientific | WARNING: |
Defined in Data.Scientific Methods (+) :: Scientific -> Scientific -> Scientific # (-) :: Scientific -> Scientific -> Scientific # (*) :: Scientific -> Scientific -> Scientific # negate :: Scientific -> Scientific # abs :: Scientific -> Scientific # signum :: Scientific -> Scientific # fromInteger :: Integer -> Scientific # | |
Num CodePoint | |
Defined in Data.Text.Encoding | |
Num DecoderState | |
Defined in Data.Text.Encoding Methods (+) :: DecoderState -> DecoderState -> DecoderState # (-) :: DecoderState -> DecoderState -> DecoderState # (*) :: DecoderState -> DecoderState -> DecoderState # negate :: DecoderState -> DecoderState # abs :: DecoderState -> DecoderState # signum :: DecoderState -> DecoderState # fromInteger :: Integer -> DecoderState # | |
Num B | |
Num DiffTime | |
Defined in Data.Time.Clock.Internal.DiffTime | |
Num NominalDiffTime | |
Defined in Data.Time.Clock.Internal.NominalDiffTime Methods (+) :: NominalDiffTime -> NominalDiffTime -> NominalDiffTime # (-) :: NominalDiffTime -> NominalDiffTime -> NominalDiffTime # (*) :: NominalDiffTime -> NominalDiffTime -> NominalDiffTime # negate :: NominalDiffTime -> NominalDiffTime # abs :: NominalDiffTime -> NominalDiffTime # signum :: NominalDiffTime -> NominalDiffTime # fromInteger :: Integer -> NominalDiffTime # | |
Num Integer | Since: base-2.1 |
Num Natural | Note that Since: base-4.8.0.0 |
Num Int | Since: base-2.1 |
Num Word | Since: base-2.1 |
RealFloat a => Num (Complex a) | Since: base-2.1 |
Num a => Num (Identity a) | Since: base-4.9.0.0 |
Defined in Data.Functor.Identity | |
Num a => Num (Down a) | Since: base-4.11.0.0 |
Num a => Num (Max a) | Since: base-4.9.0.0 |
Num a => Num (Min a) | Since: base-4.9.0.0 |
Num a => Num (Product a) | Since: base-4.7.0.0 |
Defined in Data.Semigroup.Internal | |
Num a => Num (Sum a) | Since: base-4.7.0.0 |
Integral a => Num (Ratio a) | Since: base-2.0.1 |
KnownNat n => Num (Zn n) | |
(KnownNat n, NatWithinBound Word64 n) => Num (Zn64 n) | |
Num (CountOf ty) | |
Defined in Basement.Types.OffsetSize | |
Num (Offset ty) | |
Defined in Basement.Types.OffsetSize | |
HasResolution a => Num (Fixed a) | Since: base-2.1 |
Num a => Num (Op a b) | |
Num a => Num (Const a b) | Since: base-4.9.0.0 |
Defined in Data.Functor.Const | |
(Applicative f, Num a) => Num (Ap f a) | Note that even if the underlying Commutativity:
Additive inverse:
Distributivity:
Since: base-4.12.0.0 |
Num (f a) => Num (Alt f a) | Since: base-4.8.0.0 |
Num a => Num (Tagged s a) | |
Defined in Data.Tagged |
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.
Ord
, as defined by the Haskell report, implements a total order and has the
following properties:
- Comparability
x <= y || y <= x
=True
- Transitivity
- if
x <= y && y <= z
=True
, thenx <= z
=True
- Reflexivity
x <= x
=True
- Antisymmetry
- if
x <= y && y <= x
=True
, thenx == y
=True
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
Note that (7.) and (8.) do not require min
and max
to return either of
their arguments. The result is merely required to equal one of the
arguments in terms of (==)
.
Minimal complete definition: either compare
or <=
.
Using compare
can be more efficient for complex types.
Methods
compare :: a -> a -> Ordering #
(<) :: a -> a -> Bool infix 4 #
(<=) :: a -> a -> Bool infix 4 #
(>) :: a -> a -> Bool infix 4 #
Instances
Parsing of String
s, 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:
instanceRead
T wherereadPrec
= ...readListPrec
=readListPrecDefault
Methods
Arguments
:: Int | the operator precedence of the enclosing
context (a number from |
-> 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:
That is, readsPrec
parses the string produced by
showsPrec
, and delivers the value that
showsPrec
started with.
Instances
Read Key | |
Read DotNetTime | |
Defined in Data.Aeson.Types.Internal Methods readsPrec :: Int -> ReadS DotNetTime # readList :: ReadS [DotNetTime] # readPrec :: ReadPrec DotNetTime # readListPrec :: ReadPrec [DotNetTime] # | |
Read Value | |
Read Base64 Source # | |
Read Format Source # | |
Read AccessKey Source # | |
Read Region Source # | |
Read Seconds Source # | |
Read All | Since: base-2.1 |
Read Any | Since: base-2.1 |
Read Version | Since: base-2.1 |
Read Void | Reading a Since: base-4.8.0.0 |
Read CBool | |
Read CChar | |
Read CClock | |
Read CDouble | |
Read CFloat | |
Read CInt | |
Read CIntMax | |
Read CIntPtr | |
Read CLLong | |
Read CLong | |
Read CPtrdiff | |
Read CSChar | |
Read CSUSeconds | |
Defined in Foreign.C.Types Methods readsPrec :: Int -> ReadS CSUSeconds # readList :: ReadS [CSUSeconds] # readPrec :: ReadPrec CSUSeconds # readListPrec :: ReadPrec [CSUSeconds] # | |
Read CShort | |
Read CSigAtomic | |
Defined in Foreign.C.Types Methods readsPrec :: Int -> ReadS CSigAtomic # readList :: ReadS [CSigAtomic] # readPrec :: ReadPrec CSigAtomic # readListPrec :: ReadPrec [CSigAtomic] # | |
Read CSize | |
Read CTime | |
Read CUChar | |
Read CUInt | |
Read CUIntMax | |
Read CUIntPtr | |
Read CULLong | |
Read CULong | |
Read CUSeconds | |
Read CUShort | |
Read CWchar | |
Read IntPtr | |
Read WordPtr | |
Read Associativity | Since: base-4.6.0.0 |
Defined in GHC.Generics Methods readsPrec :: Int -> ReadS Associativity # readList :: ReadS [Associativity] # | |
Read DecidedStrictness | Since: base-4.9.0.0 |
Defined in GHC.Generics Methods readsPrec :: Int -> ReadS DecidedStrictness # readList :: ReadS [DecidedStrictness] # | |
Read Fixity | Since: base-4.6.0.0 |
Read SourceStrictness | Since: base-4.9.0.0 |
Defined in GHC.Generics Methods readsPrec :: Int -> ReadS SourceStrictness # readList :: ReadS [SourceStrictness] # | |
Read SourceUnpackedness | Since: base-4.9.0.0 |
Defined in GHC.Generics Methods readsPrec :: Int -> ReadS SourceUnpackedness # readList :: ReadS [SourceUnpackedness] # | |
Read SeekMode | Since: base-4.2.0.0 |
Read ExitCode | |
Read BufferMode | Since: base-4.2.0.0 |
Defined in GHC.IO.Handle.Types Methods readsPrec :: Int -> ReadS BufferMode # readList :: ReadS [BufferMode] # readPrec :: ReadPrec BufferMode # readListPrec :: ReadPrec [BufferMode] # | |
Read Newline | Since: base-4.3.0.0 |
Read NewlineMode | Since: base-4.3.0.0 |
Defined in GHC.IO.Handle.Types Methods readsPrec :: Int -> ReadS NewlineMode # readList :: ReadS [NewlineMode] # readPrec :: ReadPrec NewlineMode # readListPrec :: ReadPrec [NewlineMode] # | |
Read IOMode | Since: base-4.2.0.0 |
Read Int16 | Since: base-2.1 |
Read Int32 | Since: base-2.1 |
Read Int64 | Since: base-2.1 |
Read Int8 | Since: base-2.1 |
Read GCDetails | Since: base-4.10.0.0 |
Read RTSStats | Since: base-4.10.0.0 |
Read SomeChar | |
Read SomeSymbol | Since: base-4.7.0.0 |
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 |
Read GeneralCategory | Since: base-2.1 |
Defined in GHC.Read Methods readsPrec :: Int -> ReadS GeneralCategory # readList :: ReadS [GeneralCategory] # | |
Read Word16 | Since: base-2.1 |
Read Word32 | Since: base-2.1 |
Read Word64 | Since: base-2.1 |
Read Word8 | Since: base-2.1 |
Read Lexeme | Since: base-2.1 |
Read ByteString | |
Defined in Data.ByteString.Internal Methods readsPrec :: Int -> ReadS ByteString # readList :: ReadS [ByteString] # readPrec :: ReadPrec ByteString # readListPrec :: ReadPrec [ByteString] # | |
Read ByteString | |
Defined in Data.ByteString.Lazy.Internal Methods readsPrec :: Int -> ReadS ByteString # readList :: ReadS [ByteString] # readPrec :: ReadPrec ByteString # readListPrec :: ReadPrec [ByteString] # | |
Read ShortByteString | |
Defined in Data.ByteString.Short.Internal Methods readsPrec :: Int -> ReadS ShortByteString # readList :: ReadS [ShortByteString] # | |
Read IntSet | |
Read Ordering | Since: base-2.1 |
Read Cookie | |
Read CookieJar | |
Read Proxy | |
Read ProxySecureMode | |
Defined in Network.HTTP.Client.Types Methods readsPrec :: Int -> ReadS ProxySecureMode # readList :: ReadS [ProxySecureMode] # | |
Read StdMethod | |
Read IP | |
Read IPv4 | |
Read IPv6 | |
Read IPRange | |
Read AddrInfoFlag | |
Defined in Network.Socket.Info Methods readsPrec :: Int -> ReadS AddrInfoFlag # readList :: ReadS [AddrInfoFlag] # | |
Read NameInfoFlag | |
Defined in Network.Socket.Info Methods readsPrec :: Int -> ReadS NameInfoFlag # readList :: ReadS [NameInfoFlag] # | |
Read Family | |
Read PortNumber | |
Defined in Network.Socket.Types Methods readsPrec :: Int -> ReadS PortNumber # readList :: ReadS [PortNumber] # readPrec :: ReadPrec PortNumber # readListPrec :: ReadPrec [PortNumber] # | |
Read SocketType | |
Defined in Network.Socket.Types Methods readsPrec :: Int -> ReadS SocketType # readList :: ReadS [SocketType] # readPrec :: ReadPrec SocketType # readListPrec :: ReadPrec [SocketType] # | |
Read Scientific | Supports the skipping of parentheses and whitespaces. Example: > read " ( (( -1.0e+3 ) ))" :: Scientific -1000.0 (Note: This |
Defined in Data.Scientific Methods readsPrec :: Int -> ReadS Scientific # readList :: ReadS [Scientific] # readPrec :: ReadPrec Scientific # readListPrec :: ReadPrec [Scientific] # | |
Read ShortText | |
Read DatatypeVariant | |
Defined in Language.Haskell.TH.Datatype Methods readsPrec :: Int -> ReadS DatatypeVariant # readList :: ReadS [DatatypeVariant] # | |
Read Month | Read as |
Read Quarter | Read as |
Read QuarterOfYear | |
Defined in Data.Time.Calendar.Quarter Methods readsPrec :: Int -> ReadS QuarterOfYear # readList :: ReadS [QuarterOfYear] # | |
Read DayOfWeek | |
Read DiffTime | |
Read NominalDiffTime | |
Defined in Data.Time.Clock.Internal.NominalDiffTime Methods readsPrec :: Int -> ReadS NominalDiffTime # readList :: ReadS [NominalDiffTime] # | |
Read UUID | |
Read UnpackedUUID | |
Read DictionaryHash | |
Read Integer | Since: base-2.1 |
Read Natural | Since: base-4.8.0.0 |
Read () | Since: base-2.1 |
Read Bool | Since: base-2.1 |
Read Char | Since: base-2.1 |
Read Double | Since: base-2.1 |
Read Float | Since: base-2.1 |
Read Int | Since: base-2.1 |
Read Word | Since: base-4.5.0.0 |
Read v => Read (KeyMap v) | |
Read (Time a) Source # | |
Read a => Read (ZipList a) | Since: base-4.7.0.0 |
Read a => Read (Complex a) | Since: base-2.1 |
Read a => Read (Identity a) | This instance would be equivalent to the derived instances of the
Since: base-4.8.0.0 |
Read a => Read (First a) | Since: base-2.1 |
Read a => Read (Last a) | Since: base-2.1 |
Read a => Read (Down a) | This instance would be equivalent to the derived instances of the
Since: base-4.7.0.0 |
Read a => Read (First a) | Since: base-4.9.0.0 |
Read a => Read (Last a) | Since: base-4.9.0.0 |
Read a => Read (Max a) | Since: base-4.9.0.0 |
Read a => Read (Min a) | Since: base-4.9.0.0 |
Read m => Read (WrappedMonoid m) | Since: base-4.9.0.0 |
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 (Dual a) | Since: base-2.1 |
Read a => Read (Product a) | Since: base-2.1 |
Read a => Read (Sum a) | Since: base-2.1 |
Read p => Read (Par1 p) | Since: base-4.7.0.0 |
(Integral a, Read a) => Read (Ratio a) | Since: base-2.1 |
(Read s, FoldCase s) => Read (CI s) | |
Read e => Read (IntMap e) | |
Read a => Read (Seq a) | |
Read a => Read (ViewL a) | |
Read a => Read (ViewR a) | |
(Read a, Ord a) => Read (Set a) | |
Read a => Read (Tree a) | |
HashAlgorithm a => Read (Digest a) | |
Read1 f => Read (Fix f) | |
(Functor f, Read1 f) => Read (Mu f) | |
(Functor f, Read1 f) => Read (Nu f) | |
Read a => Read (DNonEmpty a) | |
Read a => Read (DList a) | |
Read (AddrRange IPv4) | |
Read (AddrRange IPv6) | |
Read mono => Read (NonNull mono) | |
Read a => Read (Array a) | |
Read a => Read (SmallArray a) | |
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 (Maybe a) | |
(Eq a, Hashable a, Read a) => Read (HashSet a) | |
Read a => Read (Vector a) | |
(Read a, Prim a) => Read (Vector a) | |
(Read a, Storable a) => Read (Vector a) | |
Read a => Read (NonEmpty a) | Since: base-4.11.0.0 |
Read a => Read (Maybe a) | Since: base-2.1 |
Read a => Read (a) | Since: base-4.15 |
Read a => Read [a] | Since: base-2.1 |
(Read a, Read b) => Read (Either a b) | Since: base-3.0 |
HasResolution a => Read (Fixed a) | Since: base-4.3.0.0 |
Read (Proxy t) | Since: base-4.7.0.0 |
(Read a, Read b) => Read (Arg a b) | Since: base-4.9.0.0 |
(Ix a, Read a, Read b) => Read (Array a b) | Since: base-2.1 |
Read (U1 p) | Since: base-4.9.0.0 |
Read (V1 p) | Since: base-4.9.0.0 |
(Ord k, Read k, Read e) => Read (Map k e) | |
(Read1 f, Read a) => Read (Cofree f a) | |
(Read1 f, Read a) => Read (Free f a) | |
(Functor f, Read (f a)) => Read (Yoneda f a) | |
(Read a, Read b) => Read (Either a b) | |
(Read a, Read b) => Read (These a b) | |
(Read a, Read b) => Read (Pair a b) | |
(Read a, Read b) => Read (These a b) | |
(Eq k, Hashable k, Read k, Read e) => Read (HashMap k e) | |
(Read a, Read b) => Read (a, b) | Since: base-2.1 |
Read a => Read (Const a b) | This instance would be equivalent to the derived instances of the
Since: base-4.8.0.0 |
Read (f a) => Read (Ap f a) | Since: base-4.12.0.0 |
Read (f a) => Read (Alt f a) | Since: base-4.8.0.0 |
a ~ b => Read (a :~: b) | Since: base-4.7.0.0 |
Read (f p) => Read (Rec1 f p) | Since: base-4.7.0.0 |
Read (p (Fix p a) a) => Read (Fix p a) | |
Read (p a a) => Read (Join p a) | |
(Read a, Read (f b)) => Read (CofreeF f a b) | |
Read (w (CofreeF f a (CofreeT f w a))) => Read (CofreeT f w a) | |
(Read a, Read (f b)) => Read (FreeF f a b) | |
(Read1 f, Read1 m, Read a) => Read (FreeT f m a) | |
Read b => Read (Tagged s b) | |
(Read (f a), Read (g a), Read a) => Read (These1 f g a) | |
(Read e, Read1 m, Read a) => Read (ErrorT e m a) | |
(Read e, Read1 m, Read a) => Read (ExceptT e m a) | |
(Read a, Read b, Read c) => Read (a, b, c) | Since: base-2.1 |
(Read1 f, Read1 g, Read a) => Read (Product f g a) | Since: base-4.9.0.0 |
(Read1 f, Read1 g, Read a) => Read (Sum f g a) | Since: base-4.9.0.0 |
a ~~ b => Read (a :~~: b) | Since: base-4.10.0.0 |
(Read (f p), Read (g p)) => Read ((f :*: g) p) | Since: base-4.7.0.0 |
(Read (f p), Read (g p)) => Read ((f :+: g) p) | Since: base-4.7.0.0 |
Read c => Read (K1 i c p) | Since: base-4.7.0.0 |
(Read a, Read b, Read c, Read d) => Read (a, b, c, d) | Since: base-2.1 |
(Read1 f, Read1 g, Read a) => Read (Compose f g a) | Since: base-4.9.0.0 |
Read (f (g p)) => Read ((f :.: g) p) | Since: base-4.7.0.0 |
Read (f p) => Read (M1 i c f p) | Since: base-4.7.0.0 |
Read (f a) => Read (Clown f a b) | |
Read (p b a) => Read (Flip p a b) | |
Read (g b) => Read (Joker g a b) | |
Read (p a b) => Read (WrappedBifunctor p a b) | |
Defined in Data.Bifunctor.Wrapped Methods readsPrec :: Int -> ReadS (WrappedBifunctor p a b) # readList :: ReadS [WrappedBifunctor p a b] # readPrec :: ReadPrec (WrappedBifunctor p a b) # readListPrec :: ReadPrec [WrappedBifunctor p a b] # | |
(Read a, Read b, Read c, Read d, Read e) => Read (a, b, c, d, e) | Since: base-2.1 |
(Read (f a b), Read (g a b)) => Read (Product f g a b) | |
(Read (p a b), Read (q a b)) => Read (Sum p q a b) | |
(Read a, Read b, Read c, Read d, Read e, Read f) => Read (a, b, c, d, e, f) | Since: base-2.1 |
Read (f (p a b)) => Read (Tannen f p a b) | |
(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 |
(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 |
Read (p (f a) (g b)) => Read (Biff p f g a b) | |
(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 |
(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 |
(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 |
(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 |
(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 |
(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 |
(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 |
Defined in GHC.Read |
class (Num a, Ord a) => Real a where #
Methods
toRational :: a -> Rational #
the rational equivalent of its real argument with full precision
Instances
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
yields decodeFloat
x(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) <=
, where abs
m < b^dd
is
the value of
.
In particular, floatDigits
x
. If the type
contains a negative zero, also decodeFloat
0 = (0,0)
.
The result of decodeFloat
(-0.0) = (0,0)
is unspecified if either of
decodeFloat
x
or isNaN
x
is isInfinite
xTrue
.
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
is one of the two closest representable
floating-point numbers to encodeFloat
m nm*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
corresponds to the second component of decodeFloat
.
and for finite nonzero exponent
0 = 0x
,
.
If exponent
x = snd (decodeFloat
x) + floatDigits
xx
is a finite floating-point number, it is equal in value to
, where significand
x * b ^^ exponent
xb
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
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
True
if the argument is an IEEE floating point number
a version of arctangent taking two real floating-point arguments.
For real floating x
and y
,
computes the angle
(from the positive x-axis) of the vector from the origin to the
point atan2
y x(x,y)
.
returns a value in the range [atan2
y x-pi
,
pi
]. It follows the Common Lisp semantics for the origin when
signed zeroes are supported.
, with atan2
y 1y
in a type
that is RealFloat
, should return the same value as
.
A default definition of atan
yatan2
is provided, but implementors
can provide a more accurate implementation.
Instances
class (Real a, Fractional a) => RealFrac a where #
Extracting components of fractions.
Minimal complete definition
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 asx
; andf
is a fraction with the same type and sign asx
, and with absolute value less than1
.
The default definitions of the ceiling
, floor
, truncate
and round
functions are in terms of properFraction
.
truncate :: Integral b => a -> b #
returns the integer nearest truncate
xx
between zero and x
round :: Integral b => a -> b #
returns the nearest integer to round
xx
;
the even integer if x
is equidistant between two integers
ceiling :: Integral b => a -> b #
returns the least integer not less than ceiling
xx
floor :: Integral b => a -> b #
returns the greatest integer not greater than floor
xx
Instances
RealFrac Number | |
RealFrac CDouble | |
RealFrac CFloat | |
RealFrac Scientific | WARNING: the methods of the |
Defined in Data.Scientific Methods properFraction :: Integral b => Scientific -> (b, Scientific) # truncate :: Integral b => Scientific -> b # round :: Integral b => Scientific -> b # ceiling :: Integral b => Scientific -> b # floor :: Integral b => Scientific -> b # | |
RealFrac DiffTime | |
RealFrac NominalDiffTime | |
Defined in Data.Time.Clock.Internal.NominalDiffTime Methods properFraction :: Integral b => NominalDiffTime -> (b, NominalDiffTime) # truncate :: Integral b => NominalDiffTime -> b # round :: Integral b => NominalDiffTime -> b # ceiling :: Integral b => NominalDiffTime -> b # floor :: Integral b => NominalDiffTime -> b # | |
RealFrac a => RealFrac (Identity a) | Since: base-4.9.0.0 |
RealFrac a => RealFrac (Down a) | Since: base-4.14.0.0 |
Integral a => RealFrac (Ratio a) | Since: base-2.0.1 |
HasResolution a => RealFrac (Fixed a) | Since: base-2.1 |
RealFrac a => RealFrac (Const a b) | Since: base-4.9.0.0 |
RealFrac a => RealFrac (Tagged s a) | |
Conversion of values to readable String
s.
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 thand
(associativity is ignored). Thus, ifd
is0
then the result is never surrounded in parentheses; ifd
is11
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,
produces the stringshow
(Leaf 1 :^: Leaf 2 :^: Leaf 3)"Leaf 1 :^: (Leaf 2 :^: Leaf 3)"
.
Methods
Arguments
:: Int | the operator precedence of the enclosing
context (a number from |
-> a | the value to be converted to a |
-> 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:
That is, readsPrec
parses the string produced by
showsPrec
, and delivers the value that showsPrec
started with.
Instances
class Monad m => MonadFail (m :: Type -> Type) where #
When a value is bound in do
-notation, the pattern on the left
hand side of <-
might not match. In this case, this class
provides a function to recover.
A Monad
without a MonadFail
instance may only be used in conjunction
with pattern that always match, such as newtypes, tuples, data types with
only a single data constructor, and irrefutable patterns (~pat
).
Instances of MonadFail
should satisfy the following law: fail s
should
be a left zero for >>=
,
fail s >>= f = fail s
If your Monad
is also MonadPlus
, a popular definition is
fail _ = mzero
Since: base-4.9.0.0
Instances
Class for string-like datastructures; used by the overloaded string extension (-XOverloadedStrings in GHC).
Methods
fromString :: String -> a #
Instances
class Functor f => Applicative (f :: Type -> Type) where #
A functor with application, providing operations to
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:
As a consequence of these laws, the Functor
instance for f
will satisfy
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
(which implies that pure
and <*>
satisfy the applicative functor laws).
Methods
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.
Example
Used in combination with (
, <$>
)(
can be used to build a record.<*>
)
>>>
data MyState = MyState {arg1 :: Foo, arg2 :: Bar, arg3 :: Baz}
>>>
produceFoo :: Applicative f => f Foo
>>>
produceBar :: Applicative f => f Bar
>>>
produceBaz :: Applicative f => f Baz
>>>
mkState :: Applicative f => f MyState
>>>
mkState = MyState <$> produceFoo <*> produceBar <*> produceBaz
(*>) :: f a -> f b -> f b infixl 4 #
Sequence actions, discarding the value of the first argument.
Examples
If used in conjunction with the Applicative instance for Maybe
,
you can chain Maybe computations, with a possible "early return"
in case of Nothing
.
>>>
Just 2 *> Just 3
Just 3
>>>
Nothing *> Just 3
Nothing
Of course a more interesting use case would be to have effectful computations instead of just returning pure values.
>>>
import Data.Char
>>>
import Text.ParserCombinators.ReadP
>>>
let p = string "my name is " *> munch1 isAlpha <* eof
>>>
readP_to_S p "my name is Simon"
[("Simon","")]
(<*) :: f a -> f b -> f a infixl 4 #
Sequence actions, discarding the value of the second argument.
Instances
Applicative IResult | |
Applicative Parser | |
Applicative Result | |
Applicative ZipList | f <$> ZipList xs1 <*> ... <*> ZipList xsN = ZipList (zipWithN f xs1 ... xsN) where (\a b c -> stimes c [a, b]) <$> 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 |
Applicative Complex | Since: base-4.9.0.0 |
Applicative Identity | Since: base-4.8.0.0 |
Applicative First | Since: base-4.8.0.0 |
Applicative Last | Since: base-4.8.0.0 |
Applicative Down | Since: base-4.11.0.0 |
Applicative First | Since: base-4.9.0.0 |
Applicative Last | Since: base-4.9.0.0 |
Applicative Max | Since: base-4.9.0.0 |
Applicative Min | Since: base-4.9.0.0 |
Applicative Dual | Since: base-4.8.0.0 |
Applicative Product | Since: base-4.8.0.0 |
Applicative Sum | Since: base-4.8.0.0 |
Applicative STM | Since: base-4.8.0.0 |
Applicative Par1 | Since: base-4.9.0.0 |
Applicative P | Since: base-4.5.0.0 |
Applicative ReadP | Since: base-4.6.0.0 |
Applicative ReadPrec | Since: base-4.6.0.0 |
Applicative Put | |
Applicative Seq | Since: containers-0.5.4 |
Applicative Tree | |
Applicative CryptoFailable | |
Defined in Crypto.Error.Types Methods pure :: a -> CryptoFailable a # (<*>) :: CryptoFailable (a -> b) -> CryptoFailable a -> CryptoFailable b # liftA2 :: (a -> b -> c) -> CryptoFailable a -> CryptoFailable b -> CryptoFailable c # (*>) :: CryptoFailable a -> CryptoFailable b -> CryptoFailable b # (<*) :: CryptoFailable a -> CryptoFailable b -> CryptoFailable a # | |
Applicative DNonEmpty | |
Defined in Data.DList.DNonEmpty.Internal | |
Applicative DList | |
Applicative IO | Since: base-2.1 |
Applicative Array | |
Applicative SmallArray | |
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 Q | |
Applicative Vector | |
Applicative Id | |
Applicative AttrParser | |
Defined in Text.XML.Stream.Parse Methods pure :: a -> AttrParser a # (<*>) :: AttrParser (a -> b) -> AttrParser a -> AttrParser b # liftA2 :: (a -> b -> c) -> AttrParser a -> AttrParser b -> AttrParser c # (*>) :: AttrParser a -> AttrParser b -> AttrParser b # (<*) :: AttrParser a -> AttrParser b -> AttrParser a # | |
Applicative NameMatcher | |
Defined in Text.XML.Stream.Parse Methods pure :: a -> NameMatcher a # (<*>) :: NameMatcher (a -> b) -> NameMatcher a -> NameMatcher b # liftA2 :: (a -> b -> c) -> NameMatcher a -> NameMatcher b -> NameMatcher c # (*>) :: NameMatcher a -> NameMatcher b -> NameMatcher b # (<*) :: NameMatcher a -> NameMatcher b -> NameMatcher a # | |
Applicative Stream | |
Applicative NonEmpty | Since: base-4.9.0.0 |
Applicative Maybe | Since: base-2.1 |
Applicative Solo | Since: base-4.15 |
Applicative [] | Since: base-2.1 |
Representable f => Applicative (Co f) | |
Applicative (Parser i) | |
Monad m => Applicative (WrappedMonad m) | Since: base-2.1 |
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 # | |
Arrow a => Applicative (ArrowMonad a) | Since: base-4.6.0.0 |
Defined in Control.Arrow Methods pure :: a0 -> ArrowMonad a a0 # (<*>) :: ArrowMonad a (a0 -> b) -> ArrowMonad a a0 -> ArrowMonad a b # liftA2 :: (a0 -> b -> c) -> ArrowMonad a a0 -> ArrowMonad a b -> ArrowMonad a c # (*>) :: ArrowMonad a a0 -> ArrowMonad a b -> ArrowMonad a b # (<*) :: ArrowMonad a a0 -> ArrowMonad a b -> ArrowMonad a a0 # | |
Applicative (Either e) | Since: base-3.0 |
Applicative (Proxy :: Type -> Type) | Since: base-4.7.0.0 |
Applicative (U1 :: Type -> Type) | Since: base-4.9.0.0 |
Monad m => Applicative (ZipSource m) | |
Defined in Data.Conduit.Internal.Conduit | |
Alternative f => Applicative (Cofree f) | |
Functor f => Applicative (Free f) | |
Applicative f => Applicative (Yoneda f) | |
Applicative f => Applicative (Indexing f) | |
Defined in Control.Lens.Internal.Indexed | |
Applicative f => Applicative (Indexing64 f) | |
Defined in Control.Lens.Internal.Indexed Methods pure :: a -> Indexing64 f a # (<*>) :: Indexing64 f (a -> b) -> Indexing64 f a -> Indexing64 f b # liftA2 :: (a -> b -> c) -> Indexing64 f a -> Indexing64 f b -> Indexing64 f c # (*>) :: Indexing64 f a -> Indexing64 f b -> Indexing64 f b # (<*) :: Indexing64 f a -> Indexing64 f b -> Indexing64 f a # | |
Applicative (ReifiedFold s) | |
Defined in Control.Lens.Reified Methods pure :: a -> ReifiedFold s a # (<*>) :: ReifiedFold s (a -> b) -> ReifiedFold s a -> ReifiedFold s b # liftA2 :: (a -> b -> c) -> ReifiedFold s a -> ReifiedFold s b -> ReifiedFold s c # (*>) :: ReifiedFold s a -> ReifiedFold s b -> ReifiedFold s b # (<*) :: ReifiedFold s a -> ReifiedFold s b -> ReifiedFold s a # | |
Applicative (ReifiedGetter s) | |
Defined in Control.Lens.Reified Methods pure :: a -> ReifiedGetter s a # (<*>) :: ReifiedGetter s (a -> b) -> ReifiedGetter s a -> ReifiedGetter s b # liftA2 :: (a -> b -> c) -> ReifiedGetter s a -> ReifiedGetter s b -> ReifiedGetter s c # (*>) :: ReifiedGetter s a -> ReifiedGetter s b -> ReifiedGetter s b # (<*) :: ReifiedGetter s a -> ReifiedGetter s b -> ReifiedGetter s a # | |
Applicative f => Applicative (WrappedPoly f) | |
Defined in Data.MonoTraversable Methods pure :: a -> WrappedPoly f a # (<*>) :: WrappedPoly f (a -> b) -> WrappedPoly f a -> WrappedPoly f b # liftA2 :: (a -> b -> c) -> WrappedPoly f a -> WrappedPoly f b -> WrappedPoly f c # (*>) :: WrappedPoly f a -> WrappedPoly f b -> WrappedPoly f b # (<*) :: WrappedPoly f a -> WrappedPoly f b -> WrappedPoly f a # | |
Applicative m => Applicative (ResourceT m) | |
Defined in Control.Monad.Trans.Resource.Internal | |
Semigroup a => Applicative (These a) | |
Semigroup a => Applicative (These a) | |
Monoid a => Applicative ((,) a) | For tuples, the ("hello ", (+15)) <*> ("world!", 2002) ("hello world!",2017) Since: base-2.1 |
Arrow a => Applicative (WrappedArrow a b) | Since: base-2.1 |
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 # | |
Applicative m => Applicative (Kleisli m a) | Since: base-4.14.0.0 |
Defined in Control.Arrow | |
Monoid m => Applicative (Const m :: Type -> Type) | Since: base-2.0.1 |
Applicative f => Applicative (Ap f) | Since: base-4.12.0.0 |
Applicative f => Applicative (Alt f) | Since: base-4.8.0.0 |
Applicative f => Applicative (Rec1 f) | Since: base-4.9.0.0 |
Applicative (Mag a b) | |
Biapplicative p => Applicative (Fix p) | |
Biapplicative p => Applicative (Join p) | |
Monad m => Applicative (ZipSink i m) | |
Defined in Data.Conduit.Internal.Conduit | |
(Applicative f, Monad f) => Applicative (WhenMissing f x) | Equivalent to Since: containers-0.5.9 |
Defined in Data.IntMap.Internal Methods pure :: a -> WhenMissing f x a # (<*>) :: WhenMissing f x (a -> b) -> WhenMissing f x a -> WhenMissing f x b # liftA2 :: (a -> b -> c) -> WhenMissing f x a -> WhenMissing f x b -> WhenMissing f x c # (*>) :: WhenMissing f x a -> WhenMissing f x b -> WhenMissing f x b # (<*) :: WhenMissing f x a -> WhenMissing f x b -> WhenMissing f x a # | |
(Alternative f, Applicative w) => Applicative (CofreeT f w) | |
Defined in Control.Comonad.Trans.Cofree | |
(Functor f, Monad m) => Applicative (FreeT f m) | |
Defined in Control.Monad.Trans.Free | |
(Generic1 f, Applicative (Rep1 f)) => Applicative (Generically1 f) | |
Defined in GHC.Generics.Generically Methods pure :: a -> Generically1 f a # (<*>) :: Generically1 f (a -> b) -> Generically1 f a -> Generically1 f b # liftA2 :: (a -> b -> c) -> Generically1 f a -> Generically1 f b -> Generically1 f c # (*>) :: Generically1 f a -> Generically1 f b -> Generically1 f b # (<*) :: Generically1 f a -> Generically1 f b -> Generically1 f a # | |
(Applicative f, Applicative g) => Applicative (Day f g) | |
Applicative (Indexed i a) | |
Defined in Control.Lens.Internal.Indexed | |
Monoid m => Applicative (Holes t m) | |
(Applicative (Rep p), Representable p) => Applicative (Prep p) | |
Applicative (Tagged s) | |
(Functor m, Monad m) => Applicative (ErrorT e m) | |
Defined in Control.Monad.Trans.Error | |
(Functor m, Monad m) => Applicative (ExceptT e m) | |
Defined in Control.Monad.Trans.Except | |
(Monoid a, Monoid b) => Applicative ((,,) a b) | Since: base-4.14.0.0 |
(Applicative f, Applicative g) => Applicative (Product f g) | Since: base-4.9.0.0 |
Defined in Data.Functor.Product | |
(Applicative f, Applicative g) => Applicative (f :*: g) | Since: base-4.9.0.0 |
Monoid c => Applicative (K1 i c :: Type -> Type) | Since: base-4.12.0.0 |
Applicative (ConduitT i o m) | |
Defined in Data.Conduit.Internal.Conduit Methods pure :: a -> ConduitT i o m a # (<*>) :: ConduitT i o m (a -> b) -> ConduitT i o m a -> ConduitT i o m b # liftA2 :: (a -> b -> c) -> ConduitT i o m a -> ConduitT i o m b -> ConduitT i o m c # (*>) :: ConduitT i o m a -> ConduitT i o m b -> ConduitT i o m b # (<*) :: ConduitT i o m a -> ConduitT i o m b -> ConduitT i o m a # | |
Monad m => Applicative (ZipConduit i o m) | |
Defined in Data.Conduit.Internal.Conduit Methods pure :: a -> ZipConduit i o m a # (<*>) :: ZipConduit i o m (a -> b) -> ZipConduit i o m a -> ZipConduit i o m b # liftA2 :: (a -> b -> c) -> ZipConduit i o m a -> ZipConduit i o m b -> ZipConduit i o m c # (*>) :: ZipConduit i o m a -> ZipConduit i o m b -> ZipConduit i o m b # (<*) :: ZipConduit i o m a -> ZipConduit i o m b -> ZipConduit i o m a # | |
(Monad f, Applicative f) => Applicative (WhenMatched f x y) | Equivalent to Since: containers-0.5.9 |
Defined in Data.IntMap.Internal Methods pure :: a -> WhenMatched f x y a # (<*>) :: WhenMatched f x y (a -> b) -> WhenMatched f x y a -> WhenMatched f x y b # liftA2 :: (a -> b -> c) -> WhenMatched f x y a -> WhenMatched f x y b -> WhenMatched f x y c # (*>) :: WhenMatched f x y a -> WhenMatched f x y b -> WhenMatched f x y b # (<*) :: WhenMatched f x y a -> WhenMatched f x y b -> WhenMatched f x y a # | |
(Applicative f, Monad f) => Applicative (WhenMissing f k x) | Equivalent to Since: containers-0.5.9 |
Defined in Data.Map.Internal Methods pure :: a -> WhenMissing f k x a # (<*>) :: WhenMissing f k x (a -> b) -> WhenMissing f k x a -> WhenMissing f k x b # liftA2 :: (a -> b -> c) -> WhenMissing f k x a -> WhenMissing f k x b -> WhenMissing f k x c # (*>) :: WhenMissing f k x a -> WhenMissing f k x b -> WhenMissing f k x b # (<*) :: WhenMissing f k x a -> WhenMissing f k x b -> WhenMissing f k x a # | |
(Monoid a, Monoid b, Monoid c) => Applicative ((,,,) a b c) | Since: base-4.14.0.0 |
Defined in GHC.Base | |
Applicative ((->) r) | Since: base-2.1 |
(Applicative f, Applicative g) => Applicative (Compose f g) | Since: base-4.9.0.0 |
Defined in Data.Functor.Compose | |
(Applicative f, Applicative g) => Applicative (f :.: g) | Since: base-4.9.0.0 |
Applicative f => Applicative (M1 i c f) | Since: base-4.9.0.0 |
(Monad f, Applicative f) => Applicative (WhenMatched f k x y) | Equivalent to Since: containers-0.5.9 |
Defined in Data.Map.Internal Methods pure :: a -> WhenMatched f k x y a # (<*>) :: WhenMatched f k x y (a -> b) -> WhenMatched f k x y a -> WhenMatched f k x y b # liftA2 :: (a -> b -> c) -> WhenMatched f k x y a -> WhenMatched f k x y b -> WhenMatched f k x y c # (*>) :: WhenMatched f k x y a -> WhenMatched f k x y b -> WhenMatched f k x y b # (<*) :: WhenMatched f k x y a -> WhenMatched f k x y b -> WhenMatched f k x y a # | |
Reifies s (ReifiedApplicative f) => Applicative (ReflectedApplicative f s) | |
Defined in Data.Reflection Methods pure :: a -> ReflectedApplicative f s a # (<*>) :: ReflectedApplicative f s (a -> b) -> ReflectedApplicative f s a -> ReflectedApplicative f s b # liftA2 :: (a -> b -> c) -> ReflectedApplicative f s a -> ReflectedApplicative f s b -> ReflectedApplicative f s c # (*>) :: ReflectedApplicative f s a -> ReflectedApplicative f s b -> ReflectedApplicative f s b # (<*) :: ReflectedApplicative f s a -> ReflectedApplicative f s b -> ReflectedApplicative f s a # | |
Monad state => Applicative (Builder collection mutCollection step state err) | |
Defined in Basement.MutableBuilder Methods pure :: a -> Builder collection mutCollection step state err a # (<*>) :: Builder collection mutCollection step state err (a -> b) -> Builder collection mutCollection step state err a -> Builder collection mutCollection step state err b # liftA2 :: (a -> b -> c) -> Builder collection mutCollection step state err a -> Builder collection mutCollection step state err b -> Builder collection mutCollection step state err c # (*>) :: Builder collection mutCollection step state err a -> Builder collection mutCollection step state err b -> Builder collection mutCollection step state err b # (<*) :: Builder collection mutCollection step state err a -> Builder collection mutCollection step state err b -> Builder collection mutCollection step state err a # | |
Monad m => Applicative (Pipe l i o u m) | |
Defined in Data.Conduit.Internal.Pipe Methods pure :: a -> Pipe l i o u m a # (<*>) :: Pipe l i o u m (a -> b) -> Pipe l i o u m a -> Pipe l i o u m b # liftA2 :: (a -> b -> c) -> Pipe l i o u m a -> Pipe l i o u m b -> Pipe l i o u m c # (*>) :: Pipe l i o u m a -> Pipe l i o u m b -> Pipe l i o u m b # (<*) :: Pipe l i o u m a -> Pipe l i o u m b -> Pipe l i o u m a # |
class Foldable (t :: TYPE LiftedRep -> Type) where #
The Foldable class represents data structures that can be reduced to a summary value one element at a time. Strict left-associative folds are a good fit for space-efficient reduction, while lazy right-associative folds are a good fit for corecursive iteration, or for folds that short-circuit after processing an initial subsequence of the structure's elements.
Instances can be derived automatically by enabling the DeriveFoldable
extension. For example, a derived instance for a binary tree might be:
{-# LANGUAGE DeriveFoldable #-} data Tree a = Empty | Leaf a | Node (Tree a) a (Tree a) deriving Foldable
A more detailed description can be found in the Overview section of Data.Foldable.
For the class laws see the Laws section of Data.Foldable.
Methods
foldMap :: Monoid m => (a -> m) -> t a -> m #
Map each element of the structure into a monoid, and combine the
results with (
. This fold is right-associative and lazy in the
accumulator. For strict left-associative folds consider <>
)foldMap'
instead.
Examples
Basic usage:
>>>
foldMap Sum [1, 3, 5]
Sum {getSum = 9}
>>>
foldMap Product [1, 3, 5]
Product {getProduct = 15}
>>>
foldMap (replicate 3) [1, 2, 3]
[1,1,1,2,2,2,3,3,3]
When a Monoid's (
is lazy in its second argument, <>
)foldMap
can
return a result even from an unbounded structure. For example, lazy
accumulation enables Data.ByteString.Builder to efficiently serialise
large data structures and produce the output incrementally:
>>>
import qualified Data.ByteString.Lazy as L
>>>
import qualified Data.ByteString.Builder as B
>>>
let bld :: Int -> B.Builder; bld i = B.intDec i <> B.word8 0x20
>>>
let lbs = B.toLazyByteString $ foldMap bld [0..]
>>>
L.take 64 lbs
"0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24"
foldr :: (a -> b -> b) -> b -> t a -> b #
Right-associative fold of a structure, lazy in the accumulator.
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, given an
operator lazy in its right argument, foldr
can produce a terminating
expression from an unbounded list.
For a general Foldable
structure this should be semantically identical
to,
foldr f z =foldr
f z .toList
Examples
Basic usage:
>>>
foldr (||) False [False, True, False]
True
>>>
foldr (||) False []
False
>>>
foldr (\c acc -> acc ++ [c]) "foo" ['a', 'b', 'c', 'd']
"foodcba"
Infinite structures
⚠️ Applying foldr
to infinite structures usually doesn't terminate.
It may still terminate under one of the following conditions:
- the folding function is short-circuiting
- the folding function is lazy on its second argument
Short-circuiting
(
short-circuits on ||
)True
values, so the following terminates
because there is a True
value finitely far from the left side:
>>>
foldr (||) False (True : repeat False)
True
But the following doesn't terminate:
>>>
foldr (||) False (repeat False ++ [True])
* Hangs forever *
Laziness in the second argument
Applying foldr
to infinite structures terminates when the operator is
lazy in its second argument (the initial accumulator is never used in
this case, and so could be left undefined
, but []
is more clear):
>>>
take 5 $ foldr (\i acc -> i : fmap (+3) acc) [] (repeat 1)
[1,4,7,10,13]
foldl :: (b -> a -> b) -> b -> t a -> b #
Left-associative fold of a structure, lazy in the accumulator. This is rarely what you want, but can work well for structures with efficient right-to-left sequencing and an operator that is lazy in its left argument.
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. Like all left-associative folds,
foldl
will diverge if given an infinite list.
If you want an efficient strict left-fold, you probably want to use
foldl'
instead of foldl
. The reason for this is that the 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 \(\mathcal{O}(n)\) 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
Examples
The first example is a strict fold, which in practice is best performed
with foldl'
.
>>>
foldl (+) 42 [1,2,3,4]
52
Though the result below is lazy, the input is reversed before prepending it to the initial accumulator, so corecursion begins only after traversing the entire input string.
>>>
foldl (\acc c -> c : acc) "abcd" "efgh"
"hgfeabcd"
A left fold of a structure that is infinite on the right cannot terminate, even when for any finite input the fold just returns the initial accumulator:
>>>
foldl (\a _ -> a) 0 $ repeat 1
* Hangs forever *
WARNING: When it comes to lists, you always want to use either foldl'
or foldr
instead.
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.
This function is non-total and will raise a runtime exception if the structure happens to be empty.
Examples
Basic usage:
>>>
foldr1 (+) [1..4]
10
>>>
foldr1 (+) []
Exception: Prelude.foldr1: empty list
>>>
foldr1 (+) Nothing
*** Exception: foldr1: empty structure
>>>
foldr1 (-) [1..4]
-2
>>>
foldr1 (&&) [True, False, True, True]
False
>>>
foldr1 (||) [False, False, True, True]
True
>>>
foldr1 (+) [1..]
* Hangs forever *
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.
This function is non-total and will raise a runtime exception if the structure happens to be empty.
foldl1
f =foldl1
f .toList
Examples
Basic usage:
>>>
foldl1 (+) [1..4]
10
>>>
foldl1 (+) []
*** Exception: Prelude.foldl1: empty list
>>>
foldl1 (+) Nothing
*** Exception: foldl1: empty structure
>>>
foldl1 (-) [1..4]
-8
>>>
foldl1 (&&) [True, False, True, True]
False
>>>
foldl1 (||) [False, False, True, True]
True
>>>
foldl1 (+) [1..]
* Hangs forever *
Test whether the structure is empty. The default implementation is Left-associative and lazy in both the initial element and the accumulator. Thus optimised for structures where the first element can be accessed in constant time. Structures where this is not the case should have a non-default implementation.
Examples
Basic usage:
>>>
null []
True
>>>
null [1]
False
null
is expected to terminate even for infinite structures.
The default implementation terminates provided the structure
is bounded on the left (there is a leftmost element).
>>>
null [1..]
False
Since: base-4.8.0.0
Returns the size/length of a finite structure as an Int
. The
default implementation just counts elements starting with the leftmost.
Instances for structures that can compute the element count faster
than via element-by-element counting, should provide a specialised
implementation.
Examples
Basic usage:
>>>
length []
0
>>>
length ['a', 'b', 'c']
3>>>
length [1..]
* Hangs forever *
Since: base-4.8.0.0
elem :: Eq a => a -> t a -> Bool infix 4 #
Does the element occur in the structure?
Note: elem
is often used in infix form.
Examples
Basic usage:
>>>
3 `elem` []
False
>>>
3 `elem` [1,2]
False
>>>
3 `elem` [1,2,3,4,5]
True
For infinite structures, the default implementation of elem
terminates if the sought-after value exists at a finite distance
from the left side of the structure:
>>>
3 `elem` [1..]
True
>>>
3 `elem` ([4..] ++ [3])
* Hangs forever *
Since: base-4.8.0.0
maximum :: Ord a => t a -> a #
The largest element of a non-empty structure.
This function is non-total and will raise a runtime exception if the structure happens to be empty. A structure that supports random access and maintains its elements in order should provide a specialised implementation to return the maximum in faster than linear time.
Examples
Basic usage:
>>>
maximum [1..10]
10
>>>
maximum []
*** Exception: Prelude.maximum: empty list
>>>
maximum Nothing
*** Exception: maximum: empty structure
WARNING: This function is partial for possibly-empty structures like lists.
Since: base-4.8.0.0
minimum :: Ord a => t a -> a #
The least element of a non-empty structure.
This function is non-total and will raise a runtime exception if the structure happens to be empty. A structure that supports random access and maintains its elements in order should provide a specialised implementation to return the minimum in faster than linear time.
Examples
Basic usage:
>>>
minimum [1..10]
1
>>>
minimum []
*** Exception: Prelude.minimum: empty list
>>>
minimum Nothing
*** Exception: minimum: empty structure
WARNING: This function is partial for possibly-empty structures like lists.
Since: base-4.8.0.0
The sum
function computes the sum of the numbers of a structure.
Examples
Basic usage:
>>>
sum []
0
>>>
sum [42]
42
>>>
sum [1..10]
55
>>>
sum [4.1, 2.0, 1.7]
7.8
>>>
sum [1..]
* Hangs forever *
Since: base-4.8.0.0
product :: Num a => t a -> a #
The product
function computes the product of the numbers of a
structure.
Examples
Basic usage:
>>>
product []
1
>>>
product [42]
42
>>>
product [1..10]
3628800
>>>
product [4.1, 2.0, 1.7]
13.939999999999998
>>>
product [1..]
* Hangs forever *
Since: base-4.8.0.0
Instances
Foldable KeyMap | |
Defined in Data.Aeson.KeyMap Methods fold :: Monoid m => KeyMap m -> m # foldMap :: Monoid m => (a -> m) -> KeyMap a -> m # foldMap' :: Monoid m => (a -> m) -> KeyMap a -> m # foldr :: (a -> b -> b) -> b -> KeyMap a -> b # foldr' :: (a -> b -> b) -> b -> KeyMap a -> b # foldl :: (b -> a -> b) -> b -> KeyMap a -> b # foldl' :: (b -> a -> b) -> b -> KeyMap a -> b # foldr1 :: (a -> a -> a) -> KeyMap a -> a # foldl1 :: (a -> a -> a) -> KeyMap a -> a # elem :: Eq a => a -> KeyMap a -> Bool # maximum :: Ord a => KeyMap a -> a # minimum :: Ord a => KeyMap a -> a # | |
Foldable IResult | |
Defined in Data.Aeson.Types.Internal Methods fold :: Monoid m => IResult m -> m # foldMap :: Monoid m => (a -> m) -> IResult a -> m # foldMap' :: Monoid m => (a -> m) -> IResult a -> m # foldr :: (a -> b -> b) -> b -> IResult a -> b # foldr' :: (a -> b -> b) -> b -> IResult a -> b # foldl :: (b -> a -> b) -> b -> IResult a -> b # foldl' :: (b -> a -> b) -> b -> IResult a -> b # foldr1 :: (a -> a -> a) -> IResult a -> a # foldl1 :: (a -> a -> a) -> IResult a -> a # elem :: Eq a => a -> IResult a -> Bool # maximum :: Ord a => IResult a -> a # minimum :: Ord a => IResult a -> a # | |
Foldable Result | |
Defined in Data.Aeson.Types.Internal Methods fold :: Monoid m => Result m -> m # foldMap :: Monoid m => (a -> m) -> Result a -> m # foldMap' :: Monoid m => (a -> m) -> Result a -> m # foldr :: (a -> b -> b) -> b -> Result a -> b # foldr' :: (a -> b -> b) -> b -> Result a -> b # foldl :: (b -> a -> b) -> b -> Result a -> b # foldl' :: (b -> a -> b) -> b -> Result a -> b # foldr1 :: (a -> a -> a) -> Result a -> a # foldl1 :: (a -> a -> a) -> Result a -> a # elem :: Eq a => a -> Result a -> Bool # maximum :: Ord a => Result a -> a # minimum :: Ord a => Result a -> a # | |
Foldable ZipList | Since: base-4.9.0.0 |
Defined in Control.Applicative Methods fold :: Monoid m => ZipList m -> m # foldMap :: Monoid m => (a -> m) -> ZipList a -> 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 # elem :: Eq a => a -> ZipList a -> Bool # maximum :: Ord a => ZipList a -> a # minimum :: Ord a => ZipList a -> a # | |
Foldable Complex | Since: base-4.9.0.0 |
Defined in Data.Complex Methods fold :: Monoid m => Complex m -> m # foldMap :: Monoid m => (a -> m) -> Complex a -> 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 # elem :: Eq a => a -> Complex a -> Bool # maximum :: Ord a => Complex a -> a # minimum :: Ord a => Complex a -> a # | |
Foldable Identity | Since: base-4.8.0.0 |
Defined in Data.Functor.Identity Methods fold :: Monoid m => Identity m -> m # foldMap :: Monoid m => (a -> m) -> Identity a -> 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 # elem :: Eq a => a -> Identity a -> Bool # maximum :: Ord a => Identity a -> a # minimum :: Ord a => Identity a -> a # | |
Foldable First | Since: base-4.8.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => First m -> m # foldMap :: Monoid m => (a -> m) -> First a -> 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 # elem :: Eq a => a -> First a -> Bool # maximum :: Ord a => First a -> a # minimum :: Ord a => First a -> a # | |
Foldable Last | Since: base-4.8.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => Last m -> m # foldMap :: Monoid m => (a -> m) -> Last a -> 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 # elem :: Eq a => a -> Last a -> Bool # maximum :: Ord a => Last a -> a # | |
Foldable Down | Since: base-4.12.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => Down m -> m # foldMap :: Monoid m => (a -> m) -> Down a -> 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 # elem :: Eq a => a -> Down a -> Bool # maximum :: Ord a => Down a -> a # | |
Foldable First | Since: base-4.9.0.0 |
Defined in Data.Semigroup Methods fold :: Monoid m => First m -> m # foldMap :: Monoid m => (a -> m) -> First a -> 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 # elem :: Eq a => a -> First a -> Bool # maximum :: Ord a => First a -> a # minimum :: Ord a => First a -> a # | |
Foldable Last | Since: base-4.9.0.0 |
Defined in Data.Semigroup Methods fold :: Monoid m => Last m -> m # foldMap :: Monoid m => (a -> m) -> Last a -> 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 # elem :: Eq a => a -> Last a -> Bool # maximum :: Ord a => Last a -> a # | |
Foldable Max | Since: base-4.9.0.0 |
Defined in Data.Semigroup Methods fold :: Monoid m => Max m -> m # foldMap :: Monoid m => (a -> m) -> Max a -> 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 # elem :: Eq a => a -> Max a -> Bool # maximum :: Ord a => Max a -> a # | |
Foldable Min | Since: base-4.9.0.0 |
Defined in Data.Semigroup Methods fold :: Monoid m => Min m -> m # foldMap :: Monoid m => (a -> m) -> Min a -> 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 # elem :: Eq a => a -> Min a -> Bool # maximum :: Ord a => Min a -> a # | |
Foldable Dual | Since: base-4.8.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => Dual m -> m # foldMap :: Monoid m => (a -> m) -> Dual a -> 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 # elem :: Eq a => a -> Dual a -> Bool # maximum :: Ord a => Dual a -> a # | |
Foldable Product | Since: base-4.8.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => Product m -> m # foldMap :: Monoid m => (a -> m) -> Product a -> 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 # elem :: Eq a => a -> Product a -> Bool # maximum :: Ord a => Product a -> a # minimum :: Ord a => Product a -> a # | |
Foldable Sum | Since: base-4.8.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => Sum m -> m # foldMap :: Monoid m => (a -> m) -> Sum a -> 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 # elem :: Eq a => a -> Sum a -> Bool # maximum :: Ord a => Sum a -> a # | |
Foldable Par1 | Since: base-4.9.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => Par1 m -> m # foldMap :: Monoid m => (a -> m) -> Par1 a -> 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 # elem :: Eq a => a -> Par1 a -> Bool # maximum :: Ord a => Par1 a -> a # | |
Foldable IntMap | Folds in order of increasing key. |
Defined in Data.IntMap.Internal Methods fold :: Monoid m => IntMap m -> m # foldMap :: Monoid m => (a -> m) -> IntMap a -> m # foldMap' :: Monoid m => (a -> m) -> IntMap a -> m # foldr :: (a -> b -> b) -> b -> IntMap a -> b # foldr' :: (a -> b -> b) -> b -> IntMap a -> b # foldl :: (b -> a -> b) -> b -> IntMap a -> b # foldl' :: (b -> a -> b) -> b -> IntMap a -> b # foldr1 :: (a -> a -> a) -> IntMap a -> a # foldl1 :: (a -> a -> a) -> IntMap a -> a # elem :: Eq a => a -> IntMap a -> Bool # maximum :: Ord a => IntMap a -> a # minimum :: Ord a => IntMap a -> a # | |
Foldable Digit | |
Defined in Data.Sequence.Internal Methods fold :: Monoid m => Digit m -> m # foldMap :: Monoid m => (a -> m) -> Digit a -> m # foldMap' :: Monoid m => (a -> m) -> Digit a -> m # foldr :: (a -> b -> b) -> b -> Digit a -> b # foldr' :: (a -> b -> b) -> b -> Digit a -> b # foldl :: (b -> a -> b) -> b -> Digit a -> b # foldl' :: (b -> a -> b) -> b -> Digit a -> b # foldr1 :: (a -> a -> a) -> Digit a -> a # foldl1 :: (a -> a -> a) -> Digit a -> a # elem :: Eq a => a -> Digit a -> Bool # maximum :: Ord a => Digit a -> a # minimum :: Ord a => Digit a -> a # | |
Foldable Elem | |
Defined in Data.Sequence.Internal Methods fold :: Monoid m => Elem m -> m # foldMap :: Monoid m => (a -> m) -> Elem a -> m # foldMap' :: Monoid m => (a -> m) -> Elem a -> m # foldr :: (a -> b -> b) -> b -> Elem a -> b # foldr' :: (a -> b -> b) -> b -> Elem a -> b # foldl :: (b -> a -> b) -> b -> Elem a -> b # foldl' :: (b -> a -> b) -> b -> Elem a -> b # foldr1 :: (a -> a -> a) -> Elem a -> a # foldl1 :: (a -> a -> a) -> Elem a -> a # elem :: Eq a => a -> Elem a -> Bool # maximum :: Ord a => Elem a -> a # | |
Foldable FingerTree | |
Defined in Data.Sequence.Internal Methods fold :: Monoid m => FingerTree m -> m # foldMap :: Monoid m => (a -> m) -> FingerTree a -> m # foldMap' :: Monoid m => (a -> m) -> FingerTree a -> m # foldr :: (a -> b -> b) -> b -> FingerTree a -> b # foldr' :: (a -> b -> b) -> b -> FingerTree a -> b # foldl :: (b -> a -> b) -> b -> FingerTree a -> b # foldl' :: (b -> a -> b) -> b -> FingerTree a -> b # foldr1 :: (a -> a -> a) -> FingerTree a -> a # foldl1 :: (a -> a -> a) -> FingerTree a -> a # toList :: FingerTree a -> [a] # null :: FingerTree a -> Bool # length :: FingerTree a -> Int # elem :: Eq a => a -> FingerTree a -> Bool # maximum :: Ord a => FingerTree a -> a # minimum :: Ord a => FingerTree a -> a # sum :: Num a => FingerTree a -> a # product :: Num a => FingerTree a -> a # | |
Foldable Node | |
Defined in Data.Sequence.Internal Methods fold :: Monoid m => Node m -> m # foldMap :: Monoid m => (a -> m) -> Node a -> m # foldMap' :: Monoid m => (a -> m) -> Node a -> m # foldr :: (a -> b -> b) -> b -> Node a -> b # foldr' :: (a -> b -> b) -> b -> Node a -> b # foldl :: (b -> a -> b) -> b -> Node a -> b # foldl' :: (b -> a -> b) -> b -> Node a -> b # foldr1 :: (a -> a -> a) -> Node a -> a # foldl1 :: (a -> a -> a) -> Node a -> a # elem :: Eq a => a -> Node a -> Bool # maximum :: Ord a => Node a -> a # | |
Foldable Seq | |
Defined in Data.Sequence.Internal Methods fold :: Monoid m => Seq m -> m # foldMap :: Monoid m => (a -> m) -> Seq a -> m # foldMap' :: Monoid m => (a -> m) -> Seq a -> m # foldr :: (a -> b -> b) -> b -> Seq a -> b # foldr' :: (a -> b -> b) -> b -> Seq a -> b # foldl :: (b -> a -> b) -> b -> Seq a -> b # foldl' :: (b -> a -> b) -> b -> Seq a -> b # foldr1 :: (a -> a -> a) -> Seq a -> a # foldl1 :: (a -> a -> a) -> Seq a -> a # elem :: Eq a => a -> Seq a -> Bool # maximum :: Ord a => Seq a -> a # | |
Foldable ViewL | |
Defined in Data.Sequence.Internal Methods fold :: Monoid m => ViewL m -> m # foldMap :: Monoid m => (a -> m) -> ViewL a -> m # foldMap' :: Monoid m => (a -> m) -> ViewL a -> m # foldr :: (a -> b -> b) -> b -> ViewL a -> b # foldr' :: (a -> b -> b) -> b -> ViewL a -> b # foldl :: (b -> a -> b) -> b -> ViewL a -> b # foldl' :: (b -> a -> b) -> b -> ViewL a -> b # foldr1 :: (a -> a -> a) -> ViewL a -> a # foldl1 :: (a -> a -> a) -> ViewL a -> a # elem :: Eq a => a -> ViewL a -> Bool # maximum :: Ord a => ViewL a -> a # minimum :: Ord a => ViewL a -> a # | |
Foldable ViewR | |
Defined in Data.Sequence.Internal Methods fold :: Monoid m => ViewR m -> m # foldMap :: Monoid m => (a -> m) -> ViewR a -> m # foldMap' :: Monoid m => (a -> m) -> ViewR a -> m # foldr :: (a -> b -> b) -> b -> ViewR a -> b # foldr' :: (a -> b -> b) -> b -> ViewR a -> b # foldl :: (b -> a -> b) -> b -> ViewR a -> b # foldl' :: (b -> a -> b) -> b -> ViewR a -> b # foldr1 :: (a -> a -> a) -> ViewR a -> a # foldl1 :: (a -> a -> a) -> ViewR a -> a # elem :: Eq a => a -> ViewR a -> Bool # maximum :: Ord a => ViewR a -> a # minimum :: Ord a => ViewR a -> a # | |
Foldable Set | Folds in order of increasing key. |
Defined in Data.Set.Internal Methods fold :: Monoid m => Set m -> m # foldMap :: Monoid m => (a -> m) -> Set a -> m # foldMap' :: Monoid m => (a -> m) -> Set a -> m # foldr :: (a -> b -> b) -> b -> Set a -> b # foldr' :: (a -> b -> b) -> b -> Set a -> b # foldl :: (b -> a -> b) -> b -> Set a -> b # foldl' :: (b -> a -> b) -> b -> Set a -> b # foldr1 :: (a -> a -> a) -> Set a -> a # foldl1 :: (a -> a -> a) -> Set a -> a # elem :: Eq a => a -> Set a -> Bool # maximum :: Ord a => Set a -> a # | |
Foldable Tree | |
Defined in Data.Tree Methods fold :: Monoid m => Tree m -> m # foldMap :: Monoid m => (a -> m) -> Tree a -> m # foldMap' :: Monoid m => (a -> m) -> Tree a -> m # foldr :: (a -> b -> b) -> b -> Tree a -> b # foldr' :: (a -> b -> b) -> b -> Tree a -> b # foldl :: (b -> a -> b) -> b -> Tree a -> b # foldl' :: (b -> a -> b) -> b -> Tree a -> b # foldr1 :: (a -> a -> a) -> Tree a -> a # foldl1 :: (a -> a -> a) -> Tree a -> a # elem :: Eq a => a -> Tree a -> Bool # maximum :: Ord a => Tree a -> a # | |
Foldable DNonEmpty | |
Defined in Data.DList.DNonEmpty.Internal Methods fold :: Monoid m => DNonEmpty m -> m # foldMap :: Monoid m => (a -> m) -> DNonEmpty a -> m # foldMap' :: Monoid m => (a -> m) -> DNonEmpty a -> m # foldr :: (a -> b -> b) -> b -> DNonEmpty a -> b # foldr' :: (a -> b -> b) -> b -> DNonEmpty a -> b # foldl :: (b -> a -> b) -> b -> DNonEmpty a -> b # foldl' :: (b -> a -> b) -> b -> DNonEmpty a -> b # foldr1 :: (a -> a -> a) -> DNonEmpty a -> a # foldl1 :: (a -> a -> a) -> DNonEmpty a -> a # toList :: DNonEmpty a -> [a] # length :: DNonEmpty a -> Int # elem :: Eq a => a -> DNonEmpty a -> Bool # maximum :: Ord a => DNonEmpty a -> a # minimum :: Ord a => DNonEmpty a -> a # | |
Foldable DList | |
Defined in Data.DList.Internal Methods fold :: Monoid m => DList m -> m # foldMap :: Monoid m => (a -> m) -> DList a -> m # foldMap' :: Monoid m => (a -> m) -> DList a -> m # foldr :: (a -> b -> b) -> b -> DList a -> b # foldr' :: (a -> b -> b) -> b -> DList a -> b # foldl :: (b -> a -> b) -> b -> DList a -> b # foldl' :: (b -> a -> b) -> b -> DList a -> b # foldr1 :: (a -> a -> a) -> DList a -> a # foldl1 :: (a -> a -> a) -> DList a -> a # elem :: Eq a => a -> DList a -> Bool # maximum :: Ord a => DList a -> a # minimum :: Ord a => DList a -> a # | |
Foldable Hashed | |
Defined in Data.Hashable.Class Methods fold :: Monoid m => Hashed m -> m # foldMap :: Monoid m => (a -> m) -> Hashed a -> m # foldMap' :: Monoid m => (a -> m) -> Hashed a -> m # foldr :: (a -> b -> b) -> b -> Hashed a -> b # foldr' :: (a -> b -> b) -> b -> Hashed a -> b # foldl :: (b -> a -> b) -> b -> Hashed a -> b # foldl' :: (b -> a -> b) -> b -> Hashed a -> b # foldr1 :: (a -> a -> a) -> Hashed a -> a # foldl1 :: (a -> a -> a) -> Hashed a -> a # elem :: Eq a => a -> Hashed a -> Bool # maximum :: Ord a => Hashed a -> a # minimum :: Ord a => Hashed a -> a # | |
Foldable HistoriedResponse | |
Defined in Network.HTTP.Client Methods fold :: Monoid m => HistoriedResponse m -> m # foldMap :: Monoid m => (a -> m) -> HistoriedResponse a -> m # foldMap' :: Monoid m => (a -> m) -> HistoriedResponse a -> m # foldr :: (a -> b -> b) -> b -> HistoriedResponse a -> b # foldr' :: (a -> b -> b) -> b -> HistoriedResponse a -> b # foldl :: (b -> a -> b) -> b -> HistoriedResponse a -> b # foldl' :: (b -> a -> b) -> b -> HistoriedResponse a -> b # foldr1 :: (a -> a -> a) -> HistoriedResponse a -> a # foldl1 :: (a -> a -> a) -> HistoriedResponse a -> a # toList :: HistoriedResponse a -> [a] # null :: HistoriedResponse a -> Bool # length :: HistoriedResponse a -> Int # elem :: Eq a => a -> HistoriedResponse a -> Bool # maximum :: Ord a => HistoriedResponse a -> a # minimum :: Ord a => HistoriedResponse a -> a # sum :: Num a => HistoriedResponse a -> a # product :: Num a => HistoriedResponse a -> a # | |
Foldable Response | |
Defined in Network.HTTP.Client.Types Methods fold :: Monoid m => Response m -> m # foldMap :: Monoid m => (a -> m) -> Response a -> m # foldMap' :: Monoid m => (a -> m) -> Response a -> m # foldr :: (a -> b -> b) -> b -> Response a -> b # foldr' :: (a -> b -> b) -> b -> Response a -> b # foldl :: (b -> a -> b) -> b -> Response a -> b # foldl' :: (b -> a -> b) -> b -> Response a -> b # foldr1 :: (a -> a -> a) -> Response a -> a # foldl1 :: (a -> a -> a) -> Response a -> a # elem :: Eq a => a -> Response a -> Bool # maximum :: Ord a => Response a -> a # minimum :: Ord a => Response a -> a # | |
Foldable Array | |
Defined in Data.Primitive.Array Methods fold :: Monoid m => Array m -> m # foldMap :: Monoid m => (a -> m) -> Array a -> 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 # elem :: Eq a => a -> Array a -> Bool # maximum :: Ord a => Array a -> a # minimum :: Ord a => Array a -> a # | |
Foldable SmallArray | |
Defined in Data.Primitive.SmallArray Methods fold :: Monoid m => SmallArray m -> m # foldMap :: Monoid m => (a -> m) -> SmallArray a -> 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 Maybe | |
Defined in Data.Strict.Maybe Methods fold :: Monoid m => Maybe m -> m # foldMap :: Monoid m => (a -> m) -> Maybe a -> 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 # elem :: Eq a => a -> Maybe a -> Bool # maximum :: Ord a => Maybe a -> a # minimum :: Ord a => Maybe a -> a # | |
Foldable HashSet | |
Defined in Data.HashSet.Internal Methods fold :: Monoid m => HashSet m -> m # foldMap :: Monoid m => (a -> m) -> HashSet a -> m # foldMap' :: Monoid m => (a -> m) -> HashSet a -> m # foldr :: (a -> b -> b) -> b -> HashSet a -> b # foldr' :: (a -> b -> b) -> b -> HashSet a -> b # foldl :: (b -> a -> b) -> b -> HashSet a -> b # foldl' :: (b -> a -> b) -> b -> HashSet a -> b # foldr1 :: (a -> a -> a) -> HashSet a -> a # foldl1 :: (a -> a -> a) -> HashSet a -> a # elem :: Eq a => a -> HashSet a -> Bool # maximum :: Ord a => HashSet a -> a # minimum :: Ord a => HashSet a -> a # | |
Foldable Vector | |
Defined in Data.Vector Methods fold :: Monoid m => Vector m -> m # foldMap :: Monoid m => (a -> m) -> Vector a -> m # foldMap' :: Monoid m => (a -> m) -> Vector a -> m # foldr :: (a -> b -> b) -> b -> Vector a -> b # foldr' :: (a -> b -> b) -> b -> Vector a -> b # foldl :: (b -> a -> b) -> b -> Vector a -> b # foldl' :: (b -> a -> b) -> b -> Vector a -> b # foldr1 :: (a -> a -> a) -> Vector a -> a # foldl1 :: (a -> a -> a) -> Vector a -> a # elem :: Eq a => a -> Vector a -> Bool # maximum :: Ord a => Vector a -> a # minimum :: Ord a => Vector a -> a # | |
Foldable NonEmpty | Since: base-4.9.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => NonEmpty m -> m # foldMap :: Monoid m => (a -> m) -> NonEmpty a -> 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 # elem :: Eq a => a -> NonEmpty a -> Bool # maximum :: Ord a => NonEmpty a -> a # minimum :: Ord a => NonEmpty a -> a # | |
Foldable Maybe | Since: base-2.1 |
Defined in Data.Foldable Methods fold :: Monoid m => Maybe m -> m # foldMap :: Monoid m => (a -> m) -> Maybe a -> 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 # elem :: Eq a => a -> Maybe a -> Bool # maximum :: Ord a => Maybe a -> a # minimum :: Ord a => Maybe a -> a # | |
Foldable Solo | Since: base-4.15 |
Defined in Data.Foldable Methods fold :: Monoid m => Solo m -> m # foldMap :: Monoid m => (a -> m) -> Solo a -> m # foldMap' :: Monoid m => (a -> m) -> Solo a -> m # foldr :: (a -> b -> b) -> b -> Solo a -> b # foldr' :: (a -> b -> b) -> b -> Solo a -> b # foldl :: (b -> a -> b) -> b -> Solo a -> b # foldl' :: (b -> a -> b) -> b -> Solo a -> b # foldr1 :: (a -> a -> a) -> Solo a -> a # foldl1 :: (a -> a -> a) -> Solo a -> a # elem :: Eq a => a -> Solo a -> Bool # maximum :: Ord a => Solo a -> a # | |
Foldable [] | Since: base-2.1 |
Defined in Data.Foldable Methods fold :: Monoid m => [m] -> m # foldMap :: Monoid m => (a -> m) -> [a] -> 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 # elem :: Eq a => a -> [a] -> Bool # maximum :: Ord a => [a] -> a # | |
Foldable (Either a) | Since: base-4.7.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => Either a m -> m # foldMap :: Monoid m => (a0 -> m) -> Either a a0 -> 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] # 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 # | |
Foldable (Proxy :: TYPE LiftedRep -> Type) | Since: base-4.7.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => Proxy m -> m # foldMap :: Monoid m => (a -> m) -> Proxy a -> 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 # elem :: Eq a => a -> Proxy a -> Bool # maximum :: Ord a => Proxy a -> a # minimum :: Ord a => Proxy a -> a # | |
Foldable (Arg a) | Since: base-4.9.0.0 |
Defined in Data.Semigroup Methods fold :: Monoid m => Arg a m -> m # foldMap :: Monoid m => (a0 -> m) -> Arg a a0 -> 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 # elem :: Eq a0 => a0 -> Arg a a0 -> Bool # maximum :: Ord a0 => Arg a a0 -> a0 # minimum :: Ord a0 => Arg a a0 -> a0 # | |
Foldable (Array i) | Since: base-4.8.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => Array i m -> m # foldMap :: Monoid m => (a -> m) -> Array i a -> 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 # elem :: Eq a => a -> Array i a -> Bool # maximum :: Ord a => Array i a -> a # minimum :: Ord a => Array i a -> a # | |
Foldable (U1 :: TYPE LiftedRep -> Type) | Since: base-4.9.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => U1 m -> m # foldMap :: Monoid m => (a -> m) -> U1 a -> 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 # elem :: Eq a => a -> U1 a -> Bool # maximum :: Ord a => U1 a -> a # | |
Foldable (UAddr :: TYPE LiftedRep -> Type) | Since: base-4.9.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => UAddr m -> m # foldMap :: Monoid m => (a -> m) -> UAddr a -> m # foldMap' :: Monoid m => (a -> m) -> UAddr a -> m # foldr :: (a -> b -> b) -> b -> UAddr a -> b # foldr' :: (a -> b -> b) -> b -> UAddr a -> b # foldl :: (b -> a -> b) -> b -> UAddr a -> b # foldl' :: (b -> a -> b) -> b -> UAddr a -> b # foldr1 :: (a -> a -> a) -> UAddr a -> a # foldl1 :: (a -> a -> a) -> UAddr a -> a # elem :: Eq a => a -> UAddr a -> Bool # maximum :: Ord a => UAddr a -> a # minimum :: Ord a => UAddr a -> a # | |
Foldable (UChar :: TYPE LiftedRep -> Type) | Since: base-4.9.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => UChar m -> m # foldMap :: Monoid m => (a -> m) -> UChar a -> m # foldMap' :: Monoid m => (a -> m) -> UChar a -> m # foldr :: (a -> b -> b) -> b -> UChar a -> b # foldr' :: (a -> b -> b) -> b -> UChar a -> b # foldl :: (b -> a -> b) -> b -> UChar a -> b # foldl' :: (b -> a -> b) -> b -> UChar a -> b # foldr1 :: (a -> a -> a) -> UChar a -> a # foldl1 :: (a -> a -> a) -> UChar a -> a # elem :: Eq a => a -> UChar a -> Bool # maximum :: Ord a => UChar a -> a # minimum :: Ord a => UChar a -> a # | |
Foldable (UDouble :: TYPE LiftedRep -> Type) | Since: base-4.9.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => UDouble m -> m # foldMap :: Monoid m => (a -> m) -> UDouble a -> m # foldMap' :: Monoid m => (a -> m) -> UDouble a -> m # foldr :: (a -> b -> b) -> b -> UDouble a -> b # foldr' :: (a -> b -> b) -> b -> UDouble a -> b # foldl :: (b -> a -> b) -> b -> UDouble a -> b # foldl' :: (b -> a -> b) -> b -> UDouble a -> b # foldr1 :: (a -> a -> a) -> UDouble a -> a # foldl1 :: (a -> a -> a) -> UDouble a -> a # elem :: Eq a => a -> UDouble a -> Bool # maximum :: Ord a => UDouble a -> a # minimum :: Ord a => UDouble a -> a # | |
Foldable (UFloat :: TYPE LiftedRep -> Type) | Since: base-4.9.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => UFloat m -> m # foldMap :: Monoid m => (a -> m) -> UFloat a -> m # foldMap' :: Monoid m => (a -> m) -> UFloat a -> m # foldr :: (a -> b -> b) -> b -> UFloat a -> b # foldr' :: (a -> b -> b) -> b -> UFloat a -> b # foldl :: (b -> a -> b) -> b -> UFloat a -> b # foldl' :: (b -> a -> b) -> b -> UFloat a -> b # foldr1 :: (a -> a -> a) -> UFloat a -> a # foldl1 :: (a -> a -> a) -> UFloat a -> a # elem :: Eq a => a -> UFloat a -> Bool # maximum :: Ord a => UFloat a -> a # minimum :: Ord a => UFloat a -> a # | |
Foldable (UInt :: TYPE LiftedRep -> Type) | Since: base-4.9.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => UInt m -> m # foldMap :: Monoid m => (a -> m) -> UInt a -> m # foldMap' :: Monoid m => (a -> m) -> UInt a -> m # foldr :: (a -> b -> b) -> b -> UInt a -> b # foldr' :: (a -> b -> b) -> b -> UInt a -> b # foldl :: (b -> a -> b) -> b -> UInt a -> b # foldl' :: (b -> a -> b) -> b -> UInt a -> b # foldr1 :: (a -> a -> a) -> UInt a -> a # foldl1 :: (a -> a -> a) -> UInt a -> a # elem :: Eq a => a -> UInt a -> Bool # maximum :: Ord a => UInt a -> a # | |
Foldable (UWord :: TYPE LiftedRep -> Type) | Since: base-4.9.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => UWord m -> m # foldMap :: Monoid m => (a -> m) -> UWord a -> m # foldMap' :: Monoid m => (a -> m) -> UWord a -> m # foldr :: (a -> b -> b) -> b -> UWord a -> b # foldr' :: (a -> b -> b) -> b -> UWord a -> b # foldl :: (b -> a -> b) -> b -> UWord a -> b # foldl' :: (b -> a -> b) -> b -> UWord a -> b # foldr1 :: (a -> a -> a) -> UWord a -> a # foldl1 :: (a -> a -> a) -> UWord a -> a # elem :: Eq a => a -> UWord a -> Bool # maximum :: Ord a => UWord a -> a # minimum :: Ord a => UWord a -> a # | |
Foldable (V1 :: TYPE LiftedRep -> Type) | Since: base-4.9.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => V1 m -> m # foldMap :: Monoid m => (a -> m) -> V1 a -> 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 # elem :: Eq a => a -> V1 a -> Bool # maximum :: Ord a => V1 a -> a # | |
Foldable (Map k) | Folds in order of increasing key. |
Defined in Data.Map.Internal Methods fold :: Monoid m => Map k m -> m # foldMap :: Monoid m => (a -> m) -> Map k a -> m # foldMap' :: Monoid m => (a -> m) -> Map k a -> m # foldr :: (a -> b -> b) -> b -> Map k a -> b # foldr' :: (a -> b -> b) -> b -> Map k a -> b # foldl :: (b -> a -> b) -> b -> Map k a -> b # foldl' :: (b -> a -> b) -> b -> Map k a -> b # foldr1 :: (a -> a -> a) -> Map k a -> a # foldl1 :: (a -> a -> a) -> Map k a -> a # elem :: Eq a => a -> Map k a -> Bool # maximum :: Ord a => Map k a -> a # minimum :: Ord a => Map k a -> a # | |
Foldable f => Foldable (Cofree f) | |
Defined in Control.Comonad.Cofree Methods fold :: Monoid m => Cofree f m -> m # foldMap :: Monoid m => (a -> m) -> Cofree f a -> m # foldMap' :: Monoid m => (a -> m) -> Cofree f a -> m # foldr :: (a -> b -> b) -> b -> Cofree f a -> b # foldr' :: (a -> b -> b) -> b -> Cofree f a -> b # foldl :: (b -> a -> b) -> b -> Cofree f a -> b # foldl' :: (b -> a -> b) -> b -> Cofree f a -> b # foldr1 :: (a -> a -> a) -> Cofree f a -> a # foldl1 :: (a -> a -> a) -> Cofree f a -> a # elem :: Eq a => a -> Cofree f a -> Bool # maximum :: Ord a => Cofree f a -> a # minimum :: Ord a => Cofree f a -> a # | |
Foldable f => Foldable (Free f) | |
Defined in Control.Monad.Free Methods fold :: Monoid m => Free f m -> m # foldMap :: Monoid m => (a -> m) -> Free f a -> m # foldMap' :: Monoid m => (a -> m) -> Free f a -> m # foldr :: (a -> b -> b) -> b -> Free f a -> b # foldr' :: (a -> b -> b) -> b -> Free f a -> b # foldl :: (b -> a -> b) -> b -> Free f a -> b # foldl' :: (b -> a -> b) -> b -> Free f a -> b # foldr1 :: (a -> a -> a) -> Free f a -> a # foldl1 :: (a -> a -> a) -> Free f a -> a # elem :: Eq a => a -> Free f a -> Bool # maximum :: Ord a => Free f a -> a # minimum :: Ord a => Free f a -> a # | |
Foldable f => Foldable (Yoneda f) | |
Defined in Data.Functor.Yoneda Methods fold :: Monoid m => Yoneda f m -> m # foldMap :: Monoid m => (a -> m) -> Yoneda f a -> m # foldMap' :: Monoid m => (a -> m) -> Yoneda f a -> m # foldr :: (a -> b -> b) -> b -> Yoneda f a -> b # foldr' :: (a -> b -> b) -> b -> Yoneda f a -> b # foldl :: (b -> a -> b) -> b -> Yoneda f a -> b # foldl' :: (b -> a -> b) -> b -> Yoneda f a -> b # foldr1 :: (a -> a -> a) -> Yoneda f a -> a # foldl1 :: (a -> a -> a) -> Yoneda f a -> a # elem :: Eq a => a -> Yoneda f a -> Bool # maximum :: Ord a => Yoneda f a -> a # minimum :: Ord a => Yoneda f a -> a # | |
MonoFoldable mono => Foldable (WrappedMono mono) | |
Defined in Data.MonoTraversable Methods fold :: Monoid m => WrappedMono mono m -> m # foldMap :: Monoid m => (a -> m) -> WrappedMono mono a -> m # foldMap' :: Monoid m => (a -> m) -> WrappedMono mono a -> m # foldr :: (a -> b -> b) -> b -> WrappedMono mono a -> b # foldr' :: (a -> b -> b) -> b -> WrappedMono mono a -> b # foldl :: (b -> a -> b) -> b -> WrappedMono mono a -> b # foldl' :: (b -> a -> b) -> b -> WrappedMono mono a -> b # foldr1 :: (a -> a -> a) -> WrappedMono mono a -> a # foldl1 :: (a -> a -> a) -> WrappedMono mono a -> a # toList :: WrappedMono mono a -> [a] # null :: WrappedMono mono a -> Bool # length :: WrappedMono mono a -> Int # elem :: Eq a => a -> WrappedMono mono a -> Bool # maximum :: Ord a => WrappedMono mono a -> a # minimum :: Ord a => WrappedMono mono a -> a # sum :: Num a => WrappedMono mono a -> a # product :: Num a => WrappedMono mono a -> a # | |
Foldable f => Foldable (WrappedPoly f) | |
Defined in Data.MonoTraversable Methods fold :: Monoid m => WrappedPoly f m -> m # foldMap :: Monoid m => (a -> m) -> WrappedPoly f a -> m # foldMap' :: Monoid m => (a -> m) -> WrappedPoly f a -> m # foldr :: (a -> b -> b) -> b -> WrappedPoly f a -> b # foldr' :: (a -> b -> b) -> b -> WrappedPoly f a -> b # foldl :: (b -> a -> b) -> b -> WrappedPoly f a -> b # foldl' :: (b -> a -> b) -> b -> WrappedPoly f a -> b # foldr1 :: (a -> a -> a) -> WrappedPoly f a -> a # foldl1 :: (a -> a -> a) -> WrappedPoly f a -> a # toList :: WrappedPoly f a -> [a] # null :: WrappedPoly f a -> Bool # length :: WrappedPoly f a -> Int # elem :: Eq a => a -> WrappedPoly f a -> Bool # maximum :: Ord a => WrappedPoly f a -> a # minimum :: Ord a => WrappedPoly f a -> a # sum :: Num a => WrappedPoly f a -> a # product :: Num a => WrappedPoly f a -> a # | |
Foldable (Either e) | |
Defined in Data.Strict.Either Methods fold :: Monoid m => Either e m -> m # foldMap :: Monoid m => (a -> m) -> Either e a -> m # foldMap' :: Monoid m => (a -> m) -> Either e a -> m # foldr :: (a -> b -> b) -> b -> Either e a -> b # foldr' :: (a -> b -> b) -> b -> Either e a -> b # foldl :: (b -> a -> b) -> b -> Either e a -> b # foldl' :: (b -> a -> b) -> b -> Either e a -> b # foldr1 :: (a -> a -> a) -> Either e a -> a # foldl1 :: (a -> a -> a) -> Either e a -> a # elem :: Eq a => a -> Either e a -> Bool # maximum :: Ord a => Either e a -> a # minimum :: Ord a => Either e a -> a # | |
Foldable (These a) | |
Defined in Data.Strict.These Methods fold :: Monoid m => These a m -> m # foldMap :: Monoid m => (a0 -> m) -> These a a0 -> m # foldMap' :: Monoid m => (a0 -> m) -> These a a0 -> m # foldr :: (a0 -> b -> b) -> b -> These a a0 -> b # foldr' :: (a0 -> b -> b) -> b -> These a a0 -> b # foldl :: (b -> a0 -> b) -> b -> These a a0 -> b # foldl' :: (b -> a0 -> b) -> b -> These a a0 -> b # foldr1 :: (a0 -> a0 -> a0) -> These a a0 -> a0 # foldl1 :: (a0 -> a0 -> a0) -> These a a0 -> a0 # toList :: These a a0 -> [a0] # elem :: Eq a0 => a0 -> These a a0 -> Bool # maximum :: Ord a0 => These a a0 -> a0 # minimum :: Ord a0 => These a a0 -> a0 # | |
Foldable (Pair e) | |
Defined in Data.Strict.Tuple Methods fold :: Monoid m => Pair e m -> m # foldMap :: Monoid m => (a -> m) -> Pair e a -> m # foldMap' :: Monoid m => (a -> m) -> Pair e a -> m # foldr :: (a -> b -> b) -> b -> Pair e a -> b # foldr' :: (a -> b -> b) -> b -> Pair e a -> b # foldl :: (b -> a -> b) -> b -> Pair e a -> b # foldl' :: (b -> a -> b) -> b -> Pair e a -> b # foldr1 :: (a -> a -> a) -> Pair e a -> a # foldl1 :: (a -> a -> a) -> Pair e a -> a # elem :: Eq a => a -> Pair e a -> Bool # maximum :: Ord a => Pair e a -> a # minimum :: Ord a => Pair e a -> a # | |
Foldable (These a) | |
Defined in Data.These Methods fold :: Monoid m => These a m -> m # foldMap :: Monoid m => (a0 -> m) -> These a a0 -> m # foldMap' :: Monoid m => (a0 -> m) -> These a a0 -> m # foldr :: (a0 -> b -> b) -> b -> These a a0 -> b # foldr' :: (a0 -> b -> b) -> b -> These a a0 -> b # foldl :: (b -> a0 -> b) -> b -> These a a0 -> b # foldl' :: (b -> a0 -> b) -> b -> These a a0 -> b # foldr1 :: (a0 -> a0 -> a0) -> These a a0 -> a0 # foldl1 :: (a0 -> a0 -> a0) -> These a a0 -> a0 # toList :: These a a0 -> [a0] # elem :: Eq a0 => a0 -> These a a0 -> Bool # maximum :: Ord a0 => These a a0 -> a0 # minimum :: Ord a0 => These a a0 -> a0 # | |
Foldable (HashMap k) | |
Defined in Data.HashMap.Internal Methods fold :: Monoid m => HashMap k m -> m # foldMap :: Monoid m => (a -> m) -> HashMap k a -> m # foldMap' :: Monoid m => (a -> m) -> HashMap k a -> m # foldr :: (a -> b -> b) -> b -> HashMap k a -> b # foldr' :: (a -> b -> b) -> b -> HashMap k a -> b # foldl :: (b -> a -> b) -> b -> HashMap k a -> b # foldl' :: (b -> a -> b) -> b -> HashMap k a -> b # foldr1 :: (a -> a -> a) -> HashMap k a -> a # foldl1 :: (a -> a -> a) -> HashMap k a -> a # toList :: HashMap k a -> [a] # length :: HashMap k a -> Int # elem :: Eq a => a -> HashMap k a -> Bool # maximum :: Ord a => HashMap k a -> a # minimum :: Ord a => HashMap k a -> a # | |
Foldable ((,) a) | Since: base-4.7.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => (a, m) -> m # foldMap :: Monoid m => (a0 -> m) -> (a, a0) -> 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 # elem :: Eq a0 => a0 -> (a, a0) -> Bool # maximum :: Ord a0 => (a, a0) -> a0 # minimum :: Ord a0 => (a, a0) -> a0 # | |
Foldable (Const m :: TYPE LiftedRep -> Type) | Since: base-4.7.0.0 |
Defined in Data.Functor.Const Methods fold :: Monoid m0 => Const m m0 -> m0 # foldMap :: Monoid m0 => (a -> m0) -> Const m a -> 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 # elem :: Eq a => a -> Const m a -> Bool # maximum :: Ord a => Const m a -> a # minimum :: Ord a => Const m a -> a # | |
Foldable f => Foldable (Ap f) | Since: base-4.12.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => Ap f m -> m # foldMap :: Monoid m => (a -> m) -> Ap f a -> 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 # elem :: Eq a => a -> Ap f a -> Bool # maximum :: Ord a => Ap f a -> a # | |
Foldable f => Foldable (Alt f) | Since: base-4.12.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => Alt f m -> m # foldMap :: Monoid m => (a -> m) -> Alt f a -> 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 # elem :: Eq a => a -> Alt f a -> Bool # maximum :: Ord a => Alt f a -> a # minimum :: Ord a => Alt f a -> a # | |
Foldable f => Foldable (Rec1 f) | Since: base-4.9.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => Rec1 f m -> m # foldMap :: Monoid m => (a -> m) -> Rec1 f a -> 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 # elem :: Eq a => a -> Rec1 f a -> Bool # maximum :: Ord a => Rec1 f a -> a # minimum :: Ord a => Rec1 f a -> a # | |
Bifoldable p => Foldable (Fix p) | |
Defined in Data.Bifunctor.Fix Methods fold :: Monoid m => Fix p m -> m # foldMap :: Monoid m => (a -> m) -> Fix p a -> m # foldMap' :: Monoid m => (a -> m) -> Fix p a -> m # foldr :: (a -> b -> b) -> b -> Fix p a -> b # foldr' :: (a -> b -> b) -> b -> Fix p a -> b # foldl :: (b -> a -> b) -> b -> Fix p a -> b # foldl' :: (b -> a -> b) -> b -> Fix p a -> b # foldr1 :: (a -> a -> a) -> Fix p a -> a # foldl1 :: (a -> a -> a) -> Fix p a -> a # elem :: Eq a => a -> Fix p a -> Bool # maximum :: Ord a => Fix p a -> a # minimum :: Ord a => Fix p a -> a # | |
Bifoldable p => Foldable (Join p) | |
Defined in Data.Bifunctor.Join Methods fold :: Monoid m => Join p m -> m # foldMap :: Monoid m => (a -> m) -> Join p a -> m # foldMap' :: Monoid m => (a -> m) -> Join p a -> m # foldr :: (a -> b -> b) -> b -> Join p a -> b # foldr' :: (a -> b -> b) -> b -> Join p a -> b # foldl :: (b -> a -> b) -> b -> Join p a -> b # foldl' :: (b -> a -> b) -> b -> Join p a -> b # foldr1 :: (a -> a -> a) -> Join p a -> a # foldl1 :: (a -> a -> a) -> Join p a -> a # elem :: Eq a => a -> Join p a -> Bool # maximum :: Ord a => Join p a -> a # minimum :: Ord a => Join p a -> a # | |
Foldable f => Foldable (CofreeF f a) | |
Defined in Control.Comonad.Trans.Cofree Methods fold :: Monoid m => CofreeF f a m -> m # foldMap :: Monoid m => (a0 -> m) -> CofreeF f a a0 -> m # foldMap' :: Monoid m => (a0 -> m) -> CofreeF f a a0 -> m # foldr :: (a0 -> b -> b) -> b -> CofreeF f a a0 -> b # foldr' :: (a0 -> b -> b) -> b -> CofreeF f a a0 -> b # foldl :: (b -> a0 -> b) -> b -> CofreeF f a a0 -> b # foldl' :: (b -> a0 -> b) -> b -> CofreeF f a a0 -> b # foldr1 :: (a0 -> a0 -> a0) -> CofreeF f a a0 -> a0 # foldl1 :: (a0 -> a0 -> a0) -> CofreeF f a a0 -> a0 # toList :: CofreeF f a a0 -> [a0] # null :: CofreeF f a a0 -> Bool # length :: CofreeF f a a0 -> Int # elem :: Eq a0 => a0 -> CofreeF f a a0 -> Bool # maximum :: Ord a0 => CofreeF f a a0 -> a0 # minimum :: Ord a0 => CofreeF f a a0 -> a0 # | |
(Foldable f, Foldable w) => Foldable (CofreeT f w) | |
Defined in Control.Comonad.Trans.Cofree Methods fold :: Monoid m => CofreeT f w m -> m # foldMap :: Monoid m => (a -> m) -> CofreeT f w a -> m # foldMap' :: Monoid m => (a -> m) -> CofreeT f w a -> m # foldr :: (a -> b -> b) -> b -> CofreeT f w a -> b # foldr' :: (a -> b -> b) -> b -> CofreeT f w a -> b # foldl :: (b -> a -> b) -> b -> CofreeT f w a -> b # foldl' :: (b -> a -> b) -> b -> CofreeT f w a -> b # foldr1 :: (a -> a -> a) -> CofreeT f w a -> a # foldl1 :: (a -> a -> a) -> CofreeT f w a -> a # toList :: CofreeT f w a -> [a] # null :: CofreeT f w a -> Bool # length :: CofreeT f w a -> Int # elem :: Eq a => a -> CofreeT f w a -> Bool # maximum :: Ord a => CofreeT f w a -> a # minimum :: Ord a => CofreeT f w a -> a # | |
Foldable f => Foldable (FreeF f a) | |
Defined in Control.Monad.Trans.Free Methods fold :: Monoid m => FreeF f a m -> m # foldMap :: Monoid m => (a0 -> m) -> FreeF f a a0 -> m # foldMap' :: Monoid m => (a0 -> m) -> FreeF f a a0 -> m # foldr :: (a0 -> b -> b) -> b -> FreeF f a a0 -> b # foldr' :: (a0 -> b -> b) -> b -> FreeF f a a0 -> b # foldl :: (b -> a0 -> b) -> b -> FreeF f a a0 -> b # foldl' :: (b -> a0 -> b) -> b -> FreeF f a a0 -> b # foldr1 :: (a0 -> a0 -> a0) -> FreeF f a a0 -> a0 # foldl1 :: (a0 -> a0 -> a0) -> FreeF f a a0 -> a0 # toList :: FreeF f a a0 -> [a0] # null :: FreeF f a a0 -> Bool # length :: FreeF f a a0 -> Int # elem :: Eq a0 => a0 -> FreeF f a a0 -> Bool # maximum :: Ord a0 => FreeF f a a0 -> a0 # minimum :: Ord a0 => FreeF f a a0 -> a0 # | |
(Foldable m, Foldable f) => Foldable (FreeT f m) | |
Defined in Control.Monad.Trans.Free Methods fold :: Monoid m0 => FreeT f m m0 -> m0 # foldMap :: Monoid m0 => (a -> m0) -> FreeT f m a -> m0 # foldMap' :: Monoid m0 => (a -> m0) -> FreeT f m a -> m0 # foldr :: (a -> b -> b) -> b -> FreeT f m a -> b # foldr' :: (a -> b -> b) -> b -> FreeT f m a -> b # foldl :: (b -> a -> b) -> b -> FreeT f m a -> b # foldl' :: (b -> a -> b) -> b -> FreeT f m a -> b # foldr1 :: (a -> a -> a) -> FreeT f m a -> a # foldl1 :: (a -> a -> a) -> FreeT f m a -> a # toList :: FreeT f m a -> [a] # length :: FreeT f m a -> Int # elem :: Eq a => a -> FreeT f m a -> Bool # maximum :: Ord a => FreeT f m a -> a # minimum :: Ord a => FreeT f m a -> a # | |
Foldable (Tagged s) | |
Defined in Data.Tagged Methods fold :: Monoid m => Tagged s m -> m # foldMap :: Monoid m => (a -> m) -> Tagged s a -> m # foldMap' :: Monoid m => (a -> m) -> Tagged s a -> m # foldr :: (a -> b -> b) -> b -> Tagged s a -> b # foldr' :: (a -> b -> b) -> b -> Tagged s a -> b # foldl :: (b -> a -> b) -> b -> Tagged s a -> b # foldl' :: (b -> a -> b) -> b -> Tagged s a -> b # foldr1 :: (a -> a -> a) -> Tagged s a -> a # foldl1 :: (a -> a -> a) -> Tagged s a -> a # elem :: Eq a => a -> Tagged s a -> Bool # maximum :: Ord a => Tagged s a -> a # minimum :: Ord a => Tagged s a -> a # | |
(Foldable f, Foldable g) => Foldable (These1 f g) | |
Defined in Data.Functor.These Methods fold :: Monoid m => These1 f g m -> m # foldMap :: Monoid m => (a -> m) -> These1 f g a -> m # foldMap' :: Monoid m => (a -> m) -> These1 f g a -> m # foldr :: (a -> b -> b) -> b -> These1 f g a -> b # foldr' :: (a -> b -> b) -> b -> These1 f g a -> b # foldl :: (b -> a -> b) -> b -> These1 f g a -> b # foldl' :: (b -> a -> b) -> b -> These1 f g a -> b # foldr1 :: (a -> a -> a) -> These1 f g a -> a # foldl1 :: (a -> a -> a) -> These1 f g a -> a # toList :: These1 f g a -> [a] # null :: These1 f g a -> Bool # length :: These1 f g a -> Int # elem :: Eq a => a -> These1 f g a -> Bool # maximum :: Ord a => These1 f g a -> a # minimum :: Ord a => These1 f g a -> a # | |
Foldable f => Foldable (ErrorT e f) | |
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 # 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 # | |
Foldable f => Foldable (ExceptT e f) | |
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 # 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 # | |
(Foldable f, Foldable g) => Foldable (Product f g) | Since: base-4.9.0.0 |
Defined in Data.Functor.Product Methods fold :: Monoid m => Product f g m -> m # foldMap :: Monoid m => (a -> m) -> Product f g a -> 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 # | |
(Foldable f, Foldable g) => Foldable (Sum f g) | Since: base-4.9.0.0 |
Defined in Data.Functor.Sum Methods fold :: Monoid m => Sum f g m -> m # foldMap :: Monoid m => (a -> m) -> Sum f g a -> 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 # 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 # | |
(Foldable f, Foldable g) => Foldable (f :*: g) | Since: base-4.9.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => (f :*: g) m -> m # foldMap :: Monoid m => (a -> m) -> (f :*: g) a -> 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] # 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 # | |
(Foldable f, Foldable g) => Foldable (f :+: g) | Since: base-4.9.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => (f :+: g) m -> m # foldMap :: Monoid m => (a -> m) -> (f :+: g) a -> 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] # 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 # | |
Foldable (K1 i c :: TYPE LiftedRep -> Type) | Since: base-4.9.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => K1 i c m -> m # foldMap :: Monoid m => (a -> m) -> K1 i c a -> 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 # 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 # | |
(Foldable f, Foldable g) => Foldable (Compose f g) | Since: base-4.9.0.0 |
Defined in Data.Functor.Compose Methods fold :: Monoid m => Compose f g m -> m # foldMap :: Monoid m => (a -> m) -> Compose f g a -> 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 # | |
(Foldable f, Foldable g) => Foldable (f :.: g) | Since: base-4.9.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => (f :.: g) m -> m # foldMap :: Monoid m => (a -> m) -> (f :.: g) a -> 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] # 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 # | |
Foldable f => Foldable (M1 i c f) | Since: base-4.9.0.0 |
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 # 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 # 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 # | |
Foldable (Clown f a :: TYPE LiftedRep -> Type) | |
Defined in Data.Bifunctor.Clown Methods fold :: Monoid m => Clown f a m -> m # foldMap :: Monoid m => (a0 -> m) -> Clown f a a0 -> m # foldMap' :: Monoid m => (a0 -> m) -> Clown f a a0 -> m # foldr :: (a0 -> b -> b) -> b -> Clown f a a0 -> b # foldr' :: (a0 -> b -> b) -> b -> Clown f a a0 -> b # foldl :: (b -> a0 -> b) -> b -> Clown f a a0 -> b # foldl' :: (b -> a0 -> b) -> b -> Clown f a a0 -> b # foldr1 :: (a0 -> a0 -> a0) -> Clown f a a0 -> a0 # foldl1 :: (a0 -> a0 -> a0) -> Clown f a a0 -> a0 # toList :: Clown f a a0 -> [a0] # null :: Clown f a a0 -> Bool # length :: Clown f a a0 -> Int # elem :: Eq a0 => a0 -> Clown f a a0 -> Bool # maximum :: Ord a0 => Clown f a a0 -> a0 # minimum :: Ord a0 => Clown f a a0 -> a0 # | |
Bifoldable p => Foldable (Flip p a) | |
Defined in Data.Bifunctor.Flip Methods fold :: Monoid m => Flip p a m -> m # foldMap :: Monoid m => (a0 -> m) -> Flip p a a0 -> m # foldMap' :: Monoid m => (a0 -> m) -> Flip p a a0 -> m # foldr :: (a0 -> b -> b) -> b -> Flip p a a0 -> b # foldr' :: (a0 -> b -> b) -> b -> Flip p a a0 -> b # foldl :: (b -> a0 -> b) -> b -> Flip p a a0 -> b # foldl' :: (b -> a0 -> b) -> b -> Flip p a a0 -> b # foldr1 :: (a0 -> a0 -> a0) -> Flip p a a0 -> a0 # foldl1 :: (a0 -> a0 -> a0) -> Flip p a a0 -> a0 # toList :: Flip p a a0 -> [a0] # length :: Flip p a a0 -> Int # elem :: Eq a0 => a0 -> Flip p a a0 -> Bool # maximum :: Ord a0 => Flip p a a0 -> a0 # minimum :: Ord a0 => Flip p a a0 -> a0 # | |
Foldable g => Foldable (Joker g a) | |
Defined in Data.Bifunctor.Joker Methods fold :: Monoid m => Joker g a m -> m # foldMap :: Monoid m => (a0 -> m) -> Joker g a a0 -> m # foldMap' :: Monoid m => (a0 -> m) -> Joker g a a0 -> m # foldr :: (a0 -> b -> b) -> b -> Joker g a a0 -> b # foldr' :: (a0 -> b -> b) -> b -> Joker g a a0 -> b # foldl :: (b -> a0 -> b) -> b -> Joker g a a0 -> b # foldl' :: (b -> a0 -> b) -> b -> Joker g a a0 -> b # foldr1 :: (a0 -> a0 -> a0) -> Joker g a a0 -> a0 # foldl1 :: (a0 -> a0 -> a0) -> Joker g a a0 -> a0 # toList :: Joker g a a0 -> [a0] # null :: Joker g a a0 -> Bool # length :: Joker g a a0 -> Int # elem :: Eq a0 => a0 -> Joker g a a0 -> Bool # maximum :: Ord a0 => Joker g a a0 -> a0 # minimum :: Ord a0 => Joker g a a0 -> a0 # | |
Bifoldable p => Foldable (WrappedBifunctor p a) | |
Defined in Data.Bifunctor.Wrapped Methods fold :: Monoid m => WrappedBifunctor p a m -> m # foldMap :: Monoid m => (a0 -> m) -> WrappedBifunctor p a a0 -> m # foldMap' :: Monoid m => (a0 -> m) -> WrappedBifunctor p a a0 -> m # foldr :: (a0 -> b -> b) -> b -> WrappedBifunctor p a a0 -> b # foldr' :: (a0 -> b -> b) -> b -> WrappedBifunctor p a a0 -> b # foldl :: (b -> a0 -> b) -> b -> WrappedBifunctor p a a0 -> b # foldl' :: (b -> a0 -> b) -> b -> WrappedBifunctor p a a0 -> b # foldr1 :: (a0 -> a0 -> a0) -> WrappedBifunctor p a a0 -> a0 # foldl1 :: (a0 -> a0 -> a0) -> WrappedBifunctor p a a0 -> a0 # toList :: WrappedBifunctor p a a0 -> [a0] # null :: WrappedBifunctor p a a0 -> Bool # length :: WrappedBifunctor p a a0 -> Int # elem :: Eq a0 => a0 -> WrappedBifunctor p a a0 -> Bool # maximum :: Ord a0 => WrappedBifunctor p a a0 -> a0 # minimum :: Ord a0 => WrappedBifunctor p a a0 -> a0 # sum :: Num a0 => WrappedBifunctor p a a0 -> a0 # product :: Num a0 => WrappedBifunctor p a a0 -> a0 # | |
(Foldable (f a), Foldable (g a)) => Foldable (Product f g a) | |
Defined in Data.Bifunctor.Product Methods fold :: Monoid m => Product f g a m -> m # foldMap :: Monoid m => (a0 -> m) -> Product f g a a0 -> m # foldMap' :: Monoid m => (a0 -> m) -> Product f g a a0 -> m # foldr :: (a0 -> b -> b) -> b -> Product f g a a0 -> b # foldr' :: (a0 -> b -> b) -> b -> Product f g a a0 -> b # foldl :: (b -> a0 -> b) -> b -> Product f g a a0 -> b # foldl' :: (b -> a0 -> b) -> b -> Product f g a a0 -> b # foldr1 :: (a0 -> a0 -> a0) -> Product f g a a0 -> a0 # foldl1 :: (a0 -> a0 -> a0) -> Product f g a a0 -> a0 # toList :: Product f g a a0 -> [a0] # null :: Product f g a a0 -> Bool # length :: Product f g a a0 -> Int # elem :: Eq a0 => a0 -> Product f g a a0 -> Bool # maximum :: Ord a0 => Product f g a a0 -> a0 # minimum :: Ord a0 => Product f g a a0 -> a0 # | |
(Foldable (f a), Foldable (g a)) => Foldable (Sum f g a) | |
Defined in Data.Bifunctor.Sum Methods fold :: Monoid m => Sum f g a m -> m # foldMap :: Monoid m => (a0 -> m) -> Sum f g a a0 -> m # foldMap' :: Monoid m => (a0 -> m) -> Sum f g a a0 -> m # foldr :: (a0 -> b -> b) -> b -> Sum f g a a0 -> b # foldr' :: (a0 -> b -> b) -> b -> Sum f g a a0 -> b # foldl :: (b -> a0 -> b) -> b -> Sum f g a a0 -> b # foldl' :: (b -> a0 -> b) -> b -> Sum f g a a0 -> b # foldr1 :: (a0 -> a0 -> a0) -> Sum f g a a0 -> a0 # foldl1 :: (a0 -> a0 -> a0) -> Sum f g a a0 -> a0 # toList :: Sum f g a a0 -> [a0] # null :: Sum f g a a0 -> Bool # length :: Sum f g a a0 -> Int # elem :: Eq a0 => a0 -> Sum f g a a0 -> Bool # maximum :: Ord a0 => Sum f g a a0 -> a0 # minimum :: Ord a0 => Sum f g a a0 -> a0 # | |
(Foldable f, Bifoldable p) => Foldable (Tannen f p a) | |
Defined in Data.Bifunctor.Tannen Methods fold :: Monoid m => Tannen f p a m -> m # foldMap :: Monoid m => (a0 -> m) -> Tannen f p a a0 -> m # foldMap' :: Monoid m => (a0 -> m) -> Tannen f p a a0 -> m # foldr :: (a0 -> b -> b) -> b -> Tannen f p a a0 -> b # foldr' :: (a0 -> b -> b) -> b -> Tannen f p a a0 -> b # foldl :: (b -> a0 -> b) -> b -> Tannen f p a a0 -> b # foldl' :: (b -> a0 -> b) -> b -> Tannen f p a a0 -> b # foldr1 :: (a0 -> a0 -> a0) -> Tannen f p a a0 -> a0 # foldl1 :: (a0 -> a0 -> a0) -> Tannen f p a a0 -> a0 # toList :: Tannen f p a a0 -> [a0] # null :: Tannen f p a a0 -> Bool # length :: Tannen f p a a0 -> Int # elem :: Eq a0 => a0 -> Tannen f p a a0 -> Bool # maximum :: Ord a0 => Tannen f p a a0 -> a0 # minimum :: Ord a0 => Tannen f p a a0 -> a0 # | |
(Bifoldable p, Foldable g) => Foldable (Biff p f g a) | |
Defined in Data.Bifunctor.Biff Methods fold :: Monoid m => Biff p f g a m -> m # foldMap :: Monoid m => (a0 -> m) -> Biff p f g a a0 -> m # foldMap' :: Monoid m => (a0 -> m) -> Biff p f g a a0 -> m # foldr :: (a0 -> b -> b) -> b -> Biff p f g a a0 -> b # foldr' :: (a0 -> b -> b) -> b -> Biff p f g a a0 -> b # foldl :: (b -> a0 -> b) -> b -> Biff p f g a a0 -> b # foldl' :: (b -> a0 -> b) -> b -> Biff p f g a a0 -> b # foldr1 :: (a0 -> a0 -> a0) -> Biff p f g a a0 -> a0 # foldl1 :: (a0 -> a0 -> a0) -> Biff p f g a a0 -> a0 # toList :: Biff p f g a a0 -> [a0] # null :: Biff p f g a a0 -> Bool # length :: Biff p f g a a0 -> Int # elem :: Eq a0 => a0 -> Biff p f g a a0 -> Bool # maximum :: Ord a0 => Biff p f g a a0 -> a0 # minimum :: Ord a0 => Biff p f g a a0 -> a0 # |
class (Functor t, Foldable t) => Traversable (t :: Type -> Type) where #
Functors representing data structures that can be transformed to
structures of the same shape by performing an Applicative
(or,
therefore, Monad
) action on each element from left to right.
A more detailed description of what same shape means, the various methods, how traversals are constructed, and example advanced use-cases can be found in the Overview section of Data.Traversable.
For the class laws see the Laws section of Data.Traversable.
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_
.
Examples
Basic usage:
In the first two examples we show each evaluated action mapping to the output structure.
>>>
traverse Just [1,2,3,4]
Just [1,2,3,4]
>>>
traverse id [Right 1, Right 2, Right 3, Right 4]
Right [1,2,3,4]
In the next examples, we show that Nothing
and Left
values short
circuit the created structure.
>>>
traverse (const Nothing) [1,2,3,4]
Nothing
>>>
traverse (\x -> if odd x then Just x else Nothing) [1,2,3,4]
Nothing
>>>
traverse id [Right 1, Right 2, Right 3, Right 4, Left 0]
Left 0
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_
.
Examples
Basic usage:
For the first two examples we show sequenceA fully evaluating a a structure and collecting the results.
>>>
sequenceA [Just 1, Just 2, Just 3]
Just [1,2,3]
>>>
sequenceA [Right 1, Right 2, Right 3]
Right [1,2,3]
The next two example show Nothing
and Just
will short circuit
the resulting structure if present in the input. For more context,
check the Traversable
instances for Either
and Maybe
.
>>>
sequenceA [Just 1, Just 2, Just 3, Nothing]
Nothing
>>>
sequenceA [Right 1, Right 2, Right 3, Left 4]
Left 4
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_
.
Examples
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_
.
Examples
Basic usage:
The first two examples are instances where the input and
and output of sequence
are isomorphic.
>>>
sequence $ Right [1,2,3,4]
[Right 1,Right 2,Right 3,Right 4]
>>>
sequence $ [Right 1,Right 2,Right 3,Right 4]
Right [1,2,3,4]
The following examples demonstrate short circuit behavior
for sequence
.
>>>
sequence $ Left [1,2,3,4]
Left [1,2,3,4]
>>>
sequence $ [Left 0, Right 1,Right 2,Right 3,Right 4]
Left 0
Instances
Representable types of kind *
.
This class is derivable in GHC with the DeriveGeneric
flag on.
A Generic
instance must satisfy the following laws:
from
.to
≡id
to
.from
≡id
Instances
This class gives the integer associated with a type-level natural. There are instances of the class for every concrete literal: 0, 1, 2, etc.
Since: base-4.7.0.0
Minimal complete definition
natSing
class KnownSymbol (n :: Symbol) #
This class gives the string associated with a type-level symbol. There are instances of the class for every concrete literal: "hello", etc.
Since: base-4.7.0.0
Minimal complete definition
symbolSing
The class of semigroups (types with an associative binary operation).
Instances should satisfy the following:
Since: base-4.9.0.0
Instances
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:
- Right identity
x
<>
mempty
= x- Left identity
mempty
<>
x = x- Associativity
x
(<>
(y<>
z) = (x<>
y)<>
zSemigroup
law)- Concatenation
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 newtype
s 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
Methods
Identity of mappend
>>>
"Hello world" <> mempty
"Hello world"
An associative operation
NOTE: This method is redundant and has the default
implementation
since base-4.11.0.0.
Should it be implemented manually, since mappend
= (<>
)mappend
is a synonym for
(<>
), it is expected that the two functions are defined the same
way. In a future GHC release mappend
will be removed from Monoid
.
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.
>>>
mconcat ["Hello", " ", "Haskell", "!"]
"Hello Haskell!"
Instances
Monoid Series | |
Monoid Key | |
Monoid RawPath Source # | |
Monoid QueryString Source # | |
Defined in Amazonka.Data.Query Methods mempty :: QueryString # mappend :: QueryString -> QueryString -> QueryString # mconcat :: [QueryString] -> QueryString # | |
Monoid XML Source # | |
Monoid More | |
Monoid All | Since: base-2.1 |
Monoid Any | Since: base-2.1 |
Monoid String | |
Monoid Builder | |
Monoid ByteString | |
Defined in Data.ByteString.Internal Methods mempty :: ByteString # mappend :: ByteString -> ByteString -> ByteString # mconcat :: [ByteString] -> ByteString # | |
Monoid ByteString | |
Defined in Data.ByteString.Lazy.Internal Methods mempty :: ByteString # mappend :: ByteString -> ByteString -> ByteString # mconcat :: [ByteString] -> ByteString # | |
Monoid ShortByteString | |
Defined in Data.ByteString.Short.Internal Methods mappend :: ShortByteString -> ShortByteString -> ShortByteString # mconcat :: [ShortByteString] -> ShortByteString # | |
Monoid IntSet | |
Monoid ByteArray | |
Monoid Ordering | Since: base-2.1 |
Monoid CookieJar | Since 1.9 |
Monoid RequestBody | |
Defined in Network.HTTP.Client.Types Methods mempty :: RequestBody # mappend :: RequestBody -> RequestBody -> RequestBody # mconcat :: [RequestBody] -> RequestBody # | |
Monoid Doc | |
Monoid Builder | |
Monoid ShortText | |
Monoid CalendarDiffDays | Additive |
Defined in Data.Time.Calendar.CalendarDiffDays Methods mappend :: CalendarDiffDays -> CalendarDiffDays -> CalendarDiffDays # mconcat :: [CalendarDiffDays] -> CalendarDiffDays # | |
Monoid CalendarDiffTime | Additive |
Defined in Data.Time.LocalTime.Internal.CalendarDiffTime Methods mappend :: CalendarDiffTime -> CalendarDiffTime -> CalendarDiffTime # mconcat :: [CalendarDiffTime] -> CalendarDiffTime # | |
Monoid Attributes | |
Defined in Text.XML.Stream.Render Methods mempty :: Attributes # mappend :: Attributes -> Attributes -> Attributes # mconcat :: [Attributes] -> Attributes # | |
Monoid () | Since: base-2.1 |
Monoid (KeyMap v) | |
Monoid (IResult a) | |
Monoid (Parser a) | |
Monoid (Result a) | |
Monoid a => Monoid (Sensitive a) Source # | |
Monoid (Comparison a) |
mempty :: Comparison a mempty = Comparison _ _ -> EQ |
Defined in Data.Functor.Contravariant Methods mempty :: Comparison a # mappend :: Comparison a -> Comparison a -> Comparison a # mconcat :: [Comparison a] -> Comparison a # | |
Monoid (Equivalence a) |
mempty :: Equivalence a mempty = Equivalence _ _ -> True |
Defined in Data.Functor.Contravariant Methods mempty :: Equivalence a # mappend :: Equivalence a -> Equivalence a -> Equivalence a # mconcat :: [Equivalence a] -> Equivalence a # | |
Monoid (Predicate a) |
mempty :: Predicate a mempty = _ -> True |
Monoid a => Monoid (Identity a) | Since: base-4.9.0.0 |
Monoid (First a) | Since: base-2.1 |
Monoid (Last a) | Since: base-2.1 |
Monoid a => Monoid (Down a) | Since: base-4.11.0.0 |
(Ord a, Bounded a) => Monoid (Max a) | Since: base-4.9.0.0 |
(Ord a, Bounded a) => Monoid (Min a) | Since: base-4.9.0.0 |
Monoid m => Monoid (WrappedMonoid m) | Since: base-4.9.0.0 |
Defined in Data.Semigroup Methods mempty :: WrappedMonoid m # mappend :: WrappedMonoid m -> WrappedMonoid m -> WrappedMonoid m # mconcat :: [WrappedMonoid m] -> WrappedMonoid m # | |
Monoid a => Monoid (Dual a) | Since: base-2.1 |
Monoid (Endo a) | Since: base-2.1 |
Num a => Monoid (Product a) | Since: base-2.1 |
Num a => Monoid (Sum a) | Since: base-2.1 |
Monoid p => Monoid (Par1 p) | Since: base-4.12.0.0 |
PrimType ty => Monoid (Block ty) | |
Monoid (CountOf ty) | |
PrimType ty => Monoid (UArray ty) | |
Monoid s => Monoid (CI s) | |
Monoid (IntMap a) | |
Monoid (Seq a) | |
Monoid (MergeSet a) | |
Ord a => Monoid (Set a) | |
Monoid (DList a) | |
(Generic a, Monoid (Rep a ())) => Monoid (Generically a) | |
Defined in GHC.Generics.Generically Methods mempty :: Generically a # mappend :: Generically a -> Generically a -> Generically a # mconcat :: [Generically a] -> Generically a # | |
Monoid a => Monoid (IO a) | Since: base-4.9.0.0 |
Monoid (Doc a) | |
Monoid (Array a) | |
Monoid (PrimArray a) | Since: primitive-0.6.4.0 |
Monoid (SmallArray a) | |
Defined in Data.Primitive.SmallArray Methods mempty :: SmallArray a # mappend :: SmallArray a -> SmallArray a -> SmallArray a # mconcat :: [SmallArray a] -> SmallArray a # | |
Semigroup a => Monoid (Maybe a) | |
Monoid a => Monoid (Q a) | Since: template-haskell-2.17.0.0 |
(Hashable a, Eq a) => Monoid (HashSet a) | \(O(n+m)\) To obtain good performance, the smaller set must be presented as the first argument. Examples
|
Monoid (Vector a) | |
Prim a => Monoid (Vector a) | |
Storable a => Monoid (Vector a) | |
Semigroup a => Monoid (Maybe a) | Lift a semigroup into Since 4.11.0: constraint on inner Since: base-2.1 |
Monoid a => Monoid (a) | Since: base-4.15 |
Monoid [a] | Since: base-2.1 |
Monoid (Parser i a) | |
Monoid a => Monoid (Op a b) |
mempty :: Op a b mempty = Op _ -> mempty |
Monoid (Proxy s) | Since: base-4.7.0.0 |
Monoid (U1 p) | Since: base-4.12.0.0 |
Ord k => Monoid (Map k v) | |
Monoid (f a) => Monoid (Indexing f a) |
|
Monoid (ReifiedFold s a) | |
Defined in Control.Lens.Reified Methods mempty :: ReifiedFold s a # mappend :: ReifiedFold s a -> ReifiedFold s a -> ReifiedFold s a # mconcat :: [ReifiedFold s a] -> ReifiedFold s a # | |
(Monoid a, Monoid b) => Monoid (Pair a b) | |
(Eq k, Hashable k) => Monoid (HashMap k v) | If a key occurs in both maps, the mapping from the first will be the mapping in the result. Examples
|
Monoid b => Monoid (a -> b) | Since: base-2.1 |
(Monoid a, Monoid b) => Monoid (a, b) | Since: base-2.1 |
Monoid a => Monoid (Const a b) | Since: base-4.9.0.0 |
(Applicative f, Monoid a) => Monoid (Ap f a) | Since: base-4.12.0.0 |
Alternative f => Monoid (Alt f a) | Since: base-4.8.0.0 |
Monoid (f p) => Monoid (Rec1 f p) | Since: base-4.12.0.0 |
Monoid (ReifiedIndexedFold i s a) | |
Defined in Control.Lens.Reified Methods mempty :: ReifiedIndexedFold i s a # mappend :: ReifiedIndexedFold i s a -> ReifiedIndexedFold i s a -> ReifiedIndexedFold i s a # mconcat :: [ReifiedIndexedFold i s a] -> ReifiedIndexedFold i s a # | |
Reifies s (ReifiedMonoid a) => Monoid (ReflectedMonoid a s) | |
Defined in Data.Reflection Methods mempty :: ReflectedMonoid a s # mappend :: ReflectedMonoid a s -> ReflectedMonoid a s -> ReflectedMonoid a s # mconcat :: [ReflectedMonoid a s] -> ReflectedMonoid a s # | |
(Semigroup a, Monoid a) => Monoid (Tagged s a) | |
(Monoid a, Monoid b, Monoid c) => Monoid (a, b, c) | Since: base-2.1 |
(Monoid (f a), Monoid (g a)) => Monoid (Product f g a) | Since: base-4.16.0.0 |
(Monoid (f p), Monoid (g p)) => Monoid ((f :*: g) p) | Since: base-4.12.0.0 |
Monoid c => Monoid (K1 i c p) | Since: base-4.12.0.0 |
Monad m => Monoid (ConduitT i o m ()) | |
(Monoid a, Monoid b, Monoid c, Monoid d) => Monoid (a, b, c, d) | Since: base-2.1 |
Monoid (f (g a)) => Monoid (Compose f g a) | Since: base-4.16.0.0 |
Monoid (f (g p)) => Monoid ((f :.: g) p) | Since: base-4.12.0.0 |
Monoid (f p) => Monoid (M1 i c f p) | Since: base-4.12.0.0 |
(Monoid a, Monoid b, Monoid c, Monoid d, Monoid e) => Monoid (a, b, c, d, e) | Since: base-2.1 |
Monad m => Monoid (Pipe l i o u m ()) | |
Instances
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
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
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
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
8-bit signed integer type
Instances
16-bit signed integer type
Instances
32-bit signed integer type
Instances
64-bit signed integer type
Instances
Arbitrary precision integers. In contrast with fixed-size integral types
such as Int
, the Integer
type represents the entire infinite range of
integers.
Integers are stored in a kind of sign-magnitude form, hence do not expect two's complement form when using bit operations.
If the value is small (fit into an Int
), IS
constructor is used.
Otherwise Integer
and IN
constructors are used to store a BigNat
representing respectively the positive or the negative value magnitude.
Invariant: Integer
and IN
are used iff value doesn't fit in IS
Instances
Natural number
Invariant: numbers <= 0xffffffffffffffff use the NS
constructor
Instances
The Maybe
type encapsulates an optional value. A value of type
either contains a value of type Maybe
aa
(represented as
),
or it is empty (represented as Just
aNothing
). 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.
Instances
FromJSON1 Maybe | |
ToJSON1 Maybe | |
Defined in Data.Aeson.Types.ToJSON Methods liftToJSON :: (a -> Value) -> ([a] -> Value) -> Maybe a -> Value # liftToJSONList :: (a -> Value) -> ([a] -> Value) -> [Maybe a] -> Value # liftToEncoding :: (a -> Encoding) -> ([a] -> Encoding) -> Maybe a -> Encoding # liftToEncodingList :: (a -> Encoding) -> ([a] -> Encoding) -> [Maybe a] -> Encoding # | |
MonadFail Maybe | Since: base-4.9.0.0 |
Defined in Control.Monad.Fail | |
Foldable Maybe | Since: base-2.1 |
Defined in Data.Foldable Methods fold :: Monoid m => Maybe m -> m # foldMap :: Monoid m => (a -> m) -> Maybe a -> 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 # elem :: Eq a => a -> Maybe a -> Bool # maximum :: Ord a => Maybe a -> a # minimum :: Ord a => Maybe a -> a # | |
Eq1 Maybe | Since: base-4.9.0.0 |
Ord1 Maybe | Since: base-4.9.0.0 |
Defined in Data.Functor.Classes | |
Read1 Maybe | Since: base-4.9.0.0 |
Defined in Data.Functor.Classes | |
Show1 Maybe | Since: base-4.9.0.0 |
Traversable Maybe | Since: base-2.1 |
Alternative Maybe | Since: base-2.1 |
Applicative Maybe | Since: base-2.1 |
Functor Maybe | Since: base-2.1 |
Monad Maybe | Since: base-2.1 |
MonadPlus Maybe | Since: base-2.1 |
MonadFailure Maybe | |
NFData1 Maybe | Since: deepseq-1.4.3.0 |
Defined in Control.DeepSeq | |
MonadThrow Maybe | |
Defined in Control.Monad.Catch | |
Hashable1 Maybe | |
Defined in Data.Hashable.Class | |
Generic1 Maybe | |
(Selector s, GToJSON' enc arity (K1 i (Maybe a) :: TYPE LiftedRep -> Type), KeyValuePair enc pairs, Monoid pairs) => RecordToPairs enc pairs arity (S1 s (K1 i (Maybe a) :: TYPE LiftedRep -> Type)) | |
Defined in Data.Aeson.Types.ToJSON | |
Lift a => Lift (Maybe a :: Type) | |
(Selector s, FromJSON a) => RecordFromJSON' arity (S1 s (K1 i (Maybe a) :: Type -> Type)) | |
Defined in Data.Aeson.Types.FromJSON | |
FromJSON a => FromJSON (Maybe a) | |
ToJSON a => ToJSON (Maybe a) | |
Defined in Data.Aeson.Types.ToJSON | |
ToHashedBody a => ToBody (Maybe a) Source # | |
Defined in Amazonka.Data.Body Methods toBody :: Maybe a -> RequestBody Source # | |
ToText a => ToHeader (Maybe a) Source # | |
Defined in Amazonka.Data.Headers | |
ToLog a => ToLog (Maybe a) Source # | |
Defined in Amazonka.Data.Log Methods build :: Maybe a -> ByteStringBuilder Source # | |
ToQuery a => ToQuery (Maybe a) Source # | |
Defined in Amazonka.Data.Query Methods toQuery :: Maybe a -> QueryString Source # | |
FromXML a => FromXML (Maybe a) Source # | |
ToXML a => ToXML (Maybe a) Source # | |
AWSTruncated (Maybe Bool) Source # | |
AWSTruncated (Maybe a) Source # | |
Semigroup a => Monoid (Maybe a) | Lift a semigroup into Since 4.11.0: constraint on inner Since: base-2.1 |
Semigroup a => Semigroup (Maybe a) | Since: base-4.9.0.0 |
Generic (Maybe a) | |
SingKind a => SingKind (Maybe a) | Since: base-4.9.0.0 |
Defined in GHC.Generics Associated Types type DemoteRep (Maybe a) | |
Read a => Read (Maybe a) | Since: base-2.1 |
Show a => Show (Maybe a) | Since: base-2.1 |
Default (Maybe a) | |
Defined in Data.Default.Class | |
NFData a => NFData (Maybe a) | |
Defined in Control.DeepSeq | |
Eq a => Eq (Maybe a) | Since: base-2.1 |
Ord a => Ord (Maybe a) | Since: base-2.1 |
Hashable a => Hashable (Maybe a) | |
Defined in Data.Hashable.Class | |
At (Maybe a) | |
Ixed (Maybe a) | |
Defined in Control.Lens.At | |
MonoFoldable (Maybe a) | |
Defined in Data.MonoTraversable Methods ofoldMap :: Monoid m => (Element (Maybe a) -> m) -> Maybe a -> m # ofoldr :: (Element (Maybe a) -> b -> b) -> b -> Maybe a -> b # ofoldl' :: (a0 -> Element (Maybe a) -> a0) -> a0 -> Maybe a -> a0 # otoList :: Maybe a -> [Element (Maybe a)] # oall :: (Element (Maybe a) -> Bool) -> Maybe a -> Bool # oany :: (Element (Maybe a) -> Bool) -> Maybe a -> Bool # olength64 :: Maybe a -> Int64 # ocompareLength :: Integral i => Maybe a -> i -> Ordering # otraverse_ :: Applicative f => (Element (Maybe a) -> f b) -> Maybe a -> f () # ofor_ :: Applicative f => Maybe a -> (Element (Maybe a) -> f b) -> f () # omapM_ :: Applicative m => (Element (Maybe a) -> m ()) -> Maybe a -> m () # oforM_ :: Applicative m => Maybe a -> (Element (Maybe a) -> m ()) -> m () # ofoldlM :: Monad m => (a0 -> Element (Maybe a) -> m a0) -> a0 -> Maybe a -> m a0 # ofoldMap1Ex :: Semigroup m => (Element (Maybe a) -> m) -> Maybe a -> m # ofoldr1Ex :: (Element (Maybe a) -> Element (Maybe a) -> Element (Maybe a)) -> Maybe a -> Element (Maybe a) # ofoldl1Ex' :: (Element (Maybe a) -> Element (Maybe a) -> Element (Maybe a)) -> Maybe a -> Element (Maybe a) # headEx :: Maybe a -> Element (Maybe a) # lastEx :: Maybe a -> Element (Maybe a) # unsafeHead :: Maybe a -> Element (Maybe a) # unsafeLast :: Maybe a -> Element (Maybe a) # maximumByEx :: (Element (Maybe a) -> Element (Maybe a) -> Ordering) -> Maybe a -> Element (Maybe a) # minimumByEx :: (Element (Maybe a) -> Element (Maybe a) -> Ordering) -> Maybe a -> Element (Maybe a) # | |
MonoFunctor (Maybe a) | |
MonoPointed (Maybe a) | |
MonoTraversable (Maybe a) | |
SingI ('Nothing :: Maybe a) | Since: base-4.9.0.0 |
Defined in GHC.Generics | |
SingI a2 => SingI ('Just a2 :: Maybe a1) | Since: base-4.9.0.0 |
Defined in GHC.Generics | |
type Failure Maybe | |
Defined in Basement.Monad | |
type Rep1 Maybe | Since: base-4.6.0.0 |
type DemoteRep (Maybe a) | |
Defined in GHC.Generics | |
type Rep (Maybe a) | Since: base-4.6.0.0 |
Defined in GHC.Generics | |
data Sing (b :: Maybe a) | |
type Index (Maybe a) | |
Defined in Control.Lens.At | |
type IxValue (Maybe a) | |
Defined in Control.Lens.At | |
type Element (Maybe a) | |
Defined in Data.MonoTraversable |
Instances
FromJSON Ordering | |
ToJSON Ordering | |
Defined in Data.Aeson.Types.ToJSON | |
Monoid Ordering | Since: base-2.1 |
Semigroup Ordering | Since: base-4.9.0.0 |
Bounded Ordering | Since: base-2.1 |
Enum Ordering | Since: base-2.1 |
Generic Ordering | |
Ix Ordering | Since: base-2.1 |
Defined in GHC.Ix 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 # | |
Read Ordering | Since: base-2.1 |
Show Ordering | Since: base-2.1 |
Default Ordering | |
Defined in Data.Default.Class | |
NFData Ordering | |
Defined in Control.DeepSeq | |
Eq Ordering | |
Ord Ordering | |
Defined in GHC.Classes | |
Hashable Ordering | |
Defined in Data.Hashable.Class | |
type Rep Ordering | Since: base-4.6.0.0 |
A value of type
is a computation which, when performed,
does some I/O before returning a value of type IO
aa
.
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
Instances
8-bit unsigned integer type
Instances
16-bit unsigned integer type
Instances
32-bit unsigned integer type
Instances
64-bit unsigned integer type
Instances
The Either
type represents values with two possibilities: a value of
type
is either Either
a b
or Left
a
.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
The type
is the type of values which can be either
a Either
String
Int
String
or an Int
. The Left
constructor can be used only on
String
s, and the Right
constructor can be used only on Int
s:
>>>
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 Int
s.
>>>
:{
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"
Instances
FromJSON2 Either | |
Defined in Data.Aeson.Types.FromJSON | |
ToJSON2 Either | |
Defined in Data.Aeson.Types.ToJSON Methods liftToJSON2 :: (a -> Value) -> ([a] -> Value) -> (b -> Value) -> ([b] -> Value) -> Either a b -> Value # liftToJSONList2 :: (a -> Value) -> ([a] -> Value) -> (b -> Value) -> ([b] -> Value) -> [Either a b] -> Value # liftToEncoding2 :: (a -> Encoding) -> ([a] -> Encoding) -> (b -> Encoding) -> ([b] -> Encoding) -> Either a b -> Encoding # liftToEncodingList2 :: (a -> Encoding) -> ([a] -> Encoding) -> (b -> Encoding) -> ([b] -> Encoding) -> [Either a b] -> Encoding # | |
Bifoldable Either | Since: base-4.10.0.0 |
Bifunctor Either | Since: base-4.8.0.0 |
Bitraversable Either | Since: base-4.10.0.0 |
Defined in Data.Bitraversable Methods bitraverse :: Applicative f => (a -> f c) -> (b -> f d) -> Either a b -> f (Either c d) # | |
Eq2 Either | Since: base-4.9.0.0 |
Ord2 Either | Since: base-4.9.0.0 |
Defined in Data.Functor.Classes | |
Read2 Either | Since: base-4.9.0.0 |
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 |
NFData2 Either | Since: deepseq-1.4.3.0 |
Defined in Control.DeepSeq | |
Hashable2 Either | |
Defined in Data.Hashable.Class | |
Generic1 (Either a :: Type -> Type) | |
(Lift a, Lift b) => Lift (Either a b :: Type) | |
FromJSON a => FromJSON1 (Either a) | |
ToJSON a => ToJSON1 (Either a) | |
Defined in Data.Aeson.Types.ToJSON Methods liftToJSON :: (a0 -> Value) -> ([a0] -> Value) -> Either a a0 -> Value # liftToJSONList :: (a0 -> Value) -> ([a0] -> Value) -> [Either a a0] -> Value # liftToEncoding :: (a0 -> Encoding) -> ([a0] -> Encoding) -> Either a a0 -> Encoding # liftToEncodingList :: (a0 -> Encoding) -> ([a0] -> Encoding) -> [Either a a0] -> Encoding # | |
Foldable (Either a) | Since: base-4.7.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => Either a m -> m # foldMap :: Monoid m => (a0 -> m) -> Either a a0 -> 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] # 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 # | |
Eq a => Eq1 (Either a) | Since: base-4.9.0.0 |
Ord a => Ord1 (Either a) | Since: base-4.9.0.0 |
Defined in Data.Functor.Classes | |
Read a => Read1 (Either a) | Since: base-4.9.0.0 |
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 |
Traversable (Either a) | Since: base-4.7.0.0 |
Defined in Data.Traversable | |
Applicative (Either e) | Since: base-3.0 |
Functor (Either a) | Since: base-3.0 |
Monad (Either e) | Since: base-4.4.0.0 |
MonadFailure (Either a) | |
NFData a => NFData1 (Either a) | Since: deepseq-1.4.3.0 |
Defined in Control.DeepSeq | |
e ~ SomeException => MonadCatch (Either e) | Since: exceptions-0.8.3 |
e ~ SomeException => MonadMask (Either e) | Since: exceptions-0.8.3 |
Defined in Control.Monad.Catch | |
e ~ SomeException => MonadThrow (Either e) | |
Defined in Control.Monad.Catch | |
Hashable a => Hashable1 (Either a) | |
Defined in Data.Hashable.Class | |
(FromJSON a, FromJSON b) => FromJSON (Either a b) | |
(ToJSON a, ToJSON b) => ToJSON (Either a b) | |
Defined in Data.Aeson.Types.ToJSON | |
Semigroup (Either a b) | Since: base-4.9.0.0 |
Generic (Either a b) | |
(Read a, Read b) => Read (Either a b) | Since: base-3.0 |
(Show a, Show b) => Show (Either a b) | Since: base-3.0 |
(NFData a, NFData b) => NFData (Either a b) | |
Defined in Control.DeepSeq | |
(Eq a, Eq b) => Eq (Either a b) | Since: base-2.1 |
(Ord a, Ord b) => Ord (Either a b) | Since: base-2.1 |
(Hashable a, Hashable b) => Hashable (Either a b) | |
Defined in Data.Hashable.Class | |
MonoFoldable (Either a b) | |
Defined in Data.MonoTraversable Methods ofoldMap :: Monoid m => (Element (Either a b) -> m) -> Either a b -> m # ofoldr :: (Element (Either a b) -> b0 -> b0) -> b0 -> Either a b -> b0 # ofoldl' :: (a0 -> Element (Either a b) -> a0) -> a0 -> Either a b -> a0 # otoList :: Either a b -> [Element (Either a b)] # oall :: (Element (Either a b) -> Bool) -> Either a b -> Bool # oany :: (Element (Either a b) -> Bool) -> Either a b -> Bool # olength :: Either a b -> Int # olength64 :: Either a b -> Int64 # ocompareLength :: Integral i => Either a b -> i -> Ordering # otraverse_ :: Applicative f => (Element (Either a b) -> f b0) -> Either a b -> f () # ofor_ :: Applicative f => Either a b -> (Element (Either a b) -> f b0) -> f () # omapM_ :: Applicative m => (Element (Either a b) -> m ()) -> Either a b -> m () # oforM_ :: Applicative m => Either a b -> (Element (Either a b) -> m ()) -> m () # ofoldlM :: Monad m => (a0 -> Element (Either a b) -> m a0) -> a0 -> Either a b -> m a0 # ofoldMap1Ex :: Semigroup m => (Element (Either a b) -> m) -> Either a b -> m # ofoldr1Ex :: (Element (Either a b) -> Element (Either a b) -> Element (Either a b)) -> Either a b -> Element (Either a b) # ofoldl1Ex' :: (Element (Either a b) -> Element (Either a b) -> Element (Either a b)) -> Either a b -> Element (Either a b) # headEx :: Either a b -> Element (Either a b) # lastEx :: Either a b -> Element (Either a b) # unsafeHead :: Either a b -> Element (Either a b) # unsafeLast :: Either a b -> Element (Either a b) # maximumByEx :: (Element (Either a b) -> Element (Either a b) -> Ordering) -> Either a b -> Element (Either a b) # minimumByEx :: (Element (Either a b) -> Element (Either a b) -> Ordering) -> Either a b -> Element (Either a b) # | |
MonoFunctor (Either a b) | |
MonoPointed (Either a b) | |
MonoTraversable (Either a b) | |
type Rep1 (Either a :: Type -> Type) | Since: base-4.6.0.0 |
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 Failure (Either a) | |
Defined in Basement.Monad | |
type Rep (Either a b) | Since: base-4.6.0.0 |
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))) | |
type Element (Either a b) | |
Defined in Data.MonoTraversable |
Non-empty (and non-strict) list type.
Since: base-4.9.0.0
Constructors
a :| [a] infixr 5 |
Instances
class a ~R# b => Coercible (a :: k) (b :: k) #
Coercible
is a two-parameter class that has instances for types a
and b
if
the compiler can infer that they have the same representation. This class
does not have regular instances; instead they are created on-the-fly during
type-checking. Trying to manually declare an instance of Coercible
is an error.
Nevertheless one can pretend that the following three kinds of instances exist. First, as a trivial base-case:
instance Coercible a a
Furthermore, for every type constructor there is
an instance that allows to coerce under the type constructor. For
example, let D
be a prototypical type constructor (data
or
newtype
) with three type arguments, which have roles nominal
,
representational
resp. phantom
. Then there is an instance of
the form
instance Coercible b b' => Coercible (D a b c) (D a b' c')
Note that the nominal
type arguments are equal, the
representational
type arguments can differ, but need to have a
Coercible
instance themself, and the phantom
type arguments can be
changed arbitrarily.
The third kind of instance exists for every newtype NT = MkNT T
and
comes in two variants, namely
instance Coercible a T => Coercible a NT
instance Coercible T b => Coercible NT b
This instance is only usable if the constructor MkNT
is in scope.
If, as a library author of a type constructor like Set a
, you
want to prevent a user of your module to write
coerce :: Set T -> Set NT
,
you need to set the role of Set
's type parameter to nominal
,
by writing
type role Set nominal
For more details about this feature, please refer to Safe Coercions by Joachim Breitner, Richard A. Eisenberg, Simon Peyton Jones and Stephanie Weirich.
Since: ghc-prim-4.7.0.0
(Kind) This is the kind of type-level symbols. Declared here because class IP needs it
Instances
SingKind Symbol | Since: base-4.9.0.0 |
Defined in GHC.Generics Associated Types type DemoteRep Symbol | |
KnownSymbol a => SingI (a :: Symbol) | Since: base-4.9.0.0 |
Defined in GHC.Generics Methods sing :: Sing a | |
KnownSymbol n => Reifies (n :: Symbol) String | |
Defined in Data.Reflection | |
IsRecord (M1 S ('MetaSel ('Nothing :: Maybe Symbol) u ss ds) f) False | |
Defined in Data.Aeson.Types.Generic | |
type DemoteRep Symbol | |
Defined in GHC.Generics | |
data Sing (s :: Symbol) | |
Defined in GHC.Generics | |
type Compare (a :: Symbol) (b :: Symbol) | |
Defined in Data.Type.Ord |
either :: (a -> c) -> (b -> c) -> Either a b -> c #
Case analysis for the Either
type.
If the value is
, apply the first function to Left
aa
;
if it is
, apply the second function to Right
bb
.
Examples
We create two values of type
, one using the
Either
String
Int
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
data Scientific #
An arbitrary-precision number represented using scientific notation.
This type describes the set of all
which have a finite
decimal expansion.Real
s
A scientific number with coefficient
c
and base10Exponent
e
corresponds to the Fractional
number: fromInteger
c * 10 ^^
e
Instances
FromJSON Scientific | |
Defined in Data.Aeson.Types.FromJSON | |
ToJSON Scientific | |
Defined in Data.Aeson.Types.ToJSON Methods toJSON :: Scientific -> Value # toEncoding :: Scientific -> Encoding # toJSONList :: [Scientific] -> Value # toEncodingList :: [Scientific] -> Encoding # | |
ToJSONKey Scientific | |
Defined in Data.Aeson.Types.ToJSON | |
FromText Scientific Source # | |
Defined in Amazonka.Data.Text | |
ToText Scientific Source # | |
Defined in Amazonka.Data.Text Methods toText :: Scientific -> Text Source # | |
Data Scientific | |
Defined in Data.Scientific Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Scientific -> c Scientific # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Scientific # toConstr :: Scientific -> Constr # dataTypeOf :: Scientific -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c Scientific) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Scientific) # gmapT :: (forall b. Data b => b -> b) -> Scientific -> Scientific # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Scientific -> r # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Scientific -> r # gmapQ :: (forall d. Data d => d -> u) -> Scientific -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> Scientific -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Scientific -> m Scientific # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Scientific -> m Scientific # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Scientific -> m Scientific # | |
Num Scientific | WARNING: |
Defined in Data.Scientific Methods (+) :: Scientific -> Scientific -> Scientific # (-) :: Scientific -> Scientific -> Scientific # (*) :: Scientific -> Scientific -> Scientific # negate :: Scientific -> Scientific # abs :: Scientific -> Scientific # signum :: Scientific -> Scientific # fromInteger :: Integer -> Scientific # | |
Read Scientific | Supports the skipping of parentheses and whitespaces. Example: > read " ( (( -1.0e+3 ) ))" :: Scientific -1000.0 (Note: This |
Defined in Data.Scientific Methods readsPrec :: Int -> ReadS Scientific # readList :: ReadS [Scientific] # readPrec :: ReadPrec Scientific # readListPrec :: ReadPrec [Scientific] # | |
Fractional Scientific | WARNING: These methods also compute
|
Defined in Data.Scientific Methods (/) :: Scientific -> Scientific -> Scientific # recip :: Scientific -> Scientific # fromRational :: Rational -> Scientific # | |
Real Scientific | WARNING: Avoid applying |
Defined in Data.Scientific Methods toRational :: Scientific -> Rational # | |
RealFrac Scientific | WARNING: the methods of the |
Defined in Data.Scientific Methods properFraction :: Integral b => Scientific -> (b, Scientific) # truncate :: Integral b => Scientific -> b # round :: Integral b => Scientific -> b # ceiling :: Integral b => Scientific -> b # floor :: Integral b => Scientific -> b # | |
Show Scientific | See |
Defined in Data.Scientific Methods showsPrec :: Int -> Scientific -> ShowS # show :: Scientific -> String # showList :: [Scientific] -> ShowS # | |
Binary Scientific | Note that in the future I intend to change the type of the |
Defined in Data.Scientific | |
NFData Scientific | |
Defined in Data.Scientific Methods rnf :: Scientific -> () # | |
Eq Scientific | Scientific numbers can be safely compared for equality. No magnitude |
Defined in Data.Scientific | |
Ord Scientific | Scientific numbers can be safely compared for ordering. No magnitude |
Defined in Data.Scientific Methods compare :: Scientific -> Scientific -> Ordering # (<) :: Scientific -> Scientific -> Bool # (<=) :: Scientific -> Scientific -> Bool # (>) :: Scientific -> Scientific -> Bool # (>=) :: Scientific -> Scientific -> Bool # max :: Scientific -> Scientific -> Scientific # min :: Scientific -> Scientific -> Scientific # | |
Hashable Scientific | A hash can be safely calculated from a
|
Defined in Data.Scientific | |
Lift Scientific | Since: scientific-0.3.7.0 |
Defined in Data.Scientific Methods lift :: Quote m => Scientific -> m Exp # liftTyped :: forall (m :: Type -> Type). Quote m => Scientific -> Code m Scientific # |
class Eq a => Hashable a where #
The class of types that can be converted to a hash value.
Minimal implementation: hashWithSalt
.
Note: the hash is not guaranteed to be stable across library versions, operating systems or architectures. For stable hashing use named hashes: SHA256, CRC32 etc.
If you are looking for Hashable
instance in time
package,
check time-compat
Minimal complete definition
Nothing
Methods
hashWithSalt :: Int -> a -> Int infixl 0 #
Return a hash value for the argument, using the given salt.
The general contract of hashWithSalt
is:
- If two values are equal according to the
==
method, then applying thehashWithSalt
method on each of the two values must produce the same integer result if the same salt is used in each case. - It is not required that if two values are unequal
according to the
==
method, then applying thehashWithSalt
method on each of the two values must produce distinct integer results. However, the programmer should be aware that producing distinct integer results for unequal values may improve the performance of hashing-based data structures. - This method can be used to compute different hash values for
the same input by providing a different salt in each
application of the method. This implies that any instance
that defines
hashWithSalt
must make use of the salt in its implementation. hashWithSalt
may return negativeInt
values.
Like hashWithSalt
, but no salt is used. The default
implementation uses hashWithSalt
with some default salt.
Instances might want to implement this method to provide a more
efficient implementation than the default implementation.
Instances
(<$>) :: 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, <$>
is function
application lifted over a Functor
.
Examples
Convert from a
to a Maybe
Int
using Maybe
String
show
:
>>>
show <$> Nothing
Nothing>>>
show <$> Just 3
Just "3"
Convert from an
to an
Either
Int
Int
Either
Int
String
using show
:
>>>
show <$> 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)
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]
This is the simplest representation of UTC. It consists of the day number, and a time offset from midnight. Note that if a day has a leap second added to it, it will have 86401 seconds.
Instances
FromJSON UTCTime | |
FromJSONKey UTCTime | |
Defined in Data.Aeson.Types.FromJSON Methods | |
ToJSON UTCTime | |
Defined in Data.Aeson.Types.ToJSON | |
ToJSONKey UTCTime | |
Defined in Data.Aeson.Types.ToJSON | |
ToByteString UTCTime Source # | |
Defined in Amazonka.Data.ByteString Methods toBS :: UTCTime -> ByteString Source # | |
ToLog UTCTime Source # | |
Defined in Amazonka.Data.Log Methods build :: UTCTime -> ByteStringBuilder Source # | |
Data UTCTime | |
Defined in Data.Time.Clock.Internal.UTCTime Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> UTCTime -> c UTCTime # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c UTCTime # toConstr :: UTCTime -> Constr # dataTypeOf :: UTCTime -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c UTCTime) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c UTCTime) # gmapT :: (forall b. Data b => b -> b) -> UTCTime -> UTCTime # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> UTCTime -> r # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> UTCTime -> r # gmapQ :: (forall d. Data d => d -> u) -> UTCTime -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> UTCTime -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> UTCTime -> m UTCTime # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> UTCTime -> m UTCTime # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> UTCTime -> m UTCTime # | |
NFData UTCTime | |
Defined in Data.Time.Clock.Internal.UTCTime | |
Eq UTCTime | |
Ord UTCTime | |
Defined in Data.Time.Clock.Internal.UTCTime |
data ByteString #
A space-efficient representation of a Word8
vector, supporting many
efficient operations.
A ByteString
contains 8-bit bytes, or by using the operations from
Data.ByteString.Char8 it can be interpreted as containing 8-bit
characters.
Instances
A space efficient, packed, unboxed Unicode text type.
Instances
A map from keys to values. A map cannot contain duplicate keys; each key can map to at most one value.
Instances
Bifoldable HashMap | Since: unordered-containers-0.2.11 |
Eq2 HashMap | |
Ord2 HashMap | |
Defined in Data.HashMap.Internal | |
Show2 HashMap | |
NFData2 HashMap | Since: unordered-containers-0.2.14.0 |
Defined in Data.HashMap.Internal | |
Hashable2 HashMap | |
Defined in Data.HashMap.Internal | |
(Lift k, Lift v) => Lift (HashMap k v :: Type) | Since: unordered-containers-0.2.17.0 |
(FromJSONKey k, Eq k, Hashable k) => FromJSON1 (HashMap k) | |
ToJSONKey k => ToJSON1 (HashMap k) | |
Defined in Data.Aeson.Types.ToJSON Methods liftToJSON :: (a -> Value) -> ([a] -> Value) -> HashMap k a -> Value # liftToJSONList :: (a -> Value) -> ([a] -> Value) -> [HashMap k a] -> Value # liftToEncoding :: (a -> Encoding) -> ([a] -> Encoding) -> HashMap k a -> Encoding # liftToEncodingList :: (a -> Encoding) -> ([a] -> Encoding) -> [HashMap k a] -> Encoding # | |
Foldable (HashMap k) | |
Defined in Data.HashMap.Internal Methods fold :: Monoid m => HashMap k m -> m # foldMap :: Monoid m => (a -> m) -> HashMap k a -> m # foldMap' :: Monoid m => (a -> m) -> HashMap k a -> m # foldr :: (a -> b -> b) -> b -> HashMap k a -> b # foldr' :: (a -> b -> b) -> b -> HashMap k a -> b # foldl :: (b -> a -> b) -> b -> HashMap k a -> b # foldl' :: (b -> a -> b) -> b -> HashMap k a -> b # foldr1 :: (a -> a -> a) -> HashMap k a -> a # foldl1 :: (a -> a -> a) -> HashMap k a -> a # toList :: HashMap k a -> [a] # length :: HashMap k a -> Int # elem :: Eq a => a -> HashMap k a -> Bool # maximum :: Ord a => HashMap k a -> a # minimum :: Ord a => HashMap k a -> a # | |
Eq k => Eq1 (HashMap k) | |
Ord k => Ord1 (HashMap k) | |
Defined in Data.HashMap.Internal | |
(Eq k, Hashable k, Read k) => Read1 (HashMap k) | |
Defined in Data.HashMap.Internal | |
Show k => Show1 (HashMap k) | |
Traversable (HashMap k) | |
Defined in Data.HashMap.Internal | |
Functor (HashMap k) | |
NFData k => NFData1 (HashMap k) | Since: unordered-containers-0.2.14.0 |
Defined in Data.HashMap.Internal | |
Hashable k => Hashable1 (HashMap k) | |
Defined in Data.HashMap.Internal | |
(FromJSON v, FromJSONKey k, Eq k, Hashable k) => FromJSON (HashMap k v) | |
(ToJSON v, ToJSONKey k) => ToJSON (HashMap k v) | |
Defined in Data.Aeson.Types.ToJSON | |
(ToByteString k, ToByteString v) => ToHeader (HashMap k v) Source # | |
Defined in Amazonka.Data.Headers | |
(ToByteString k, ToByteString v) => ToHeaders (HashMap k v) Source # | |
AWSTruncated (HashMap k v) Source # | |
(Data k, Data v, Eq k, Hashable k) => Data (HashMap k v) | |
Defined in Data.HashMap.Internal Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> HashMap k v -> c (HashMap k v) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (HashMap k v) # toConstr :: HashMap k v -> Constr # dataTypeOf :: HashMap k v -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (HashMap k v)) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (HashMap k v)) # gmapT :: (forall b. Data b => b -> b) -> HashMap k v -> HashMap k v # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> HashMap k v -> r # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> HashMap k v -> r # gmapQ :: (forall d. Data d => d -> u) -> HashMap k v -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> HashMap k v -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> HashMap k v -> m (HashMap k v) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> HashMap k v -> m (HashMap k v) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> HashMap k v -> m (HashMap k v) # | |
(Eq k, Hashable k) => Monoid (HashMap k v) | If a key occurs in both maps, the mapping from the first will be the mapping in the result. Examples
|
(Eq k, Hashable k) => Semigroup (HashMap k v) | If a key occurs in both maps, the mapping from the first will be the mapping in the result. Examples
|
(Eq k, Hashable k) => IsList (HashMap k v) | |
(Eq k, Hashable k, Read k, Read e) => Read (HashMap k e) | |
(Show k, Show v) => Show (HashMap k v) | |
(NFData k, NFData v) => NFData (HashMap k v) | |
Defined in Data.HashMap.Internal | |
(Eq k, Eq v) => Eq (HashMap k v) | Note that, in the presence of hash collisions, equal
In general, the lack of substitutivity can be observed with any function that depends on the key ordering, such as folds and traversals. |
(Ord k, Ord v) => Ord (HashMap k v) | The ordering is total and consistent with the |
Defined in Data.HashMap.Internal | |
(Hashable k, Hashable v) => Hashable (HashMap k v) | |
Defined in Data.HashMap.Internal | |
(Eq k, Hashable k) => At (HashMap k a) | |
(Eq k, Hashable k) => Ixed (HashMap k a) | |
Defined in Control.Lens.At | |
(Hashable k, Eq k) => Wrapped (HashMap k a) | |
(Eq k, Hashable k) => GrowingAppend (HashMap k v) | |
Defined in Data.MonoTraversable | |
MonoFoldable (HashMap k v) | |
Defined in Data.MonoTraversable Methods ofoldMap :: Monoid m => (Element (HashMap k v) -> m) -> HashMap k v -> m # ofoldr :: (Element (HashMap k v) -> b -> b) -> b -> HashMap k v -> b # ofoldl' :: (a -> Element (HashMap k v) -> a) -> a -> HashMap k v -> a # otoList :: HashMap k v -> [Element (HashMap k v)] # oall :: (Element (HashMap k v) -> Bool) -> HashMap k v -> Bool # oany :: (Element (HashMap k v) -> Bool) -> HashMap k v -> Bool # onull :: HashMap k v -> Bool # olength :: HashMap k v -> Int # olength64 :: HashMap k v -> Int64 # ocompareLength :: Integral i => HashMap k v -> i -> Ordering # otraverse_ :: Applicative f => (Element (HashMap k v) -> f b) -> HashMap k v -> f () # ofor_ :: Applicative f => HashMap k v -> (Element (HashMap k v) -> f b) -> f () # omapM_ :: Applicative m => (Element (HashMap k v) -> m ()) -> HashMap k v -> m () # oforM_ :: Applicative m => HashMap k v -> (Element (HashMap k v) -> m ()) -> m () # ofoldlM :: Monad m => (a -> Element (HashMap k v) -> m a) -> a -> HashMap k v -> m a # ofoldMap1Ex :: Semigroup m => (Element (HashMap k v) -> m) -> HashMap k v -> m # ofoldr1Ex :: (Element (HashMap k v) -> Element (HashMap k v) -> Element (HashMap k v)) -> HashMap k v -> Element (HashMap k v) # ofoldl1Ex' :: (Element (HashMap k v) -> Element (HashMap k v) -> Element (HashMap k v)) -> HashMap k v -> Element (HashMap k v) # headEx :: HashMap k v -> Element (HashMap k v) # lastEx :: HashMap k v -> Element (HashMap k v) # unsafeHead :: HashMap k v -> Element (HashMap k v) # unsafeLast :: HashMap k v -> Element (HashMap k v) # maximumByEx :: (Element (HashMap k v) -> Element (HashMap k v) -> Ordering) -> HashMap k v -> Element (HashMap k v) # minimumByEx :: (Element (HashMap k v) -> Element (HashMap k v) -> Ordering) -> HashMap k v -> Element (HashMap k v) # | |
MonoFunctor (HashMap k v) | |
MonoTraversable (HashMap k v) | |
(t ~ HashMap k' a', Hashable k, Eq k) => Rewrapped (HashMap k a) t | Use |
Defined in Control.Lens.Wrapped | |
type Item (HashMap k v) | |
Defined in Data.HashMap.Internal | |
type Index (HashMap k a) | |
Defined in Control.Lens.At | |
type IxValue (HashMap k a) | |
Defined in Control.Lens.At | |
type Unwrapped (HashMap k a) | |
Defined in Control.Lens.Wrapped | |
type Element (HashMap k v) | |
Defined in Data.MonoTraversable |
class Bifunctor (p :: Type -> Type -> Type) where #
A bifunctor is a type constructor that takes
two type arguments and is a functor in both arguments. That
is, unlike with Functor
, a type constructor such as Either
does not need to be partially applied for a Bifunctor
instance, and the methods in this class permit mapping
functions over the Left
value or the Right
value,
or both at the same time.
Formally, the class Bifunctor
represents a bifunctor
from Hask
-> Hask
.
Intuitively it is a bifunctor where both the first and second arguments are covariant.
You can define a Bifunctor
by either defining bimap
or by
defining both first
and second
.
If you supply bimap
, you should ensure that:
bimap
id
id
≡id
If you supply first
and second
, ensure:
first
id
≡id
second
id
≡id
If you supply both, you should also ensure:
bimap
f g ≡first
f.
second
g
These ensure by parametricity:
bimap
(f.
g) (h.
i) ≡bimap
f h.
bimap
g ifirst
(f.
g) ≡first
f.
first
gsecond
(f.
g) ≡second
f.
second
g
Since: base-4.8.0.0
Methods
bimap :: (a -> b) -> (c -> d) -> p a c -> p b d #
Map over both arguments at the same time.
bimap
f g ≡first
f.
second
g
Examples
>>>
bimap toUpper (+1) ('j', 3)
('J',4)
>>>
bimap toUpper (+1) (Left 'j')
Left 'J'
>>>
bimap toUpper (+1) (Right 3)
Right 4
Instances
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
class Applicative f => Alternative (f :: Type -> Type) where #
A monoid on applicative functors.
If defined, some
and many
should be the least solutions
of the equations:
Instances
class (Alternative m, Monad m) => MonadPlus (m :: Type -> Type) where #
Monads that also support choice and failure.
Minimal complete definition
Nothing
Methods
The identity of mplus
. It should also satisfy the equations
mzero >>= f = mzero v >> mzero = mzero
The default definition is
mzero = empty
An associative operation. The default definition is
mplus = (<|>
)
Instances
Uninhabited data type
Since: base-4.8.0.0
Instances
FromJSON Void | |
FromJSONKey Void | Since: aeson-2.1.2.0 |
Defined in Data.Aeson.Types.FromJSON | |
ToJSON Void | |
Defined in Data.Aeson.Types.ToJSON | |
ToJSONKey Void | Since: aeson-2.1.2.0 |
Defined in Data.Aeson.Types.ToJSON | |
Data Void | Since: base-4.8.0.0 |
Defined in Data.Void Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Void -> c Void # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Void # dataTypeOf :: Void -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c Void) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Void) # gmapT :: (forall b. Data b => b -> b) -> Void -> Void # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Void -> r # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Void -> r # gmapQ :: (forall d. Data d => d -> u) -> Void -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> Void -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Void -> m Void # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Void -> m Void # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Void -> m Void # | |
Semigroup Void | Since: base-4.9.0.0 |
Exception Void | Since: base-4.8.0.0 |
Defined in Data.Void Methods toException :: Void -> SomeException # fromException :: SomeException -> Maybe Void # displayException :: Void -> String # | |
Generic Void | |
Ix Void | Since: base-4.8.0.0 |
Read Void | Reading a Since: base-4.8.0.0 |
Show Void | Since: base-4.8.0.0 |
NFData Void | Since: deepseq-1.4.0.0 |
Defined in Control.DeepSeq | |
Eq Void | Since: base-4.8.0.0 |
Ord Void | Since: base-4.8.0.0 |
Hashable Void | |
Defined in Data.Hashable.Class | |
Lift Void | Since: template-haskell-2.15.0.0 |
type Rep Void | Since: base-4.8.0.0 |
The Item
type function returns the type of items of the structure
l
.
Instances
class (Bifunctor t, Bifoldable t) => Bitraversable (t :: Type -> Type -> Type) where #
Bitraversable
identifies bifunctorial data structures whose elements can
be traversed in order, performing Applicative
or Monad
actions at each
element, and collecting a result structure with the same shape.
As opposed to Traversable
data structures, which have one variety of
element on which an action can be performed, Bitraversable
data structures
have two such varieties of elements.
A definition of bitraverse
must satisfy the following laws:
- Naturality
for every applicative transformationbitraverse
(t . f) (t . g) ≡ t .bitraverse
f gt
- Identity
bitraverse
Identity
Identity
≡Identity
- Composition
Compose
.fmap
(bitraverse
g1 g2) .bitraverse
f1 f2 ≡bitraverse
(Compose
.fmap
g1 . f1) (Compose
.fmap
g2 . f2)
where an applicative transformation is a function
t :: (Applicative
f,Applicative
g) => f a -> g a
preserving the Applicative
operations:
t (pure
x) =pure
x t (f<*>
x) = t f<*>
t x
and the identity functor Identity
and composition functors
Compose
are from Data.Functor.Identity and
Data.Functor.Compose.
Some simple examples are Either
and (,)
:
instance Bitraversable Either where bitraverse f _ (Left x) = Left <$> f x bitraverse _ g (Right y) = Right <$> g y instance Bitraversable (,) where bitraverse f g (x, y) = (,) <$> f x <*> g y
Bitraversable
relates to its superclasses in the following ways:
bimap
f g ≡runIdentity
.bitraverse
(Identity
. f) (Identity
. g)bifoldMap
f g =getConst
.bitraverse
(Const
. f) (Const
. g)
These are available as bimapDefault
and bifoldMapDefault
respectively.
Since: base-4.10.0.0
Minimal complete definition
Nothing
Methods
bitraverse :: Applicative f => (a -> f c) -> (b -> f d) -> t a b -> f (t c d) #
Evaluates the relevant functions at each element in the structure, running the action, and builds a new structure with the same shape, using the results produced from sequencing the actions.
bitraverse
f g ≡bisequenceA
.bimap
f g
For a version that ignores the results, see bitraverse_
.
Examples
Basic usage:
>>>
bitraverse listToMaybe (find odd) (Left [])
Nothing
>>>
bitraverse listToMaybe (find odd) (Left [1, 2, 3])
Just (Left 1)
>>>
bitraverse listToMaybe (find odd) (Right [4, 5])
Just (Right 5)
>>>
bitraverse listToMaybe (find odd) ([1, 2, 3], [4, 5])
Just (1,5)
>>>
bitraverse listToMaybe (find odd) ([], [4, 5])
Nothing
Since: base-4.10.0.0
Instances
Bitraversable Either | Since: base-4.10.0.0 |
Defined in Data.Bitraversable Methods bitraverse :: Applicative f => (a -> f c) -> (b -> f d) -> Either a b -> f (Either c d) # | |
Bitraversable Arg | Since: base-4.10.0.0 |
Defined in Data.Semigroup Methods bitraverse :: Applicative f => (a -> f c) -> (b -> f d) -> Arg a b -> f (Arg c d) # | |
Bitraversable Either | |
Defined in Data.Strict.Either Methods bitraverse :: Applicative f => (a -> f c) -> (b -> f d) -> Either a b -> f (Either c d) # | |
Bitraversable These | |
Defined in Data.Strict.These Methods bitraverse :: Applicative f => (a -> f c) -> (b -> f d) -> These a b -> f (These c d) # | |
Bitraversable Pair | |
Defined in Data.Strict.Tuple Methods bitraverse :: Applicative f => (a -> f c) -> (b -> f d) -> Pair a b -> f (Pair c d) # | |
Bitraversable These | |
Defined in Data.These Methods bitraverse :: Applicative f => (a -> f c) -> (b -> f d) -> These a b -> f (These c d) # | |
Bitraversable (,) | Since: base-4.10.0.0 |
Defined in Data.Bitraversable Methods bitraverse :: Applicative f => (a -> f c) -> (b -> f d) -> (a, b) -> f (c, d) # | |
Bitraversable (Const :: Type -> Type -> Type) | Since: base-4.10.0.0 |
Defined in Data.Bitraversable Methods bitraverse :: Applicative f => (a -> f c) -> (b -> f d) -> Const a b -> f (Const c d) # | |
Traversable f => Bitraversable (CofreeF f) | |
Defined in Control.Comonad.Trans.Cofree Methods bitraverse :: Applicative f0 => (a -> f0 c) -> (b -> f0 d) -> CofreeF f a b -> f0 (CofreeF f c d) # | |
Traversable f => Bitraversable (FreeF f) | |
Defined in Control.Monad.Trans.Free Methods bitraverse :: Applicative f0 => (a -> f0 c) -> (b -> f0 d) -> FreeF f a b -> f0 (FreeF f c d) # | |
Bitraversable (Tagged :: Type -> Type -> Type) | |
Defined in Data.Tagged Methods bitraverse :: Applicative f => (a -> f c) -> (b -> f d) -> Tagged a b -> f (Tagged c d) # | |
Bitraversable ((,,) x) | Since: base-4.10.0.0 |
Defined in Data.Bitraversable Methods bitraverse :: Applicative f => (a -> f c) -> (b -> f d) -> (x, a, b) -> f (x, c, d) # | |
Bitraversable (K1 i :: Type -> Type -> Type) | Since: base-4.10.0.0 |
Defined in Data.Bitraversable Methods bitraverse :: Applicative f => (a -> f c) -> (b -> f d) -> K1 i a b -> f (K1 i c d) # | |
Bitraversable ((,,,) x y) | Since: base-4.10.0.0 |
Defined in Data.Bitraversable Methods bitraverse :: Applicative f => (a -> f c) -> (b -> f d) -> (x, y, a, b) -> f (x, y, c, d) # | |
Traversable f => Bitraversable (Clown f :: Type -> Type -> Type) | |
Defined in Data.Bifunctor.Clown Methods bitraverse :: Applicative f0 => (a -> f0 c) -> (b -> f0 d) -> Clown f a b -> f0 (Clown f c d) # | |
Bitraversable p => Bitraversable (Flip p) | |
Defined in Data.Bifunctor.Flip Methods bitraverse :: Applicative f => (a -> f c) -> (b -> f d) -> Flip p a b -> f (Flip p c d) # | |
Traversable g => Bitraversable (Joker g :: Type -> Type -> Type) | |
Defined in Data.Bifunctor.Joker Methods bitraverse :: Applicative f => (a -> f c) -> (b -> f d) -> Joker g a b -> f (Joker g c d) # | |
Bitraversable p => Bitraversable (WrappedBifunctor p) | |
Defined in Data.Bifunctor.Wrapped Methods bitraverse :: Applicative f => (a -> f c) -> (b -> f d) -> WrappedBifunctor p a b -> f (WrappedBifunctor p c d) # | |
Bitraversable ((,,,,) x y z) | Since: base-4.10.0.0 |
Defined in Data.Bitraversable Methods bitraverse :: Applicative f => (a -> f c) -> (b -> f d) -> (x, y, z, a, b) -> f (x, y, z, c, d) # | |
(Bitraversable f, Bitraversable g) => Bitraversable (Product f g) | |
Defined in Data.Bifunctor.Product Methods bitraverse :: Applicative f0 => (a -> f0 c) -> (b -> f0 d) -> Product f g a b -> f0 (Product f g c d) # | |
(Bitraversable p, Bitraversable q) => Bitraversable (Sum p q) | |
Defined in Data.Bifunctor.Sum Methods bitraverse :: Applicative f => (a -> f c) -> (b -> f d) -> Sum p q a b -> f (Sum p q c d) # | |
Bitraversable ((,,,,,) x y z w) | Since: base-4.10.0.0 |
Defined in Data.Bitraversable Methods bitraverse :: Applicative f => (a -> f c) -> (b -> f d) -> (x, y, z, w, a, b) -> f (x, y, z, w, c, d) # | |
(Traversable f, Bitraversable p) => Bitraversable (Tannen f p) | |
Defined in Data.Bifunctor.Tannen Methods bitraverse :: Applicative f0 => (a -> f0 c) -> (b -> f0 d) -> Tannen f p a b -> f0 (Tannen f p c d) # | |
Bitraversable ((,,,,,,) x y z w v) | Since: base-4.10.0.0 |
Defined in Data.Bitraversable Methods bitraverse :: Applicative f => (a -> f c) -> (b -> f d) -> (x, y, z, w, v, a, b) -> f (x, y, z, w, v, c, d) # | |
(Bitraversable p, Traversable f, Traversable g) => Bitraversable (Biff p f g) | |
Defined in Data.Bifunctor.Biff Methods bitraverse :: Applicative f0 => (a -> f0 c) -> (b -> f0 d) -> Biff p f g a b -> f0 (Biff p f g c d) # |
bisequenceA :: (Bitraversable t, Applicative f) => t (f a) (f b) -> f (t a b) #
Alias for bisequence
.
Since: base-4.10.0.0
bisequence :: (Bitraversable t, Applicative f) => t (f a) (f b) -> f (t a b) #
Sequences all the actions in a structure, building a new structure with
the same shape using the results of the actions. For a version that ignores
the results, see bisequence_
.
bisequence
≡bitraverse
id
id
Examples
Basic usage:
>>>
bisequence (Just 4, Nothing)
Nothing
>>>
bisequence (Just 4, Just 5)
Just (4,5)
>>>
bisequence ([1, 2, 3], [4, 5])
[(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)]
Since: base-4.10.0.0
bimapM :: (Bitraversable t, Applicative f) => (a -> f c) -> (b -> f d) -> t a b -> f (t c d) #
Alias for bitraverse
.
Since: base-4.10.0.0
bimapDefault :: Bitraversable t => (a -> b) -> (c -> d) -> t a c -> t b d #
A default definition of bimap
in terms of the Bitraversable
operations.
bimapDefault
f g ≡runIdentity
.bitraverse
(Identity
. f) (Identity
. g)
Since: base-4.10.0.0
bimapAccumR :: Bitraversable t => (a -> b -> (a, c)) -> (a -> d -> (a, e)) -> a -> t b d -> (a, t c e) #
The bimapAccumR
function behaves like a combination of bimap
and
bifoldr
; it traverses a structure from right to left, threading a state
of type a
and using the given actions to compute new elements for the
structure.
Examples
Basic usage:
>>>
bimapAccumR (\acc bool -> (acc + 1, show bool)) (\acc string -> (acc * 2, reverse string)) 3 (True, "foo")
(7,("True","oof"))
Since: base-4.10.0.0
bimapAccumL :: Bitraversable t => (a -> b -> (a, c)) -> (a -> d -> (a, e)) -> a -> t b d -> (a, t c e) #
The bimapAccumL
function behaves like a combination of bimap
and
bifoldl
; it traverses a structure from left to right, threading a state
of type a
and using the given actions to compute new elements for the
structure.
Examples
Basic usage:
>>>
bimapAccumL (\acc bool -> (acc + 1, show bool)) (\acc string -> (acc * 2, reverse string)) 3 (True, "foo")
(8,("True","oof"))
Since: base-4.10.0.0
biforM :: (Bitraversable t, Applicative f) => t a b -> (a -> f c) -> (b -> f d) -> f (t c d) #
Alias for bifor
.
Since: base-4.10.0.0
bifor :: (Bitraversable t, Applicative f) => t a b -> (a -> f c) -> (b -> f d) -> f (t c d) #
bifor
is bitraverse
with the structure as the first argument. For a
version that ignores the results, see bifor_
.
Examples
Basic usage:
>>>
bifor (Left []) listToMaybe (find even)
Nothing
>>>
bifor (Left [1, 2, 3]) listToMaybe (find even)
Just (Left 1)
>>>
bifor (Right [4, 5]) listToMaybe (find even)
Just (Right 4)
>>>
bifor ([1, 2, 3], [4, 5]) listToMaybe (find even)
Just (1,4)
>>>
bifor ([], [4, 5]) listToMaybe (find even)
Nothing
Since: base-4.10.0.0
bifoldMapDefault :: (Bitraversable t, Monoid m) => (a -> m) -> (b -> m) -> t a b -> m #
A default definition of bifoldMap
in terms of the Bitraversable
operations.
bifoldMapDefault
f g ≡getConst
.bitraverse
(Const
. f) (Const
. g)
Since: base-4.10.0.0
class Bifoldable (p :: TYPE LiftedRep -> TYPE LiftedRep -> Type) where #
Bifoldable
identifies foldable structures with two different varieties
of elements (as opposed to Foldable
, which has one variety of element).
Common examples are Either
and (,)
:
instance Bifoldable Either where bifoldMap f _ (Left a) = f a bifoldMap _ g (Right b) = g b instance Bifoldable (,) where bifoldr f g z (a, b) = f a (g b z)
Some examples below also use the following BiList to showcase empty
Bifoldable behaviors when relevant (Either
and (,)
containing always exactly
resp. 1 and 2 elements):
data BiList a b = BiList [a] [b] instance Bifoldable BiList where bifoldr f g z (BiList as bs) = foldr f (foldr g z bs) as
A minimal Bifoldable
definition consists of either bifoldMap
or
bifoldr
. When defining more than this minimal set, one should ensure
that the following identities hold:
bifold
≡bifoldMap
id
id
bifoldMap
f g ≡bifoldr
(mappend
. f) (mappend
. g)mempty
bifoldr
f g z t ≡appEndo
(bifoldMap
(Endo . f) (Endo . g) t) z
If the type is also a Bifunctor
instance, it should satisfy:
bifoldMap
f g ≡bifold
.bimap
f g
which implies that
bifoldMap
f g .bimap
h i ≡bifoldMap
(f . h) (g . i)
Since: base-4.10.0.0
Methods
bifold :: Monoid m => p m m -> m #
Combines the elements of a structure using a monoid.
bifold
≡bifoldMap
id
id
Examples
Basic usage:
>>>
bifold (Right [1, 2, 3])
[1,2,3]
>>>
bifold (Left [5, 6])
[5,6]
>>>
bifold ([1, 2, 3], [4, 5])
[1,2,3,4,5]
>>>
bifold (Product 6, Product 7)
Product {getProduct = 42}
>>>
bifold (Sum 6, Sum 7)
Sum {getSum = 13}
Since: base-4.10.0.0
bifoldMap :: Monoid m => (a -> m) -> (b -> m) -> p a b -> m #
Combines the elements of a structure, given ways of mapping them to a common monoid.
bifoldMap
f g ≡bifoldr
(mappend
. f) (mappend
. g)mempty
Examples
Basic usage:
>>>
bifoldMap (take 3) (fmap digitToInt) ([1..], "89")
[1,2,3,8,9]
>>>
bifoldMap (take 3) (fmap digitToInt) (Left [1..])
[1,2,3]
>>>
bifoldMap (take 3) (fmap digitToInt) (Right "89")
[8,9]
Since: base-4.10.0.0
bifoldr :: (a -> c -> c) -> (b -> c -> c) -> c -> p a b -> c #
Combines the elements of a structure in a right associative manner.
Given a hypothetical function toEitherList :: p a b -> [Either a b]
yielding a list of all elements of a structure in order, the following
would hold:
bifoldr
f g z ≡foldr
(either
f g) z . toEitherList
Examples
Basic usage:
> bifoldr (+) (*) 3 (5, 7) 26 -- 5 + (7 * 3) > bifoldr (+) (*) 3 (7, 5) 22 -- 7 + (5 * 3) > bifoldr (+) (*) 3 (Right 5) 15 -- 5 * 3 > bifoldr (+) (*) 3 (Left 5) 8 -- 5 + 3
Since: base-4.10.0.0
bifoldl :: (c -> a -> c) -> (c -> b -> c) -> c -> p a b -> c #
Combines the elements of a structure in a left associative manner. Given
a hypothetical function toEitherList :: p a b -> [Either a b]
yielding a
list of all elements of a structure in order, the following would hold:
bifoldl
f g z ≡foldl
(acc ->either
(f acc) (g acc)) z . toEitherList
Note that if you want an efficient left-fold, you probably want to use
bifoldl'
instead of bifoldl
. The reason is that the latter does not
force the "inner" results, resulting in a thunk chain which then must be
evaluated from the outside-in.
Examples
Basic usage:
> bifoldl (+) (*) 3 (5, 7) 56 -- (5 + 3) * 7 > bifoldl (+) (*) 3 (7, 5) 50 -- (7 + 3) * 5 > bifoldl (+) (*) 3 (Right 5) 15 -- 5 * 3 > bifoldl (+) (*) 3 (Left 5) 8 -- 5 + 3
Since: base-4.10.0.0
Instances
bitraverse_ :: (Bifoldable t, Applicative f) => (a -> f c) -> (b -> f d) -> t a b -> f () #
Map each element of a structure using one of two actions, evaluate these
actions from left to right, and ignore the results. For a version that
doesn't ignore the results, see bitraverse
.
Examples
Basic usage:
>>>
bitraverse_ print (print . show) ("Hello", True)
"Hello" "True"
>>>
bitraverse_ print (print . show) (Right True)
"True"
>>>
bitraverse_ print (print . show) (Left "Hello")
"Hello"
Since: base-4.10.0.0
bisum :: (Bifoldable t, Num a) => t a a -> a #
The bisum
function computes the sum of the numbers of a structure.
Examples
Basic usage:
>>>
bisum (42, 17)
59
>>>
bisum (Right 42)
42
>>>
bisum (BiList [13, 29, 4] [18, 1, 7])
72
>>>
bisum (BiList [13, 29, 4] [])
46
>>>
bisum (BiList [] [])
0
Since: base-4.10.0.0
bisequence_ :: (Bifoldable t, Applicative f) => t (f a) (f b) -> f () #
Evaluate each action in the structure from left to right, and ignore the
results. For a version that doesn't ignore the results, see
bisequence
.
Examples
Basic usage:
>>>
bisequence_ (print "Hello", print "World")
"Hello" "World"
>>>
bisequence_ (Left (print "Hello"))
"Hello"
>>>
bisequence_ (Right (print "World"))
"World"
Since: base-4.10.0.0
bisequenceA_ :: (Bifoldable t, Applicative f) => t (f a) (f b) -> f () #
Alias for bisequence_
.
Since: base-4.10.0.0
biproduct :: (Bifoldable t, Num a) => t a a -> a #
The biproduct
function computes the product of the numbers of a
structure.
Examples
Basic usage:
>>>
biproduct (42, 17)
714
>>>
biproduct (Right 42)
42
>>>
biproduct (BiList [13, 29, 4] [18, 1, 7])
190008
>>>
biproduct (BiList [13, 29, 4] [])
1508
>>>
biproduct (BiList [] [])
1
Since: base-4.10.0.0
bior :: Bifoldable t => t Bool Bool -> Bool #
bior
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.
Examples
Basic usage:
>>>
bior (True, False)
True
>>>
bior (False, False)
False
>>>
bior (Left True)
True
Empty structures yield False
:
>>>
bior (BiList [] [])
False
A True
value finitely far from the left end yields True
(short circuit):
>>>
bior (BiList [False, False, True, False] (repeat False))
True
A True
value infinitely far from the left end hangs:
> bior (BiList (repeat False) [True]) * Hangs forever *
An infinitely False
value hangs:
> bior (BiList (repeat False) []) * Hangs forever *
Since: base-4.10.0.0
binull :: Bifoldable t => t a b -> Bool #
Test whether the structure is empty.
Examples
Basic usage:
>>>
binull (18, 42)
False
>>>
binull (Right 42)
False
>>>
binull (BiList [] [])
True
Since: base-4.10.0.0
binotElem :: (Bifoldable t, Eq a) => a -> t a a -> Bool #
bimsum :: (Bifoldable t, Alternative f) => t (f a) (f a) -> f a #
Alias for biasum
.
Since: base-4.10.0.0
biminimumBy :: Bifoldable t => (a -> a -> Ordering) -> t a a -> a #
The least element of a non-empty structure with respect to the given comparison function.
Examples
Basic usage:
>>>
biminimumBy compare (42, 17)
17
>>>
biminimumBy compare (Left 17)
17
>>>
biminimumBy compare (BiList [42, 17, 23] [-5, 18])
-5
On empty structures, this function throws an exception:
>>>
biminimumBy compare (BiList [] [])
*** Exception: bifoldr1: empty structure ...
Since: base-4.10.0.0
biminimum :: (Bifoldable t, Ord a) => t a a -> a #
The least element of a non-empty structure.
Examples
Basic usage:
>>>
biminimum (42, 17)
17
>>>
biminimum (Right 42)
42
>>>
biminimum (BiList [13, 29, 4] [18, 1, 7])
1
>>>
biminimum (BiList [13, 29, 4] [])
4
On empty structures, this function throws an exception:
>>>
biminimum (BiList [] [])
*** Exception: biminimum: empty structure ...
Since: base-4.10.0.0
bimaximumBy :: Bifoldable t => (a -> a -> Ordering) -> t a a -> a #
The largest element of a non-empty structure with respect to the given comparison function.
Examples
Basic usage:
>>>
bimaximumBy compare (42, 17)
42
>>>
bimaximumBy compare (Left 17)
17
>>>
bimaximumBy compare (BiList [42, 17, 23] [-5, 18])
42
On empty structures, this function throws an exception:
>>>
bimaximumBy compare (BiList [] [])
*** Exception: bifoldr1: empty structure ...
Since: base-4.10.0.0
bimaximum :: (Bifoldable t, Ord a) => t a a -> a #
The largest element of a non-empty structure.
Examples
Basic usage:
>>>
bimaximum (42, 17)
42
>>>
bimaximum (Right 42)
42
>>>
bimaximum (BiList [13, 29, 4] [18, 1, 7])
29
>>>
bimaximum (BiList [13, 29, 4] [])
29
On empty structures, this function throws an exception:
>>>
bimaximum (BiList [] [])
*** Exception: bimaximum: empty structure ...
Since: base-4.10.0.0
bimapM_ :: (Bifoldable t, Applicative f) => (a -> f c) -> (b -> f d) -> t a b -> f () #
Alias for bitraverse_
.
Since: base-4.10.0.0
bilength :: Bifoldable t => t a b -> Int #
Returns the size/length of a finite structure as an Int
.
Examples
Basic usage:
>>>
bilength (True, 42)
2
>>>
bilength (Right 42)
1
>>>
bilength (BiList [1,2,3] [4,5])
5
>>>
bilength (BiList [] [])
0
On infinite structures, this function hangs:
> bilength (BiList [1..] []) * Hangs forever *
Since: base-4.10.0.0
bifor_ :: (Bifoldable t, Applicative f) => t a b -> (a -> f c) -> (b -> f d) -> f () #
As bitraverse_
, but with the structure as the primary argument. For a
version that doesn't ignore the results, see bifor
.
Examples
Basic usage:
>>>
bifor_ ("Hello", True) print (print . show)
"Hello" "True"
>>>
bifor_ (Right True) print (print . show)
"True"
>>>
bifor_ (Left "Hello") print (print . show)
"Hello"
Since: base-4.10.0.0
biforM_ :: (Bifoldable t, Applicative f) => t a b -> (a -> f c) -> (b -> f d) -> f () #
Alias for bifor_
.
Since: base-4.10.0.0
bifoldrM :: (Bifoldable t, Monad m) => (a -> c -> m c) -> (b -> c -> m c) -> c -> t a b -> m c #
Right associative monadic bifold over a structure.
Since: base-4.10.0.0
bifoldr1 :: Bifoldable t => (a -> a -> a) -> t a a -> a #
A variant of bifoldr
that has no base case,
and thus may only be applied to non-empty structures.
Examples
Basic usage:
>>>
bifoldr1 (+) (5, 7)
12
>>>
bifoldr1 (+) (Right 7)
7
>>>
bifoldr1 (+) (Left 5)
5
> bifoldr1 (+) (BiList [1, 2] [3, 4]) 10 -- 1 + (2 + (3 + 4))
>>>
bifoldr1 (+) (BiList [1, 2] [])
3
On empty structures, this function throws an exception:
>>>
bifoldr1 (+) (BiList [] [])
*** Exception: bifoldr1: empty structure ...
Since: base-4.10.0.0
bifoldr' :: Bifoldable t => (a -> c -> c) -> (b -> c -> c) -> c -> t a b -> c #
As bifoldr
, but strict in the result of the reduction functions at each
step.
Since: base-4.10.0.0
bifoldlM :: (Bifoldable t, Monad m) => (a -> b -> m a) -> (a -> c -> m a) -> a -> t b c -> m a #
Left associative monadic bifold over a structure.
Examples
Basic usage:
>>>
bifoldlM (\a b -> print b >> pure a) (\a c -> print (show c) >> pure a) 42 ("Hello", True)
"Hello" "True" 42
>>>
bifoldlM (\a b -> print b >> pure a) (\a c -> print (show c) >> pure a) 42 (Right True)
"True" 42
>>>
bifoldlM (\a b -> print b >> pure a) (\a c -> print (show c) >> pure a) 42 (Left "Hello")
"Hello" 42
Since: base-4.10.0.0
bifoldl1 :: Bifoldable t => (a -> a -> a) -> t a a -> a #
A variant of bifoldl
that has no base case,
and thus may only be applied to non-empty structures.
Examples
Basic usage:
>>>
bifoldl1 (+) (5, 7)
12
>>>
bifoldl1 (+) (Right 7)
7
>>>
bifoldl1 (+) (Left 5)
5
> bifoldl1 (+) (BiList [1, 2] [3, 4]) 10 -- ((1 + 2) + 3) + 4
>>>
bifoldl1 (+) (BiList [1, 2] [])
3
On empty structures, this function throws an exception:
>>>
bifoldl1 (+) (BiList [] [])
*** Exception: bifoldl1: empty structure ...
Since: base-4.10.0.0
bifoldl' :: Bifoldable t => (a -> b -> a) -> (a -> c -> a) -> a -> t b c -> a #
As bifoldl
, but strict in the result of the reduction functions at each
step.
This ensures that each step of the bifold is forced to weak head normal form
before being applied, avoiding the collection of thunks that would otherwise
occur. This is often what you want to strictly reduce a finite structure to
a single, monolithic result (e.g., bilength
).
Since: base-4.10.0.0
bifind :: Bifoldable t => (a -> Bool) -> t a a -> Maybe a #
The bifind
function takes a predicate and a structure and returns
the leftmost element of the structure matching the predicate, or
Nothing
if there is no such element.
Examples
Basic usage:
>>>
bifind even (27, 53)
Nothing
>>>
bifind even (27, 52)
Just 52
>>>
bifind even (26, 52)
Just 26
Empty structures always yield Nothing
:
>>>
bifind even (BiList [] [])
Nothing
Since: base-4.10.0.0
bielem :: (Bifoldable t, Eq a) => a -> t a a -> Bool #
Does the element occur in the structure?
Examples
Basic usage:
>>>
bielem 42 (17, 42)
True
>>>
bielem 42 (17, 43)
False
>>>
bielem 42 (Left 42)
True
>>>
bielem 42 (Right 13)
False
>>>
bielem 42 (BiList [1..5] [1..100])
True
>>>
bielem 42 (BiList [1..5] [1..41])
False
Since: base-4.10.0.0
biconcatMap :: Bifoldable t => (a -> [c]) -> (b -> [c]) -> t a b -> [c] #
Given a means of mapping the elements of a structure to lists, computes the concatenation of all such lists in order.
Examples
Basic usage:
>>>
biconcatMap (take 3) (fmap digitToInt) ([1..], "89")
[1,2,3,8,9]
>>>
biconcatMap (take 3) (fmap digitToInt) (Left [1..])
[1,2,3]
>>>
biconcatMap (take 3) (fmap digitToInt) (Right "89")
[8,9]
Since: base-4.10.0.0
biconcat :: Bifoldable t => t [a] [a] -> [a] #
Reduces a structure of lists to the concatenation of those lists.
Examples
Basic usage:
>>>
biconcat ([1, 2, 3], [4, 5])
[1,2,3,4,5]
>>>
biconcat (Left [1, 2, 3])
[1,2,3]
>>>
biconcat (BiList [[1, 2, 3, 4, 5], [6, 7, 8]] [[9]])
[1,2,3,4,5,6,7,8,9]
Since: base-4.10.0.0
biasum :: (Bifoldable t, Alternative f) => t (f a) (f a) -> f a #
The sum of a collection of actions, generalizing biconcat
.
Examples
Basic usage:
>>>
biasum (Nothing, Nothing)
Nothing
>>>
biasum (Nothing, Just 42)
Just 42
>>>
biasum (Just 18, Nothing)
Just 18
>>>
biasum (Just 18, Just 42)
Just 18
Since: base-4.10.0.0
biany :: Bifoldable t => (a -> Bool) -> (b -> Bool) -> t a b -> Bool #
Determines whether any element of the structure satisfies its appropriate
predicate argument. Empty structures yield False
.
Examples
Basic usage:
>>>
biany even isDigit (27, 't')
False
>>>
biany even isDigit (27, '8')
True
>>>
biany even isDigit (26, 't')
True
>>>
biany even isDigit (Left 27)
False
>>>
biany even isDigit (Left 26)
True
>>>
biany even isDigit (BiList [27, 53] ['t', '8'])
True
Empty structures yield False
:
>>>
biany even isDigit (BiList [] [])
False
Since: base-4.10.0.0
biand :: Bifoldable t => t Bool Bool -> Bool #
biand
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.
Examples
Basic usage:
>>>
biand (True, False)
False
>>>
biand (True, True)
True
>>>
biand (Left True)
True
Empty structures yield True
:
>>>
biand (BiList [] [])
True
A False
value finitely far from the left end yields False
(short circuit):
>>>
biand (BiList [True, True, False, True] (repeat True))
False
A False
value infinitely far from the left end hangs:
> biand (BiList (repeat True) [False]) * Hangs forever *
An infinitely True
value hangs:
> biand (BiList (repeat True) []) * Hangs forever *
Since: base-4.10.0.0
biall :: Bifoldable t => (a -> Bool) -> (b -> Bool) -> t a b -> Bool #
Determines whether all elements of the structure satisfy their appropriate
predicate argument. Empty structures yield True
.
Examples
Basic usage:
>>>
biall even isDigit (27, 't')
False
>>>
biall even isDigit (26, '8')
True
>>>
biall even isDigit (Left 27)
False
>>>
biall even isDigit (Left 26)
True
>>>
biall even isDigit (BiList [26, 52] ['3', '8'])
True
Empty structures yield True
:
>>>
biall even isDigit (BiList [] [])
True
Since: base-4.10.0.0
biList :: Bifoldable t => t a a -> [a] #
Collects the list of elements of a structure, from left to right.
Examples
Basic usage:
>>>
biList (18, 42)
[18,42]
>>>
biList (Left 18)
[18]
Since: base-4.10.0.0
class Monad m => MonadIO (m :: Type -> Type) where #
Monads in which IO
computations may be embedded.
Any monad built by applying a sequence of monad transformers to the
IO
monad will be an instance of this class.
Instances should satisfy the following laws, which state that liftIO
is a transformer of monads:
Methods
Lift a computation from the IO
monad.
This allows us to run IO computations in any monadic stack, so long as it supports these kinds of operations
(i.e. IO
is the base monad for the stack).
Example
import Control.Monad.Trans.State -- from the "transformers" library printState :: Show s => StateT s IO () printState = do state <- get liftIO $ print state
Had we omitted
, we would have ended up with this error:liftIO
• Couldn't match type ‘IO’ with ‘StateT s IO’ Expected type: StateT s IO () Actual type: IO ()
The important part here is the mismatch between StateT s IO ()
and
.IO
()
Luckily, we know of a function that takes an
and returns an IO
a(m a)
:
,
enabling us to run the program and see the expected results:liftIO
> evalStateT printState "hello" "hello" > evalStateT printState 3 3
Instances
MonadIO IO | Since: base-4.9.0.0 |
Defined in Control.Monad.IO.Class | |
MonadIO Q | |
Defined in Language.Haskell.TH.Syntax | |
MonadIO m => MonadIO (ResourceT m) | |
Defined in Control.Monad.Trans.Resource.Internal | |
(Functor f, MonadIO m) => MonadIO (FreeT f m) | |
Defined in Control.Monad.Trans.Free | |
(Error e, MonadIO m) => MonadIO (ErrorT e m) | |
Defined in Control.Monad.Trans.Error | |
MonadIO m => MonadIO (ExceptT e m) | |
Defined in Control.Monad.Trans.Except | |
MonadIO m => MonadIO (ConduitT i o m) | |
Defined in Data.Conduit.Internal.Conduit | |
MonadIO m => MonadIO (Pipe l i o u m) | |
Defined in Data.Conduit.Internal.Pipe |
zipWithM_ :: Applicative m => (a -> b -> m c) -> [a] -> [b] -> m () #
zipWithM :: Applicative m => (a -> b -> m c) -> [a] -> [b] -> m [c] #
unless :: Applicative f => Bool -> f () -> f () #
The reverse of when
.
replicateM_ :: Applicative m => Int -> m a -> m () #
replicateM :: Applicative m => Int -> m a -> m [a] #
performs the action replicateM
n actact
n
times,
and then returns the list of results:
Examples
>>>
import Control.Monad.State
>>>
runState (replicateM 3 $ state $ \s -> (s, s + 1)) 1
([1,2,3],4)
mapAndUnzipM :: Applicative m => (a -> m (b, c)) -> [a] -> m ([b], [c]) #
The mapAndUnzipM
function maps its first argument over a list, returning
the result as a pair of lists. This function is mainly used with complicated
data structures or a state monad.
forever :: Applicative f => f a -> f b #
Repeat an action indefinitely.
Examples
A common use of forever
is to process input from network sockets,
Handle
s, and channels
(e.g. MVar
and
Chan
).
For example, here is how we might implement an echo
server, using
forever
both to listen for client connections on a network socket
and to echo client input on client connection handles:
echoServer :: Socket -> IO () echoServer socket =forever
$ do client <- accept socketforkFinally
(echo client) (\_ -> hClose client) where echo :: Handle -> IO () echo client =forever
$ hGetLine client >>= hPutStrLn client
Note that "forever" isn't necessarily non-terminating.
If the action is in a
and short-circuits after some number of iterations.
then MonadPlus
actually returns forever
mzero
, effectively short-circuiting its caller.
foldM_ :: (Foldable t, Monad m) => (b -> a -> m b) -> b -> t a -> m () #
Like foldM
, but discards the result.
foldM :: (Foldable t, Monad m) => (b -> a -> m b) -> b -> t a -> m b #
The foldM
function is analogous to foldl
, except that its result is
encapsulated in a monad. Note that foldM
works from left-to-right over
the list arguments. This could be an issue where (
and the `folded
function' are not commutative.>>
)
foldM f a1 [x1, x2, ..., xm] == do a2 <- f a1 x1 a3 <- f a2 x2 ... f am xm
If right-to-left evaluation is required, the input list should be reversed.
filterM :: Applicative m => (a -> m Bool) -> [a] -> m [a] #
This generalizes the list-based filter
function.
(>=>) :: Monad m => (a -> m b) -> (b -> m c) -> a -> m c infixr 1 #
Left-to-right composition of Kleisli arrows.
'(bs
' can be understood as the >=>
cs) ado
expression
do b <- bs a cs b
forM :: (Traversable t, Monad m) => t a -> (a -> m b) -> m (t b) #
Identity functor and monad. (a non-strict monad)
Since: base-4.8.0.0
Constructors
Identity | |
Fields
|
Instances
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
).
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]])
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.
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.
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)
class (Typeable e, Show e) => Exception e #
Any type that you wish to throw or catch as an exception must be an
instance of the Exception
class. The simplest case is a new exception
type directly below the root:
data MyException = ThisException | ThatException deriving Show instance Exception MyException
The default method definitions in the Exception
class do what we need
in this case. You can now throw and catch ThisException
and
ThatException
as exceptions:
*Main> throw ThisException `catch` \e -> putStrLn ("Caught " ++ show (e :: MyException)) Caught ThisException
In more complicated examples, you may wish to define a whole hierarchy of exceptions:
--------------------------------------------------------------------- -- Make the root exception type for all the exceptions in a compiler data SomeCompilerException = forall e . Exception e => SomeCompilerException e instance Show SomeCompilerException where show (SomeCompilerException e) = show e instance Exception SomeCompilerException compilerExceptionToException :: Exception e => e -> SomeException compilerExceptionToException = toException . SomeCompilerException compilerExceptionFromException :: Exception e => SomeException -> Maybe e compilerExceptionFromException x = do SomeCompilerException a <- fromException x cast a --------------------------------------------------------------------- -- Make a subhierarchy for exceptions in the frontend of the compiler data SomeFrontendException = forall e . Exception e => SomeFrontendException e instance Show SomeFrontendException where show (SomeFrontendException e) = show e instance Exception SomeFrontendException where toException = compilerExceptionToException fromException = compilerExceptionFromException frontendExceptionToException :: Exception e => e -> SomeException frontendExceptionToException = toException . SomeFrontendException frontendExceptionFromException :: Exception e => SomeException -> Maybe e frontendExceptionFromException x = do SomeFrontendException a <- fromException x cast a --------------------------------------------------------------------- -- Make an exception type for a particular frontend compiler exception data MismatchedParentheses = MismatchedParentheses deriving Show instance Exception MismatchedParentheses where toException = frontendExceptionToException fromException = frontendExceptionFromException
We can now catch a MismatchedParentheses
exception as
MismatchedParentheses
, SomeFrontendException
or
SomeCompilerException
, but not other types, e.g. IOException
:
*Main> throw MismatchedParentheses `catch` \e -> putStrLn ("Caught " ++ show (e :: MismatchedParentheses)) Caught MismatchedParentheses *Main> throw MismatchedParentheses `catch` \e -> putStrLn ("Caught " ++ show (e :: SomeFrontendException)) Caught MismatchedParentheses *Main> throw MismatchedParentheses `catch` \e -> putStrLn ("Caught " ++ show (e :: SomeCompilerException)) Caught MismatchedParentheses *Main> throw MismatchedParentheses `catch` \e -> putStrLn ("Caught " ++ show (e :: IOException)) *** Exception: MismatchedParentheses
Instances
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
.
sequence_
is just like sequenceA_
, but specialised to monadic
actions.
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.
Examples
Basic usage:
>>>
or []
False
>>>
or [True]
True
>>>
or [False]
False
>>>
or [True, True, False]
True
>>>
or (True : repeat False) -- Infinite list [True,False,False,False,...
True
>>>
or (repeat False)
* Hangs forever *
notElem :: (Foldable t, Eq a) => a -> t a -> Bool infix 4 #
notElem
is the negation of elem
.
Examples
Basic usage:
>>>
3 `notElem` []
True
>>>
3 `notElem` [1,2]
True
>>>
3 `notElem` [1,2,3,4,5]
False
For infinite structures, notElem
terminates if the value exists at a
finite distance from the left side of the structure:
>>>
3 `notElem` [1..]
False
>>>
3 `notElem` ([4..] ++ [3])
* Hangs forever *
concatMap :: Foldable t => (a -> [b]) -> t a -> [b] #
Map a function over all the elements of a container and concatenate the resulting lists.
Examples
Basic usage:
>>>
concatMap (take 3) [[1..], [10..], [100..], [1000..]]
[1,2,3,10,11,12,100,101,102,1000,1001,1002]
>>>
concatMap (take 3) (Just [1..])
[1,2,3]
concat :: Foldable t => t [a] -> [a] #
The concatenation of all the elements of a container of lists.
Examples
Basic usage:
>>>
concat (Just [1, 2, 3])
[1,2,3]
>>>
concat (Left 42)
[]
>>>
concat [[1, 2, 3], [4, 5], [6], []]
[1,2,3,4,5,6]
any :: Foldable t => (a -> Bool) -> t a -> Bool #
Determines whether any element of the structure satisfies the predicate.
Examples
Basic usage:
>>>
any (> 3) []
False
>>>
any (> 3) [1,2]
False
>>>
any (> 3) [1,2,3,4,5]
True
>>>
any (> 3) [1..]
True
>>>
any (> 3) [0, -1..]
* Hangs forever *
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.
Examples
Basic usage:
>>>
and []
True
>>>
and [True]
True
>>>
and [False]
False
>>>
and [True, True, False]
False
>>>
and (False : repeat True) -- Infinite list [False,True,True,True,...
False
>>>
and (repeat True)
* Hangs forever *
all :: Foldable t => (a -> Bool) -> t a -> Bool #
Determines whether all elements of the structure satisfy the predicate.
Examples
Basic usage:
>>>
all (> 3) []
True
>>>
all (> 3) [1,2]
False
>>>
all (> 3) [1,2,3,4,5]
False
>>>
all (> 3) [1..]
False
>>>
all (> 3) [4..]
* Hangs forever *
words
breaks a string up into a list of words, which were delimited
by white space.
>>>
words "Lorem ipsum\ndolor"
["Lorem","ipsum","dolor"]
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
contains at least as many elements as newlines in lines
ss
.
Maybe monoid returning the leftmost non-Nothing value.
is isomorphic to First
a
, but precedes it
historically.Alt
Maybe
a
>>>
getFirst (First (Just "hello") <> First Nothing <> First (Just "world"))
Just "hello"
Instances
FromJSON1 First | |
ToJSON1 First | |
Defined in Data.Aeson.Types.ToJSON Methods liftToJSON :: (a -> Value) -> ([a] -> Value) -> First a -> Value # liftToJSONList :: (a -> Value) -> ([a] -> Value) -> [First a] -> Value # liftToEncoding :: (a -> Encoding) -> ([a] -> Encoding) -> First a -> Encoding # liftToEncodingList :: (a -> Encoding) -> ([a] -> Encoding) -> [First a] -> Encoding # | |
Foldable First | Since: base-4.8.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => First m -> m # foldMap :: Monoid m => (a -> m) -> First a -> 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 # elem :: Eq a => a -> First a -> Bool # maximum :: Ord a => First a -> a # minimum :: Ord a => First a -> a # | |
Traversable First | Since: base-4.8.0.0 |
Applicative First | Since: base-4.8.0.0 |
Functor First | Since: base-4.8.0.0 |
Monad First | Since: base-4.8.0.0 |
NFData1 First | Since: deepseq-1.4.3.0 |
Defined in Control.DeepSeq | |
FromJSON a => FromJSON (First a) | |
ToJSON a => ToJSON (First a) | |
Defined in Data.Aeson.Types.ToJSON | |
Monoid (First a) | Since: base-2.1 |
Semigroup (First a) | Since: base-4.9.0.0 |
Generic (First a) | |
Read a => Read (First a) | Since: base-2.1 |
Show a => Show (First a) | Since: base-2.1 |
Default (First a) | |
Defined in Data.Default.Class | |
NFData a => NFData (First a) | Since: deepseq-1.4.0.0 |
Defined in Control.DeepSeq | |
Eq a => Eq (First a) | Since: base-2.1 |
Ord a => Ord (First a) | Since: base-2.1 |
Wrapped (First a) | |
Generic1 First | |
t ~ First b => Rewrapped (First a) t | |
Defined in Control.Lens.Wrapped | |
type Rep (First a) | Since: base-4.7.0.0 |
Defined in Data.Monoid | |
type Unwrapped (First a) | |
Defined in Control.Lens.Wrapped | |
type Rep1 First | Since: base-4.7.0.0 |
Defined in Data.Monoid |
A type synonym for Natural
.
Prevously, this was an opaque data type, but it was changed to a type synonym.
Since: base-4.16.0.0
Proxy
is a type that holds no data, but has a phantom parameter of
arbitrary type (or even kind). Its use is to provide type information, even
though there is no value available of that type (or it may be too costly to
create one).
Historically,
is a safer alternative to the
Proxy
:: Proxy
a
idiom.undefined
:: a
>>>
Proxy :: Proxy (Void, Int -> Int)
Proxy
Proxy can even hold types of higher kinds,
>>>
Proxy :: Proxy Either
Proxy
>>>
Proxy :: Proxy Functor
Proxy
>>>
Proxy :: Proxy complicatedStructure
Proxy
Constructors
Proxy |
Instances
Generic1 (Proxy :: k -> Type) | |
Representable (Proxy :: Type -> Type) | |
FromJSON1 (Proxy :: Type -> Type) | |
ToJSON1 (Proxy :: TYPE LiftedRep -> Type) | |
Defined in Data.Aeson.Types.ToJSON Methods liftToJSON :: (a -> Value) -> ([a] -> Value) -> Proxy a -> Value # liftToJSONList :: (a -> Value) -> ([a] -> Value) -> [Proxy a] -> Value # liftToEncoding :: (a -> Encoding) -> ([a] -> Encoding) -> Proxy a -> Encoding # liftToEncodingList :: (a -> Encoding) -> ([a] -> Encoding) -> [Proxy a] -> Encoding # | |
Foldable (Proxy :: TYPE LiftedRep -> Type) | Since: base-4.7.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => Proxy m -> m # foldMap :: Monoid m => (a -> m) -> Proxy a -> 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 # elem :: Eq a => a -> Proxy a -> Bool # maximum :: Ord a => Proxy a -> a # minimum :: Ord a => Proxy a -> a # | |
Eq1 (Proxy :: Type -> Type) | Since: base-4.9.0.0 |
Ord1 (Proxy :: Type -> Type) | Since: base-4.9.0.0 |
Defined in Data.Functor.Classes | |
Read1 (Proxy :: Type -> Type) | Since: base-4.9.0.0 |
Defined in Data.Functor.Classes | |
Show1 (Proxy :: TYPE LiftedRep -> Type) | Since: base-4.9.0.0 |
Contravariant (Proxy :: Type -> Type) | |
Traversable (Proxy :: Type -> Type) | Since: base-4.7.0.0 |
Alternative (Proxy :: Type -> Type) | Since: base-4.9.0.0 |
Applicative (Proxy :: Type -> Type) | Since: base-4.7.0.0 |
Functor (Proxy :: Type -> Type) | Since: base-4.7.0.0 |
Monad (Proxy :: Type -> Type) | Since: base-4.7.0.0 |
MonadPlus (Proxy :: Type -> Type) | Since: base-4.9.0.0 |
NFData1 (Proxy :: TYPE LiftedRep -> Type) | Since: deepseq-1.4.3.0 |
Defined in Control.DeepSeq | |
Hashable1 (Proxy :: Type -> Type) | |
Defined in Data.Hashable.Class | |
FromJSON (Proxy a) | |
ToJSON (Proxy a) | |
Defined in Data.Aeson.Types.ToJSON | |
Monoid (Proxy s) | Since: base-4.7.0.0 |
Semigroup (Proxy s) | Since: base-4.9.0.0 |
Bounded (Proxy t) | Since: base-4.7.0.0 |
Enum (Proxy s) | Since: base-4.7.0.0 |
Generic (Proxy t) | |
Ix (Proxy s) | Since: base-4.7.0.0 |
Defined in Data.Proxy | |
Read (Proxy t) | Since: base-4.7.0.0 |
Show (Proxy s) | Since: base-4.7.0.0 |
NFData (Proxy a) | Since: deepseq-1.4.0.0 |
Defined in Control.DeepSeq | |
Eq (Proxy s) | Since: base-4.7.0.0 |
Ord (Proxy s) | Since: base-4.7.0.0 |
Hashable (Proxy a) | |
Defined in Data.Hashable.Class | |
MonoFoldable (Proxy a) | Since: mono-traversable-1.0.11.0 |
Defined in Data.MonoTraversable Methods ofoldMap :: Monoid m => (Element (Proxy a) -> m) -> Proxy a -> m # ofoldr :: (Element (Proxy a) -> b -> b) -> b -> Proxy a -> b # ofoldl' :: (a0 -> Element (Proxy a) -> a0) -> a0 -> Proxy a -> a0 # otoList :: Proxy a -> [Element (Proxy a)] # oall :: (Element (Proxy a) -> Bool) -> Proxy a -> Bool # oany :: (Element (Proxy a) -> Bool) -> Proxy a -> Bool # olength64 :: Proxy a -> Int64 # ocompareLength :: Integral i => Proxy a -> i -> Ordering # otraverse_ :: Applicative f => (Element (Proxy a) -> f b) -> Proxy a -> f () # ofor_ :: Applicative f => Proxy a -> (Element (Proxy a) -> f b) -> f () # omapM_ :: Applicative m => (Element (Proxy a) -> m ()) -> Proxy a -> m () # oforM_ :: Applicative m => Proxy a -> (Element (Proxy a) -> m ()) -> m () # ofoldlM :: Monad m => (a0 -> Element (Proxy a) -> m a0) -> a0 -> Proxy a -> m a0 # ofoldMap1Ex :: Semigroup m => (Element (Proxy a) -> m) -> Proxy a -> m # ofoldr1Ex :: (Element (Proxy a) -> Element (Proxy a) -> Element (Proxy a)) -> Proxy a -> Element (Proxy a) # ofoldl1Ex' :: (Element (Proxy a) -> Element (Proxy a) -> Element (Proxy a)) -> Proxy a -> Element (Proxy a) # headEx :: Proxy a -> Element (Proxy a) # lastEx :: Proxy a -> Element (Proxy a) # unsafeHead :: Proxy a -> Element (Proxy a) # unsafeLast :: Proxy a -> Element (Proxy a) # maximumByEx :: (Element (Proxy a) -> Element (Proxy a) -> Ordering) -> Proxy a -> Element (Proxy a) # minimumByEx :: (Element (Proxy a) -> Element (Proxy a) -> Ordering) -> Proxy a -> Element (Proxy a) # | |
MonoFunctor (Proxy a) | Since: mono-traversable-1.0.11.0 |
MonoPointed (Proxy a) | Since: mono-traversable-1.0.11.0 |
MonoTraversable (Proxy a) | Since: mono-traversable-1.0.11.0 |
type Rep1 (Proxy :: k -> Type) | Since: base-4.6.0.0 |
type Rep (Proxy :: Type -> Type) | |
type Rep (Proxy t) | Since: base-4.6.0.0 |
type Element (Proxy a) | |
Defined in Data.MonoTraversable |
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
.) If there is no legal lexeme at the
beginning of the input string, lex
"" = [("","")]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
lcm :: Integral a => a -> a -> a #
is the smallest positive integer that both lcm
x yx
and y
divide.
gcd :: Integral a => a -> a -> a #
is the non-negative factor of both gcd
x yx
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 44
.
= gcd
0 00
.
(That is, the common divisor that is "greatest" in the divisibility
preordering.)
Note: Since for signed fixed-width integer types,
,
the result may be negative if one of the arguments is abs
minBound
< 0
(and
necessarily is if the other is minBound
0
or
) for such types.minBound
(^^) :: (Fractional a, Integral b) => a -> b -> a infixr 8 #
raise a number to an integral power
showString :: String -> ShowS #
utility function converting a String
to a show function that
simply prepends the string unchanged.
utility function converting a Char
to a show function that
simply prepends the character unchanged.
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 the function applied
to corresponding elements, analogous to zipWith
.
It is capable of list fusion, but it is restricted to its
first list argument and its resulting list.
zipWith3 (,,) xs ys zs == zip3 xs ys zs zipWith3 f [x1,x2,x3..] [y1,y2,y3..] [z1,z2,z3..] == [f x1 y1 z1, f x2 y2 z2, f x3 y3 z3..]
zipWith :: (a -> b -> c) -> [a] -> [b] -> [c] #
\(\mathcal{O}(\min(m,n))\). zipWith
generalises zip
by zipping with the
function given as the first argument, instead of a tupling function.
zipWith (,) xs ys == zip xs ys zipWith f [x1,x2,x3..] [y1,y2,y3..] == [f x1 y1, f x2 y2, f x3 y3..]
For example,
is applied to two lists to produce the list of
corresponding sums:zipWith
(+)
>>>
zipWith (+) [1, 2, 3] [4, 5, 6]
[5,7,9]
zipWith
is right-lazy:
>>>
let f = undefined
>>>
zipWith f [] undefined
[]
zipWith
is capable of list fusion, but it is restricted to its
first list argument and its resulting list.
unzip :: [(a, b)] -> ([a], [b]) #
unzip
transforms a list of pairs into a list of first components
and a list of second components.
>>>
unzip []
([],[])>>>
unzip [(1, 'a'), (2, 'b')]
([1,2],"ab")
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]
[]
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.
\(\mathcal{O}(1)\). Extract the elements after the head of a list, which must be non-empty.
>>>
tail [1, 2, 3]
[2,3]>>>
tail [1]
[]>>>
tail []
*** Exception: Prelude.tail: empty list
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 (
when take
n xs, drop
n xs)n
is not _|_
(splitAt _|_ xs = _|_
).
splitAt
is an instance of the more general genericSplitAt
,
in which n
may be of any integral type.
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])
scanr1 :: (a -> a -> a) -> [a] -> [a] #
\(\mathcal{O}(n)\). scanr1
is a variant of scanr
that has no starting
value argument.
>>>
scanr1 (+) [1..4]
[10,9,7,4]>>>
scanr1 (+) []
[]>>>
scanr1 (-) [1..4]
[-2,3,-1,4]>>>
scanr1 (&&) [True, False, True, True]
[False,False,True,True]>>>
scanr1 (||) [True, True, False, False]
[True,True,False,False]>>>
force $ scanr1 (+) [1..]
*** Exception: stack overflow
scanr :: (a -> b -> b) -> b -> [a] -> [b] #
\(\mathcal{O}(n)\). scanr
is the right-to-left dual of scanl
. Note that the order of parameters on the accumulating function are reversed compared to scanl
.
Also note that
head (scanr f z xs) == foldr f z xs.
>>>
scanr (+) 0 [1..4]
[10,9,7,4,0]>>>
scanr (+) 42 []
[42]>>>
scanr (-) 100 [1..4]
[98,-97,99,-96,100]>>>
scanr (\nextChar reversedString -> nextChar : reversedString) "foo" ['a', 'b', 'c', 'd']
["abcdfoo","bcdfoo","cdfoo","dfoo","foo"]>>>
force $ scanr (+) 0 [1..]
*** Exception: stack overflow
scanl1 :: (a -> a -> a) -> [a] -> [a] #
\(\mathcal{O}(n)\). scanl1
is a variant of scanl
that has no starting
value argument:
scanl1 f [x1, x2, ...] == [x1, x1 `f` x2, ...]
>>>
scanl1 (+) [1..4]
[1,3,6,10]>>>
scanl1 (+) []
[]>>>
scanl1 (-) [1..4]
[1,-1,-4,-8]>>>
scanl1 (&&) [True, False, True, True]
[True,False,False,False]>>>
scanl1 (||) [False, False, True, True]
[False,False,True,True]>>>
scanl1 (+) [1..]
* Hangs forever *
scanl :: (b -> a -> b) -> b -> [a] -> [b] #
\(\mathcal{O}(n)\). 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
>>>
scanl (+) 0 [1..4]
[0,1,3,6,10]>>>
scanl (+) 42 []
[42]>>>
scanl (-) 100 [1..4]
[100,99,97,94,90]>>>
scanl (\reversedString nextChar -> nextChar : reversedString) "foo" ['a', 'b', 'c', 'd']
["foo","afoo","bafoo","cbafoo","dcbafoo"]>>>
scanl (+) 0 [1..]
* Hangs forever *
reverse
xs
returns the elements of xs
in reverse order.
xs
must be finite.
>>>
reverse []
[]>>>
reverse [42]
[42]>>>
reverse [2,5,7]
[7,5,2]>>>
reverse [1..]
* Hangs forever *
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.
>>>
replicate 0 True
[]>>>
replicate (-1) True
[]>>>
replicate 4 True
[True,True,True,True]
repeat
x
is an infinite list, with x
the value of every element.
>>>
take 20 $ repeat 17
[17,17,17,17,17,17,17,17,17...
lookup :: Eq a => a -> [(a, b)] -> Maybe b #
\(\mathcal{O}(n)\). lookup
key assocs
looks up a key in an association
list.
>>>
lookup 2 []
Nothing>>>
lookup 2 [(1, "first")]
Nothing>>>
lookup 2 [(1, "first"), (2, "second"), (3, "third")]
Just "second"
\(\mathcal{O}(n)\). Extract the last element of a list, which must be finite and non-empty.
>>>
last [1, 2, 3]
3>>>
last [1..]
* Hangs forever *>>>
last []
*** Exception: Prelude.last: empty list
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.
>>>
take 10 $ iterate not True
[True,False,True,False...>>>
take 10 $ iterate (+3) 42
[42,45,48,51,54,57,60,63...
\(\mathcal{O}(n)\). Return all the elements of a list except the last one. The list must be non-empty.
>>>
init [1, 2, 3]
[1,2]>>>
init [1]
[]>>>
init []
*** Exception: Prelude.init: empty list
\(\mathcal{O}(1)\). Extract the first element of a list, which must be non-empty.
>>>
head [1, 2, 3]
1>>>
head [1..]
1>>>
head []
*** Exception: Prelude.head: empty list
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.
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.
>>>
cycle []
*** Exception: Prelude.cycle: empty list>>>
take 20 $ cycle [42]
[42,42,42,42,42,42,42,42,42,42...>>>
take 20 $ cycle [2, 5, 7]
[2,5,7,2,5,7,2,5,7,2,5,7...
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],[])
(!!) :: [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.
>>>
['a', 'b', 'c'] !! 0
'a'>>>
['a', 'b', 'c'] !! 2
'c'>>>
['a', 'b', 'c'] !! 3
*** Exception: Prelude.!!: index too large>>>
['a', 'b', 'c'] !! (-1)
*** Exception: Prelude.!!: negative index
maybeToList :: Maybe a -> [a] #
The maybeToList
function returns an empty list when given
Nothing
or a singleton list when given Just
.
Examples
Basic usage:
>>>
maybeToList (Just 7)
[7]
>>>
maybeToList Nothing
[]
One can use maybeToList
to avoid pattern matching when combined
with a function that (safely) works on lists:
>>>
import Text.Read ( readMaybe )
>>>
sum $ maybeToList (readMaybe "3")
3>>>
sum $ maybeToList (readMaybe "")
0
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
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
""
mapMaybe :: (a -> Maybe b) -> [a] -> [b] #
The mapMaybe
function is a version of map
which can throw
out elements. In particular, the functional argument returns
something of type
. If this is Maybe
bNothing
, no element
is added on to the result list. If it is
, then Just
bb
is
included in the result list.
Examples
Using
is a shortcut for mapMaybe
f x
in most cases:catMaybes
$ map
f x
>>>
import Text.Read ( readMaybe )
>>>
let readMaybeInt = readMaybe :: String -> Maybe Int
>>>
mapMaybe readMaybeInt ["1", "Foo", "3"]
[1,3]>>>
catMaybes $ map readMaybeInt ["1", "Foo", "3"]
[1,3]
If we map the Just
constructor, the entire list should be returned:
>>>
mapMaybe Just [1,2,3]
[1,2,3]
listToMaybe :: [a] -> Maybe a #
The listToMaybe
function returns Nothing
on an empty list
or
where Just
aa
is the first element of the list.
Examples
Basic usage:
>>>
listToMaybe []
Nothing
>>>
listToMaybe [9]
Just 9
>>>
listToMaybe [1,2,3]
Just 1
Composing maybeToList
with listToMaybe
should be the identity
on singleton/empty lists:
>>>
maybeToList $ listToMaybe [5]
[5]>>>
maybeToList $ listToMaybe []
[]
But not on lists with more than one element:
>>>
maybeToList $ listToMaybe [1,2,3]
[1]
fromMaybe :: a -> Maybe a -> a #
The fromMaybe
function takes a default value and a Maybe
value. If the Maybe
is Nothing
, it returns the default value;
otherwise, it returns the value contained in the Maybe
.
Examples
Basic usage:
>>>
fromMaybe "" (Just "Hello, World!")
"Hello, World!"
>>>
fromMaybe "" Nothing
""
Read an integer from a string using readMaybe
. If we fail to
parse an integer, we want to return 0
by default:
>>>
import Text.Read ( readMaybe )
>>>
fromMaybe 0 (readMaybe "5")
5>>>
fromMaybe 0 (readMaybe "")
0
fromJust :: HasCallStack => Maybe a -> a #
catMaybes :: [Maybe a] -> [a] #
The catMaybes
function takes a list of Maybe
s and returns
a list of all the Just
values.
Examples
Basic usage:
>>>
catMaybes [Just 1, Nothing, Just 3]
[1,3]
When constructing a list of Maybe
values, catMaybes
can be used
to return all of the "success" results (if the list is the result
of a map
, then mapMaybe
would be more appropriate):
>>>
import Text.Read ( readMaybe )
>>>
[readMaybe x :: Maybe Int | x <- ["1", "Foo", "3"] ]
[Just 1,Nothing,Just 3]>>>
catMaybes $ [readMaybe x :: Maybe Int | x <- ["1", "Foo", "3"] ]
[1,3]
void :: Functor f => f a -> f () #
discards or ignores the result of evaluation, such
as the return value of an void
valueIO
action.
Examples
Replace the contents of a
with unit:Maybe
Int
>>>
void Nothing
Nothing>>>
void (Just 3)
Just ()
Replace the contents of an
with unit, resulting in an Either
Int
Int
:Either
Int
()
>>>
void (Left 8675309)
Left 8675309>>>
void (Right 8675309)
Right ()
Replace every element of a list with unit:
>>>
void [1,2,3]
[(),(),()]
Replace the second element of a pair with unit:
>>>
void (1,2)
(1,())
Discard the result of an IO
action:
>>>
mapM print [1,2]
1 2 [(),()]>>>
void $ mapM print [1,2]
1 2
uncurry :: (a -> b -> c) -> (a, b) -> c #
uncurry
converts a curried function to a function on pairs.
Examples
>>>
uncurry (+) (1,2)
3
>>>
uncurry ($) (show, 1)
"1"
>>>
map (uncurry max) [(1,2), (3,4), (6,8)]
[2,4,8]
when :: Applicative f => Bool -> f () -> f () #
Conditional execution of Applicative
expressions. For example,
when debug (putStrLn "Debugging")
will output the string Debugging
if the Boolean value debug
is True
, and otherwise do nothing.
until :: (a -> Bool) -> (a -> a) -> a -> a #
yields the result of applying until
p ff
until p
holds.
liftM5 :: Monad m => (a1 -> a2 -> a3 -> a4 -> a5 -> r) -> m a1 -> m a2 -> m a3 -> m a4 -> m a5 -> m r #
Promote a function to a monad, scanning the monadic arguments from
left to right (cf. liftM2
).
liftM4 :: Monad m => (a1 -> a2 -> a3 -> a4 -> r) -> m a1 -> m a2 -> m a3 -> m a4 -> m r #
Promote a function to a monad, scanning the monadic arguments from
left to right (cf. liftM2
).
liftM3 :: Monad m => (a1 -> a2 -> a3 -> r) -> m a1 -> m a2 -> m a3 -> m r #
Promote a function to a monad, scanning the monadic arguments from
left to right (cf. liftM2
).
liftM2 :: Monad m => (a1 -> a2 -> r) -> m a1 -> m a2 -> m r #
Promote a function to a monad, scanning the monadic arguments from left to right. For example,
liftM2 (+) [0,1] [0,2] = [0,2,1,3] liftM2 (+) (Just 1) Nothing = Nothing
flip :: (a -> b -> c) -> b -> a -> c #
takes its (first) two arguments in the reverse order of flip
ff
.
>>>
flip (++) "hello" "world"
"worldhello"
(=<<) :: Monad m => (a -> m b) -> m a -> m b infixr 1 #
Same as >>=
, but with the arguments interchanged.
($!) :: forall (r :: RuntimeRep) a (b :: TYPE r). (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.
undefined :: forall (r :: RuntimeRep) (a :: TYPE r). HasCallStack => a #
errorWithoutStackTrace :: forall (r :: RuntimeRep) (a :: TYPE r). [Char] -> a #
A variant of error
that does not produce a stack trace.
Since: base-4.9.0.0
error :: forall (r :: RuntimeRep) (a :: TYPE r). HasCallStack => [Char] -> a #
error
stops execution and displays an error message.
data SomeException #
The SomeException
type is the root of the exception type hierarchy.
When an exception of type e
is thrown, behind the scenes it is
encapsulated in a SomeException
.
Instances
A CI s
provides Case Insensitive comparison for the string-like type
s
(for example: String
, Text
, ByteString
, etc.).
Note that CI s
has an instance for IsString
which together with the
OverloadedStrings
language extension allows you to write case insensitive
string literals as in:
> ("Content-Type" ::CI
Text
) == ("CONTENT-TYPE" ::CI
Text
) True
Instances
ToByteString a => ToByteString (CI a) Source # | |
Defined in Amazonka.Data.ByteString Methods toBS :: CI a -> ByteString Source # | |
ToLog a => ToLog (CI a) Source # | |
Defined in Amazonka.Data.Log Methods build :: CI a -> ByteStringBuilder Source # | |
ToLog [Header] Source # | |
Defined in Amazonka.Data.Log Methods build :: [Header] -> ByteStringBuilder Source # | |
(FoldCase a, FromText a) => FromText (CI a) Source # | |
ToText a => ToText (CI a) Source # | |
Data s => Data (CI s) | |
Defined in Data.CaseInsensitive.Internal Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> CI s -> c (CI s) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (CI s) # dataTypeOf :: CI s -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (CI s)) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (CI s)) # gmapT :: (forall b. Data b => b -> b) -> CI s -> CI s # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> CI s -> r # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> CI s -> r # gmapQ :: (forall d. Data d => d -> u) -> CI s -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> CI s -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> CI s -> m (CI s) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> CI s -> m (CI s) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> CI s -> m (CI s) # | |
(IsString s, FoldCase s) => IsString (CI s) | |
Defined in Data.CaseInsensitive.Internal Methods fromString :: String -> CI s # | |
Monoid s => Monoid (CI s) | |
Semigroup s => Semigroup (CI s) | |
(Read s, FoldCase s) => Read (CI s) | |
Show s => Show (CI s) | |
FoldCase (CI s) | |
Defined in Data.CaseInsensitive.Internal | |
NFData s => NFData (CI s) | |
Defined in Data.CaseInsensitive.Internal | |
Eq s => Eq (CI s) | |
Ord s => Ord (CI s) | |
Hashable s => Hashable (CI s) | |
Defined in Data.CaseInsensitive.Internal |
class MonadIO m => MonadResource (m :: Type -> Type) #
A Monad
which allows for safe resource allocation. In theory, any monad
transformer stack which includes a ResourceT
can be an instance of
MonadResource
.
Note: runResourceT
has a requirement for a MonadUnliftIO m
monad,
which allows control operations to be lifted. A MonadResource
does not
have this requirement. This means that transformers such as ContT
can be
an instance of MonadResource
. However, the ContT
wrapper will need to be
unwrapped before calling runResourceT
.
Since 0.3.0
Minimal complete definition
Instances
class MonadTrans (t :: (Type -> Type) -> Type -> Type) where #
The class of monad transformers. Instances should satisfy the
following laws, which state that lift
is a monad transformation:
Methods
lift :: Monad m => m a -> t m a #
Lift a computation from the argument monad to the constructed monad.
Instances
MonadTrans Free | This is not a true monad transformer. It is only a monad transformer "up to |
Defined in Control.Monad.Free | |
MonadTrans Yoneda | |
Defined in Data.Functor.Yoneda | |
MonadTrans ResourceT | |
Defined in Control.Monad.Trans.Resource.Internal | |
Alternative f => MonadTrans (CofreeT f) | |
Defined in Control.Comonad.Trans.Cofree | |
Functor f => MonadTrans (FreeT f) | |
Defined in Control.Monad.Trans.Free | |
MonadTrans (ErrorT e) | |
Defined in Control.Monad.Trans.Error | |
MonadTrans (ExceptT e) | |
Defined in Control.Monad.Trans.Except | |
MonadTrans (ConduitT i o) | |
Defined in Data.Conduit.Internal.Conduit | |
MonadTrans (Pipe l i o u) | |
Defined in Data.Conduit.Internal.Pipe |
This is a length of time, as measured by a clock.
Conversion functions such as fromInteger
and realToFrac
will treat it as seconds.
For example, (0.010 :: DiffTime)
corresponds to 10 milliseconds.
It has a precision of one picosecond (= 10^-12 s). Enumeration functions will treat it as picoseconds.
Instances
FromJSON DiffTime | This instance includes a bounds check to prevent maliciously
large inputs to fill up the memory of the target system. You can
newtype |
ToJSON DiffTime | |
Defined in Data.Aeson.Types.ToJSON | |
Data DiffTime | |
Defined in Data.Time.Clock.Internal.DiffTime Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> DiffTime -> c DiffTime # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c DiffTime # toConstr :: DiffTime -> Constr # dataTypeOf :: DiffTime -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c DiffTime) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c DiffTime) # gmapT :: (forall b. Data b => b -> b) -> DiffTime -> DiffTime # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> DiffTime -> r # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> DiffTime -> r # gmapQ :: (forall d. Data d => d -> u) -> DiffTime -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> DiffTime -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> DiffTime -> m DiffTime # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> DiffTime -> m DiffTime # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> DiffTime -> m DiffTime # | |
Enum DiffTime | |
Defined in Data.Time.Clock.Internal.DiffTime | |
Num DiffTime | |
Defined in Data.Time.Clock.Internal.DiffTime | |
Read DiffTime | |
Fractional DiffTime | |
Real DiffTime | |
Defined in Data.Time.Clock.Internal.DiffTime Methods toRational :: DiffTime -> Rational # | |
RealFrac DiffTime | |
Show DiffTime | |
NFData DiffTime | |
Defined in Data.Time.Clock.Internal.DiffTime | |
Eq DiffTime | |
Ord DiffTime | |
Defined in Data.Time.Clock.Internal.DiffTime |
A class of types that can be fully evaluated.
Since: deepseq-1.1.0.0
Minimal complete definition
Nothing
Methods
rnf
should reduce its argument to normal form (that is, fully
evaluate all sub-components), and then return ()
.
Generic
NFData
deriving
Starting with GHC 7.2, you can automatically derive instances
for types possessing a Generic
instance.
Note: Generic1
can be auto-derived starting with GHC 7.4
{-# LANGUAGE DeriveGeneric #-} import GHC.Generics (Generic, Generic1) import Control.DeepSeq data Foo a = Foo a String deriving (Eq, Generic, Generic1) instance NFData a => NFData (Foo a) instance NFData1 Foo data Colour = Red | Green | Blue deriving Generic instance NFData Colour
Starting with GHC 7.10, the example above can be written more
concisely by enabling the new DeriveAnyClass
extension:
{-# LANGUAGE DeriveGeneric, DeriveAnyClass #-} import GHC.Generics (Generic) import Control.DeepSeq data Foo a = Foo a String deriving (Eq, Generic, Generic1, NFData, NFData1) data Colour = Red | Green | Blue deriving (Generic, NFData)
Compatibility with previous deepseq
versions
Prior to version 1.4.0.0, the default implementation of the rnf
method was defined as
rnf
a =seq
a ()
However, starting with deepseq-1.4.0.0
, the default
implementation is based on DefaultSignatures
allowing for
more accurate auto-derived NFData
instances. If you need the
previously used exact default rnf
method implementation
semantics, use
instance NFData Colour where rnf x = seq x ()
or alternatively
instance NFData Colour where rnf = rwhnf
or
{-# LANGUAGE BangPatterns #-} instance NFData Colour where rnf !_ = ()
Instances
A set of values. A set cannot contain duplicate values.
Instances
ToJSON1 HashSet | |
Defined in Data.Aeson.Types.ToJSON Methods liftToJSON :: (a -> Value) -> ([a] -> Value) -> HashSet a -> Value # liftToJSONList :: (a -> Value) -> ([a] -> Value) -> [HashSet a] -> Value # liftToEncoding :: (a -> Encoding) -> ([a] -> Encoding) -> HashSet a -> Encoding # liftToEncodingList :: (a -> Encoding) -> ([a] -> Encoding) -> [HashSet a] -> Encoding # | |
Foldable HashSet | |
Defined in Data.HashSet.Internal Methods fold :: Monoid m => HashSet m -> m # foldMap :: Monoid m => (a -> m) -> HashSet a -> m # foldMap' :: Monoid m => (a -> m) -> HashSet a -> m # foldr :: (a -> b -> b) -> b -> HashSet a -> b # foldr' :: (a -> b -> b) -> b -> HashSet a -> b # foldl :: (b -> a -> b) -> b -> HashSet a -> b # foldl' :: (b -> a -> b) -> b -> HashSet a -> b # foldr1 :: (a -> a -> a) -> HashSet a -> a # foldl1 :: (a -> a -> a) -> HashSet a -> a # elem :: Eq a => a -> HashSet a -> Bool # maximum :: Ord a => HashSet a -> a # minimum :: Ord a => HashSet a -> a # | |
Eq1 HashSet | |
Ord1 HashSet | |
Defined in Data.HashSet.Internal | |
Show1 HashSet | |
NFData1 HashSet | Since: unordered-containers-0.2.14.0 |
Defined in Data.HashSet.Internal | |
Hashable1 HashSet | |
Defined in Data.HashSet.Internal | |
Lift a => Lift (HashSet a :: TYPE LiftedRep) | Since: unordered-containers-0.2.17.0 |
(Eq a, Hashable a, FromJSON a) => FromJSON (HashSet a) | |
ToJSON a => ToJSON (HashSet a) | |
Defined in Data.Aeson.Types.ToJSON | |
(Data a, Eq a, Hashable a) => Data (HashSet a) | |
Defined in Data.HashSet.Internal Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> HashSet a -> c (HashSet a) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (HashSet a) # toConstr :: HashSet a -> Constr # dataTypeOf :: HashSet a -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (HashSet a)) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (HashSet a)) # gmapT :: (forall b. Data b => b -> b) -> HashSet a -> HashSet a # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> HashSet a -> r # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> HashSet a -> r # gmapQ :: (forall d. Data d => d -> u) -> HashSet a -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> HashSet a -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> HashSet a -> m (HashSet a) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> HashSet a -> m (HashSet a) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> HashSet a -> m (HashSet a) # | |
(Hashable a, Eq a) => Monoid (HashSet a) | \(O(n+m)\) To obtain good performance, the smaller set must be presented as the first argument. Examples
|
(Hashable a, Eq a) => Semigroup (HashSet a) | \(O(n+m)\) To obtain good performance, the smaller set must be presented as the first argument. Examples
|
(Eq a, Hashable a) => IsList (HashSet a) | |
(Eq a, Hashable a, Read a) => Read (HashSet a) | |
Show a => Show (HashSet a) | |
NFData a => NFData (HashSet a) | |
Defined in Data.HashSet.Internal | |
Eq a => Eq (HashSet a) | Note that, in the presence of hash collisions, equal
In general, the lack of substitutivity can be observed with any function that depends on the key ordering, such as folds and traversals. |
Ord a => Ord (HashSet a) | |
Hashable a => Hashable (HashSet a) | |
Defined in Data.HashSet.Internal | |
(Eq k, Hashable k) => At (HashSet k) | |
(Eq a, Hashable a) => Contains (HashSet a) | |
(Eq k, Hashable k) => Ixed (HashSet k) | |
Defined in Control.Lens.At | |
(Hashable a, Eq a) => Wrapped (HashSet a) | |
(Eq v, Hashable v) => GrowingAppend (HashSet v) | |
Defined in Data.MonoTraversable | |
MonoFoldable (HashSet e) | |
Defined in Data.MonoTraversable Methods ofoldMap :: Monoid m => (Element (HashSet e) -> m) -> HashSet e -> m # ofoldr :: (Element (HashSet e) -> b -> b) -> b -> HashSet e -> b # ofoldl' :: (a -> Element (HashSet e) -> a) -> a -> HashSet e -> a # otoList :: HashSet e -> [Element (HashSet e)] # oall :: (Element (HashSet e) -> Bool) -> HashSet e -> Bool # oany :: (Element (HashSet e) -> Bool) -> HashSet e -> Bool # olength64 :: HashSet e -> Int64 # ocompareLength :: Integral i => HashSet e -> i -> Ordering # otraverse_ :: Applicative f => (Element (HashSet e) -> f b) -> HashSet e -> f () # ofor_ :: Applicative f => HashSet e -> (Element (HashSet e) -> f b) -> f () # omapM_ :: Applicative m => (Element (HashSet e) -> m ()) -> HashSet e -> m () # oforM_ :: Applicative m => HashSet e -> (Element (HashSet e) -> m ()) -> m () # ofoldlM :: Monad m => (a -> Element (HashSet e) -> m a) -> a -> HashSet e -> m a # ofoldMap1Ex :: Semigroup m => (Element (HashSet e) -> m) -> HashSet e -> m # ofoldr1Ex :: (Element (HashSet e) -> Element (HashSet e) -> Element (HashSet e)) -> HashSet e -> Element (HashSet e) # ofoldl1Ex' :: (Element (HashSet e) -> Element (HashSet e) -> Element (HashSet e)) -> HashSet e -> Element (HashSet e) # headEx :: HashSet e -> Element (HashSet e) # lastEx :: HashSet e -> Element (HashSet e) # unsafeHead :: HashSet e -> Element (HashSet e) # unsafeLast :: HashSet e -> Element (HashSet e) # maximumByEx :: (Element (HashSet e) -> Element (HashSet e) -> Ordering) -> HashSet e -> Element (HashSet e) # minimumByEx :: (Element (HashSet e) -> Element (HashSet e) -> Ordering) -> HashSet e -> Element (HashSet e) # | |
Hashable a => MonoPointed (HashSet a) | |
(t ~ HashSet a', Hashable a, Eq a) => Rewrapped (HashSet a) t | Use |
Defined in Control.Lens.Wrapped | |
type Item (HashSet a) | |
Defined in Data.HashSet.Internal | |
type Index (HashSet a) | |
Defined in Control.Lens.At | |
type IxValue (HashSet k) | |
Defined in Control.Lens.At | |
type Unwrapped (HashSet a) | |
Defined in Control.Lens.Wrapped | |
type Element (HashSet e) | |
Defined in Data.MonoTraversable |
type Traversal' s a = Traversal s s a a #
typeTraversal'
=Simple
Traversal
data NominalDiffTime #
This is a length of time, as measured by UTC. It has a precision of 10^-12 s.
Conversion functions such as fromInteger
and realToFrac
will treat it as seconds.
For example, (0.010 :: NominalDiffTime)
corresponds to 10 milliseconds.
It has a precision of one picosecond (= 10^-12 s). Enumeration functions will treat it as picoseconds.
It ignores leap-seconds, so it's not necessarily a fixed amount of clock time. For instance, 23:00 UTC + 2 hours of NominalDiffTime = 01:00 UTC (+ 1 day), regardless of whether a leap-second intervened.
Instances
The Modified Julian Day is a standard count of days, with zero being the day 1858-11-17.
Instances
FromJSON Day | |
FromJSONKey Day | |
Defined in Data.Aeson.Types.FromJSON | |
ToJSON Day | |
Defined in Data.Aeson.Types.ToJSON | |
ToJSONKey Day | |
Defined in Data.Aeson.Types.ToJSON | |
Data Day | |
Defined in Data.Time.Calendar.Days Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Day -> c Day # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Day # dataTypeOf :: Day -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c Day) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Day) # gmapT :: (forall b. Data b => b -> b) -> Day -> Day # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Day -> r # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Day -> r # gmapQ :: (forall d. Data d => d -> u) -> Day -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> Day -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Day -> m Day # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Day -> m Day # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Day -> m Day # | |
Enum Day | |
Ix Day | |
NFData Day | |
Defined in Data.Time.Calendar.Days | |
Eq Day | |
Ord Day | |
type TextBuilder = Builder Source #
type ByteStringLazy = ByteString Source #
type ByteStringBuilder = Builder Source #