Safe Haskell	Trustworthy
Language	Haskell2010

Control.Foldl

Contents

Fold Types
Folding
Folds
Generic Folds
Container folds
Utilities
Re-exports

Description

This module provides efficient and streaming left folds that you can combine using Applicative style.

Import this module qualified to avoid clashing with the Prelude:

>>> import qualified Control.Foldl as Foldl

Use fold to apply a Fold to a list:

>>> Foldl.fold Foldl.sum [1..100]
5050

Folds are Applicatives, so you can combine them using Applicative combinators:

>>> import Control.Applicative
>>> let average = (/) <$> Foldl.sum <*> Foldl.genericLength

… or you can use do notation if you enable the ApplicativeDo language extension:

>>> :set -XApplicativeDo
>>> let average = do total <- Foldl.sum; count <- Foldl.genericLength; return (total / count)

… or you can use the fact that the Fold type implements Num to do this:

>>> let average = Foldl.sum / Foldl.genericLength

These combined folds will still traverse the list only once, streaming efficiently over the list in constant space without space leaks:

>>> Foldl.fold average [1..10000000]
5000000.5
>>> Foldl.fold ((,) <$> Foldl.minimum <*> Foldl.maximum) [1..10000000]
(Just 1,Just 10000000)

You might want to try enabling the -flate-dmd-anal flag when compiling executables that use this library to further improve performance.

Synopsis

data Fold a b = forall x. Fold (x -> a -> x) x (x -> b)
data FoldM m a b = forall x. FoldM (x -> a -> m x) (m x) (x -> m b)
fold :: Foldable f => Fold a b -> f a -> b
foldM :: (Foldable f, Monad m) => FoldM m a b -> f a -> m b
scan :: Fold a b -> [a] -> [b]
prescan :: Traversable t => Fold a b -> t a -> t b
postscan :: Traversable t => Fold a b -> t a -> t b
mconcat :: Monoid a => Fold a a
foldMap :: Monoid w => (a -> w) -> (w -> b) -> Fold a b
head :: Fold a (Maybe a)
last :: Fold a (Maybe a)
lastDef :: a -> Fold a a
lastN :: Int -> Fold a [a]
null :: Fold a Bool
length :: Fold a Int
and :: Fold Bool Bool
or :: Fold Bool Bool
all :: (a -> Bool) -> Fold a Bool
any :: (a -> Bool) -> Fold a Bool
sum :: Num a => Fold a a
product :: Num a => Fold a a
mean :: Fractional a => Fold a a
variance :: Fractional a => Fold a a
std :: Floating a => Fold a a
maximum :: Ord a => Fold a (Maybe a)
maximumBy :: (a -> a -> Ordering) -> Fold a (Maybe a)
minimum :: Ord a => Fold a (Maybe a)
minimumBy :: (a -> a -> Ordering) -> Fold a (Maybe a)
elem :: Eq a => a -> Fold a Bool
notElem :: Eq a => a -> Fold a Bool
find :: (a -> Bool) -> Fold a (Maybe a)
index :: Int -> Fold a (Maybe a)
lookup :: Eq a => a -> Fold (a, b) (Maybe b)
elemIndex :: Eq a => a -> Fold a (Maybe Int)
findIndex :: (a -> Bool) -> Fold a (Maybe Int)
random :: FoldM IO a (Maybe a)
randomN :: Vector v a => Int -> FoldM IO a (Maybe (v a))
mapM_ :: Monad m => (a -> m ()) -> FoldM m a ()
sink :: (Monoid w, Monad m) => (a -> m w) -> FoldM m a w
genericLength :: Num b => Fold a b
genericIndex :: Integral i => i -> Fold a (Maybe a)
list :: Fold a [a]
revList :: Fold a [a]
nub :: Ord a => Fold a [a]
eqNub :: Eq a => Fold a [a]
set :: Ord a => Fold a (Set a)
hashSet :: (Eq a, Hashable a) => Fold a (HashSet a)
map :: Ord a => Fold (a, b) (Map a b)
foldByKeyMap :: forall k a b. Ord k => Fold a b -> Fold (k, a) (Map k b)
hashMap :: (Eq a, Hashable a) => Fold (a, b) (HashMap a b)
foldByKeyHashMap :: forall k a b. (Hashable k, Eq k) => Fold a b -> Fold (k, a) (HashMap k b)
vector :: Vector v a => Fold a (v a)
vectorM :: (PrimMonad m, Vector v a) => FoldM m a (v a)
purely :: (forall x. (x -> a -> x) -> x -> (x -> b) -> r) -> Fold a b -> r
purely_ :: (forall x. (x -> a -> x) -> x -> x) -> Fold a b -> b
impurely :: (forall x. (x -> a -> m x) -> m x -> (x -> m b) -> r) -> FoldM m a b -> r
impurely_ :: Monad m => (forall x. (x -> a -> m x) -> m x -> m x) -> FoldM m a b -> m b
generalize :: Monad m => Fold a b -> FoldM m a b
simplify :: FoldM Identity a b -> Fold a b
hoists :: (forall x. m x -> n x) -> FoldM m a b -> FoldM n a b
duplicateM :: Applicative m => FoldM m a b -> FoldM m a (FoldM m a b)
_Fold1 :: (a -> a -> a) -> Fold a (Maybe a)
premap :: (a -> b) -> Fold b r -> Fold a r
premapM :: Monad m => (a -> m b) -> FoldM m b r -> FoldM m a r
prefilter :: (a -> Bool) -> Fold a r -> Fold a r
prefilterM :: Monad m => (a -> m Bool) -> FoldM m a r -> FoldM m a r
predropWhile :: (a -> Bool) -> Fold a r -> Fold a r
drop :: Natural -> Fold a b -> Fold a b
dropM :: Monad m => Natural -> FoldM m a b -> FoldM m a b
type Handler a b = forall x. (b -> Const (Dual (Endo x)) b) -> a -> Const (Dual (Endo x)) a
handles :: Handler a b -> Fold b r -> Fold a r
foldOver :: Handler s a -> Fold a b -> s -> b
newtype EndoM m a = EndoM {
- appEndoM :: a -> m a
}
type HandlerM m a b = forall x. (b -> Const (Dual (EndoM m x)) b) -> a -> Const (Dual (EndoM m x)) a
handlesM :: HandlerM m a b -> FoldM m b r -> FoldM m a r
foldOverM :: Monad m => HandlerM m s a -> FoldM m a b -> s -> m b
folded :: (Contravariant f, Applicative f, Foldable t) => (a -> f a) -> t a -> f (t a)
filtered :: Monoid m => (a -> Bool) -> (a -> m) -> a -> m
groupBy :: Ord g => (a -> g) -> Fold a r -> Fold a (Map g r)
either :: Fold a1 b1 -> Fold a2 b2 -> Fold (Either a1 a2) (b1, b2)
eitherM :: Monad m => FoldM m a1 b1 -> FoldM m a2 b2 -> FoldM m (Either a1 a2) (b1, b2)
nest :: Applicative f => Fold a b -> Fold (f a) (f b)
data RealWorld
class Monad m => PrimMonad (m :: Type -> Type)
class Foldable (t :: TYPE LiftedRep -> Type)
type family Mutable (v :: Type -> Type) = (mv :: Type -> Type -> Type) | mv -> v
class MVector (Mutable v) a => Vector (v :: Type -> Type) a

Fold Types

data Fold a b Source #

Efficient representation of a left fold that preserves the fold's step function, initial accumulator, and extraction function

This allows the Applicative instance to assemble derived folds that traverse the container only once

A 'Fold a b' processes elements of type a and results in a value of type b.

Constructors

forall x. Fold (x -> a -> x) x (x -> b)

Fold step initial extract

Instances

Instances details

Choice Fold Source #
Instance details Defined in Control.Foldl Methods left' :: Fold a b -> Fold (Either a c) (Either b c) # right' :: Fold a b -> Fold (Either c a) (Either c b) #
Profunctor Fold Source #
Instance details Defined in Control.Foldl Methods dimap :: (a -> b) -> (c -> d) -> Fold b c -> Fold a d # lmap :: (a -> b) -> Fold b c -> Fold a c # rmap :: (b -> c) -> Fold a b -> Fold a c # (#.) :: forall a b c q. Coercible c b => q b c -> Fold a b -> Fold a c # (.#) :: forall a b c q. Coercible b a => Fold b c -> q a b -> Fold a c #
Semigroupoid Fold Source #
Instance details Defined in Control.Foldl Methods o :: forall (j :: k) (k1 :: k) (i :: k). Fold j k1 -> Fold i j -> Fold i k1 #
Applicative (Fold a) Source #
Instance details Defined in Control.Foldl Methods pure :: a0 -> Fold a a0 # (<>) :: Fold a (a0 -> b) -> Fold a a0 -> Fold a b # liftA2 :: (a0 -> b -> c) -> Fold a a0 -> Fold a b -> Fold a c # (>) :: Fold a a0 -> Fold a b -> Fold a b # (<*) :: Fold a a0 -> Fold a b -> Fold a a0 #
Functor (Fold a) Source #
Instance details Defined in Control.Foldl Methods fmap :: (a0 -> b) -> Fold a a0 -> Fold a b # (<$) :: a0 -> Fold a b -> Fold a a0 #
Comonad (Fold a) Source #
Instance details Defined in Control.Foldl Methods extract :: Fold a a0 -> a0 # duplicate :: Fold a a0 -> Fold a (Fold a a0) # extend :: (Fold a a0 -> b) -> Fold a a0 -> Fold a b #
Extend (Fold a) Source #
Instance details Defined in Control.Foldl Methods duplicated :: Fold a a0 -> Fold a (Fold a a0) # extended :: (Fold a a0 -> b) -> Fold a a0 -> Fold a b #
Monoid b => Monoid (Fold a b) Source #
Instance details Defined in Control.Foldl Methods mempty :: Fold a b # mappend :: Fold a b -> Fold a b -> Fold a b # mconcat :: [Fold a b] -> Fold a b #
Semigroup b => Semigroup (Fold a b) Source #
Instance details Defined in Control.Foldl Methods (<>) :: Fold a b -> Fold a b -> Fold a b # sconcat :: NonEmpty (Fold a b) -> Fold a b # stimes :: Integral b0 => b0 -> Fold a b -> Fold a b #
Floating b => Floating (Fold a b) Source #
Instance details Defined in Control.Foldl Methods pi :: Fold a b # exp :: Fold a b -> Fold a b # log :: Fold a b -> Fold a b # sqrt :: Fold a b -> Fold a b # (**) :: Fold a b -> Fold a b -> Fold a b # logBase :: Fold a b -> Fold a b -> Fold a b # sin :: Fold a b -> Fold a b # cos :: Fold a b -> Fold a b # tan :: Fold a b -> Fold a b # asin :: Fold a b -> Fold a b # acos :: Fold a b -> Fold a b # atan :: Fold a b -> Fold a b # sinh :: Fold a b -> Fold a b # cosh :: Fold a b -> Fold a b # tanh :: Fold a b -> Fold a b # asinh :: Fold a b -> Fold a b # acosh :: Fold a b -> Fold a b # atanh :: Fold a b -> Fold a b # log1p :: Fold a b -> Fold a b # expm1 :: Fold a b -> Fold a b # log1pexp :: Fold a b -> Fold a b # log1mexp :: Fold a b -> Fold a b #
Num b => Num (Fold a b) Source #
Instance details Defined in Control.Foldl Methods (+) :: Fold a b -> Fold a b -> Fold a b # (-) :: Fold a b -> Fold a b -> Fold a b # (*) :: Fold a b -> Fold a b -> Fold a b # negate :: Fold a b -> Fold a b # abs :: Fold a b -> Fold a b # signum :: Fold a b -> Fold a b # fromInteger :: Integer -> Fold a b #
Fractional b => Fractional (Fold a b) Source #
Instance details Defined in Control.Foldl Methods (/) :: Fold a b -> Fold a b -> Fold a b # recip :: Fold a b -> Fold a b # fromRational :: Rational -> Fold a b #

data FoldM m a b Source #

Like Fold, but monadic.

A 'FoldM m a b' processes elements of type a and results in a monadic value of type m b.

Constructors

forall x. FoldM (x -> a -> m x) (m x) (x -> m b)

FoldM step initial extract

Instances

Instances details

Functor m => Profunctor (FoldM m) Source #
Instance details Defined in Control.Foldl Methods dimap :: (a -> b) -> (c -> d) -> FoldM m b c -> FoldM m a d # lmap :: (a -> b) -> FoldM m b c -> FoldM m a c # rmap :: (b -> c) -> FoldM m a b -> FoldM m a c # (#.) :: forall a b c q. Coercible c b => q b c -> FoldM m a b -> FoldM m a c # (.#) :: forall a b c q. Coercible b a => FoldM m b c -> q a b -> FoldM m a c #
Applicative m => Applicative (FoldM m a) Source #
Instance details Defined in Control.Foldl Methods pure :: a0 -> FoldM m a a0 # (<>) :: FoldM m a (a0 -> b) -> FoldM m a a0 -> FoldM m a b # liftA2 :: (a0 -> b -> c) -> FoldM m a a0 -> FoldM m a b -> FoldM m a c # (>) :: FoldM m a a0 -> FoldM m a b -> FoldM m a b # (<*) :: FoldM m a a0 -> FoldM m a b -> FoldM m a a0 #
Functor m => Functor (FoldM m a) Source #
Instance details Defined in Control.Foldl Methods fmap :: (a0 -> b) -> FoldM m a a0 -> FoldM m a b # (<$) :: a0 -> FoldM m a b -> FoldM m a a0 #
Monad m => Extend (FoldM m a) Source #
Instance details Defined in Control.Foldl Methods duplicated :: FoldM m a a0 -> FoldM m a (FoldM m a a0) # extended :: (FoldM m a a0 -> b) -> FoldM m a a0 -> FoldM m a b #
(Monoid b, Monad m) => Monoid (FoldM m a b) Source #
Instance details Defined in Control.Foldl Methods mempty :: FoldM m a b # mappend :: FoldM m a b -> FoldM m a b -> FoldM m a b # mconcat :: [FoldM m a b] -> FoldM m a b #
(Semigroup b, Monad m) => Semigroup (FoldM m a b) Source #
Instance details Defined in Control.Foldl Methods (<>) :: FoldM m a b -> FoldM m a b -> FoldM m a b # sconcat :: NonEmpty (FoldM m a b) -> FoldM m a b # stimes :: Integral b0 => b0 -> FoldM m a b -> FoldM m a b #
(Monad m, Floating b) => Floating (FoldM m a b) Source #
Instance details Defined in Control.Foldl Methods pi :: FoldM m a b # exp :: FoldM m a b -> FoldM m a b # log :: FoldM m a b -> FoldM m a b # sqrt :: FoldM m a b -> FoldM m a b # (**) :: FoldM m a b -> FoldM m a b -> FoldM m a b # logBase :: FoldM m a b -> FoldM m a b -> FoldM m a b # sin :: FoldM m a b -> FoldM m a b # cos :: FoldM m a b -> FoldM m a b # tan :: FoldM m a b -> FoldM m a b # asin :: FoldM m a b -> FoldM m a b # acos :: FoldM m a b -> FoldM m a b # atan :: FoldM m a b -> FoldM m a b # sinh :: FoldM m a b -> FoldM m a b # cosh :: FoldM m a b -> FoldM m a b # tanh :: FoldM m a b -> FoldM m a b # asinh :: FoldM m a b -> FoldM m a b # acosh :: FoldM m a b -> FoldM m a b # atanh :: FoldM m a b -> FoldM m a b # log1p :: FoldM m a b -> FoldM m a b # expm1 :: FoldM m a b -> FoldM m a b # log1pexp :: FoldM m a b -> FoldM m a b # log1mexp :: FoldM m a b -> FoldM m a b #
(Monad m, Num b) => Num (FoldM m a b) Source #
Instance details Defined in Control.Foldl Methods (+) :: FoldM m a b -> FoldM m a b -> FoldM m a b # (-) :: FoldM m a b -> FoldM m a b -> FoldM m a b # (*) :: FoldM m a b -> FoldM m a b -> FoldM m a b # negate :: FoldM m a b -> FoldM m a b # abs :: FoldM m a b -> FoldM m a b # signum :: FoldM m a b -> FoldM m a b # fromInteger :: Integer -> FoldM m a b #
(Monad m, Fractional b) => Fractional (FoldM m a b) Source #
Instance details Defined in Control.Foldl Methods (/) :: FoldM m a b -> FoldM m a b -> FoldM m a b # recip :: FoldM m a b -> FoldM m a b # fromRational :: Rational -> FoldM m a b #

Folding

fold :: Foldable f => Fold a b -> f a -> b Source #

Apply a strict left Fold to a Foldable container

foldM :: (Foldable f, Monad m) => FoldM m a b -> f a -> m b Source #

Like fold, but monadic

scan :: Fold a b -> [a] -> [b] Source #

Convert a strict left Fold into a scan

>>> Foldl.scan Foldl.length [1..5]
[0,1,2,3,4,5]

prescan :: Traversable t => Fold a b -> t a -> t b Source #

Convert a Fold into a prescan for any Traversable type

"Prescan" means that the last element of the scan is not included

>>> Foldl.prescan Foldl.length [1..5]
[0,1,2,3,4]

postscan :: Traversable t => Fold a b -> t a -> t b Source #

Convert a Fold into a postscan for any Traversable type

"Postscan" means that the first element of the scan is not included

>>> Foldl.postscan Foldl.length [1..5]
[1,2,3,4,5]

Folds

mconcat :: Monoid a => Fold a a Source #

Fold all values within a container using mappend and mempty

foldMap :: Monoid w => (a -> w) -> (w -> b) -> Fold a b Source #

Convert a "foldMap" to a Fold

head :: Fold a (Maybe a) Source #

Get the first element of a container or return Nothing if the container is empty

last :: Fold a (Maybe a) Source #

Get the last element of a container or return Nothing if the container is empty

lastDef :: a -> Fold a a Source #

Get the last element of a container or return a default value if the container is empty

lastN :: Int -> Fold a [a] Source #

Return the last N elements

null :: Fold a Bool Source #

Returns True if the container is empty, False otherwise

length :: Fold a Int Source #

Return the length of the container

and :: Fold Bool Bool Source #

Returns True if all elements are True, False otherwise

or :: Fold Bool Bool Source #

Returns True if any element is True, False otherwise

all :: (a -> Bool) -> Fold a Bool Source #

(all predicate) returns True if all elements satisfy the predicate, False otherwise

any :: (a -> Bool) -> Fold a Bool Source #

(any predicate) returns True if any element satisfies the predicate, False otherwise

sum :: Num a => Fold a a Source #

Computes the sum of all elements

product :: Num a => Fold a a Source #

Computes the product of all elements

mean :: Fractional a => Fold a a Source #

Compute a numerically stable arithmetic mean of all elements

variance :: Fractional a => Fold a a Source #

Compute a numerically stable (population) variance over all elements

std :: Floating a => Fold a a Source #

Compute a numerically stable (population) standard deviation over all elements

maximum :: Ord a => Fold a (Maybe a) Source #

Computes the maximum element

maximumBy :: (a -> a -> Ordering) -> Fold a (Maybe a) Source #

Computes the maximum element with respect to the given comparison function

minimum :: Ord a => Fold a (Maybe a) Source #

Computes the minimum element

minimumBy :: (a -> a -> Ordering) -> Fold a (Maybe a) Source #

Computes the minimum element with respect to the given comparison function

elem :: Eq a => a -> Fold a Bool Source #

(elem a) returns True if the container has an element equal to a, False otherwise

notElem :: Eq a => a -> Fold a Bool Source #

(notElem a) returns False if the container has an element equal to a, True otherwise

find :: (a -> Bool) -> Fold a (Maybe a) Source #

(find predicate) returns the first element that satisfies the predicate or Nothing if no element satisfies the predicate

index :: Int -> Fold a (Maybe a) Source #

(index n) returns the nth element of the container, or Nothing if the container has an insufficient number of elements

lookup :: Eq a => a -> Fold (a, b) (Maybe b) Source #

(lookup a) returns the element paired with the first matching item, or Nothing if none matches

elemIndex :: Eq a => a -> Fold a (Maybe Int) Source #

(elemIndex a) returns the index of the first element that equals a, or Nothing if no element matches

findIndex :: (a -> Bool) -> Fold a (Maybe Int) Source #

(findIndex predicate) returns the index of the first element that satisfies the predicate, or Nothing if no element satisfies the predicate

random :: FoldM IO a (Maybe a) Source #

Pick a random element, using reservoir sampling

randomN :: Vector v a => Int -> FoldM IO a (Maybe (v a)) Source #

Pick several random elements, using reservoir sampling

mapM_ :: Monad m => (a -> m ()) -> FoldM m a () Source #

Converts an effectful function to a fold. Specialized version of sink.

sink :: (Monoid w, Monad m) => (a -> m w) -> FoldM m a w Source #

Converts an effectful function to a fold

sink (f <> g) = sink f <> sink g -- if `(<>)` is commutative
sink mempty = mempty

Generic Folds

genericLength :: Num b => Fold a b Source #

Like length, except with a more general Num return value

genericIndex :: Integral i => i -> Fold a (Maybe a) Source #

Like index, except with a more general Integral argument

Container folds

list :: Fold a [a] Source #

Fold all values into a list

revList :: Fold a [a] Source #

Fold all values into a list, in reverse order

nub :: Ord a => Fold a [a] Source #

O(n log n). Fold values into a list with duplicates removed, while preserving their first occurrences

eqNub :: Eq a => Fold a [a] Source #

O(n^2). Fold values into a list with duplicates removed, while preserving their first occurrences

set :: Ord a => Fold a (Set a) Source #

Fold values into a set

hashSet :: (Eq a, Hashable a) => Fold a (HashSet a) Source #

Fold values into a hash-set

map :: Ord a => Fold (a, b) (Map a b) Source #

Fold pairs into a map.

foldByKeyMap :: forall k a b. Ord k => Fold a b -> Fold (k, a) (Map k b) Source #

Given a Fold, produces a Map which applies that fold to each a separated by key k.

>>> fold (foldByKeyMap Control.Foldl.sum) [("a",1), ("b",2), ("b",20), ("a",10)]
fromList [("a",11),("b",22)]

hashMap :: (Eq a, Hashable a) => Fold (a, b) (HashMap a b) Source #

Fold pairs into a hash-map.

foldByKeyHashMap :: forall k a b. (Hashable k, Eq k) => Fold a b -> Fold (k, a) (HashMap k b) Source #

Given a Fold, produces a HashMap which applies that fold to each a separated by key k.

>>> List.sort (HashMap.toList (fold (foldByKeyHashMap Control.Foldl.sum) [("a",1), ("b",2), ("b",20), ("a",10)]))
[("a",11),("b",22)]

vector :: Vector v a => Fold a (v a) Source #

Fold all values into a vector

vectorM :: (PrimMonad m, Vector v a) => FoldM m a (v a) Source #

Fold all values into a vector

This is more efficient than vector but is impure

Utilities

purely and impurely allow you to write folds compatible with the foldl library without incurring a foldl dependency. Write your fold to accept three parameters corresponding to the step function, initial accumulator, and extraction function and then users can upgrade your function to accept a Fold or FoldM using the purely or impurely combinators.

For example, the pipes library implements fold and foldM functions in Pipes.Prelude with the following type:

Pipes.Prelude.fold
    :: Monad m
    -> (x -> a -> x) -> x -> (x -> b) -> Producer a m () -> m b

Pipes.Prelude.foldM
    :: Monad m
    => (x -> a -> m x) -> m x -> (x -> m b) -> Producer a m () -> m b

Both fold and foldM is set up so that you can wrap them with either purely or impurely to accept a Fold or FoldM, respectively:

purely Pipes.Prelude.fold
    :: Monad m => Fold a b -> Producer a m () -> m b

impurely Pipes.Prelude.foldM
    :: Monad m => FoldM m a b -> Producer a m () -> m b

Other streaming libraries supporting purely and impurely include io-streams and streaming. So for example we have:

purely System.IO.Streams.fold_
    :: Fold a b -> Streams.InputStream a -> IO b

impurely System.IO.Streams.foldM_
    :: FoldM IO a b -> Streams.InputStream a -> IO b

The monotraversable package makes it convenient to apply a Fold or FoldM to pure containers that do not allow a general Foldable instance, like unboxed vectors:

purely ofoldlUnwrap
    :: MonoFoldable mono
    => Fold (Element mono) b -> mono -> b

impurely ofoldMUnwrap
    :: MonoFoldable mono
    => FoldM m (Element mono) b -> mono -> m b

purely :: (forall x. (x -> a -> x) -> x -> (x -> b) -> r) -> Fold a b -> r Source #

Upgrade a fold to accept the Fold type

purely_ :: (forall x. (x -> a -> x) -> x -> x) -> Fold a b -> b Source #

Upgrade a more traditional fold to accept the Fold type

impurely :: (forall x. (x -> a -> m x) -> m x -> (x -> m b) -> r) -> FoldM m a b -> r Source #

Upgrade a monadic fold to accept the FoldM type

impurely_ :: Monad m => (forall x. (x -> a -> m x) -> m x -> m x) -> FoldM m a b -> m b Source #

Upgrade a more traditional monadic fold to accept the FoldM type

generalize :: Monad m => Fold a b -> FoldM m a b Source #

Generalize a Fold to a FoldM

generalize (pure r) = pure r

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

simplify :: FoldM Identity a b -> Fold a b Source #

Simplify a pure FoldM to a Fold

simplify (pure r) = pure r

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

hoists :: (forall x. m x -> n x) -> FoldM m a b -> FoldM n a b Source #

Shift a FoldM from one monad to another with a morphism such as lift or liftIO; the effect is the same as hoist.

duplicateM :: Applicative m => FoldM m a b -> FoldM m a (FoldM m a b) Source #

Allows to continue feeding a FoldM even after passing it to a function that closes it.

For pure Folds, this is provided by the Comonad instance.

_Fold1 :: (a -> a -> a) -> Fold a (Maybe a) Source #

_Fold1 step returns a new Fold using just a step function that has the same type for the accumulator and the element. The result type is the accumulator type wrapped in Maybe. The initial accumulator is retrieved from the Foldable, the result is None for empty containers.

premap :: (a -> b) -> Fold b r -> Fold a r Source #

(premap f folder) returns a new Fold where f is applied at each step

fold (premap f folder) list = fold folder (List.map f list)

>>> fold (premap Sum Foldl.mconcat) [1..10]
Sum {getSum = 55}

>>> fold Foldl.mconcat (List.map Sum [1..10])
Sum {getSum = 55}

premap id = id

premap (f . g) = premap g . premap f

premap k (pure r) = pure r

premap k (f <*> x) = premap k f <*> premap k x

premapM :: Monad m => (a -> m b) -> FoldM m b r -> FoldM m a r Source #

(premapM f folder) returns a new FoldM where f is applied to each input element

premapM return = id

premapM (f <=< g) = premap g . premap f

premapM k (pure r) = pure r

premapM k (f <*> x) = premapM k f <*> premapM k x

prefilter :: (a -> Bool) -> Fold a r -> Fold a r Source #

(prefilter f folder) returns a new Fold where the folder's input is used only when the input satisfies a predicate f

This can also be done with handles (handles (filtered f)) but prefilter does not need you to depend on a lens library.

fold (prefilter p folder) list = fold folder (filter p list)

>>> fold (prefilter (>5) Control.Foldl.sum) [1..10]
40

>>> fold Control.Foldl.sum (filter (>5) [1..10])
40

prefilterM :: Monad m => (a -> m Bool) -> FoldM m a r -> FoldM m a r Source #

(prefilterM f folder) returns a new FoldM where the folder's input is used only when the input satisfies a monadic predicate f.

foldM (prefilterM p folder) list = foldM folder (filter p list)

predropWhile :: (a -> Bool) -> Fold a r -> Fold a r Source #

Transforms a Fold into one which ignores elements until they stop satisfying a predicate

fold (predropWhile p folder) list = fold folder (dropWhile p list)

>>> fold (predropWhile (>5) Control.Foldl.sum) [10,9,5,9]
14

drop :: Natural -> Fold a b -> Fold a b Source #

(drop n folder) returns a new Fold that ignores the first n inputs but otherwise behaves the same as the original fold.

fold (drop n folder) list = fold folder (Data.List.genericDrop n list)

>>> Foldl.fold (Foldl.drop 3 Foldl.sum) [10, 20, 30, 1, 2, 3]
6

>>> Foldl.fold (Foldl.drop 10 Foldl.sum) [10, 20, 30, 1, 2, 3]
0

dropM :: Monad m => Natural -> FoldM m a b -> FoldM m a b Source #

(dropM n folder) returns a new FoldM that ignores the first n inputs but otherwise behaves the same as the original fold.

foldM (dropM n folder) list = foldM folder (Data.List.genericDrop n list)

>>> Foldl.foldM (Foldl.dropM 3 (Foldl.generalize Foldl.sum)) [10, 20, 30, 1, 2, 3]
6

>>> Foldl.foldM (Foldl.dropM 10 (Foldl.generalize Foldl.sum)) [10, 20, 30, 1, 2, 3]
0

type Handler a b = forall x. (b -> Const (Dual (Endo x)) b) -> a -> Const (Dual (Endo x)) a Source #

A handler for the upstream input of a Fold

Any lens, traversal, or prism will type-check as a Handler

handles :: Handler a b -> Fold b r -> Fold a r Source #

(handles t folder) transforms the input of a Fold using a lens, traversal, or prism:

handles _1       :: Fold a r -> Fold (a, b) r
handles _Left    :: Fold a r -> Fold (Either a b) r
handles traverse :: Traversable t => Fold a r -> Fold (t a) r
handles folded   :: Foldable    t => Fold a r -> Fold (t a) r

>>> fold (handles traverse sum) [[1..5],[6..10]]
55

>>> fold (handles (traverse.traverse) sum) [[Nothing, Just 2, Just 7],[Just 13, Nothing, Just 20]]
42

>>> fold (handles (filtered even) sum) [1..10]
30

>>> fold (handles _2 Foldl.mconcat) [(1,"Hello "),(2,"World"),(3,"!")]
"Hello World!"

handles id = id

handles (f . g) = handles f . handles g

handles t (pure r) = pure r

handles t (f <*> x) = handles t f <*> handles t x

foldOver :: Handler s a -> Fold a b -> s -> b Source #

(foldOver f folder xs) folds all values from a Lens, Traversal, Prism or Fold with the given folder

>>> foldOver (_Just . both) Foldl.sum (Just (2, 3))
5

>>> foldOver (_Just . both) Foldl.sum Nothing
0

Foldl.foldOver f folder xs == Foldl.fold folder (xs^..f)

Foldl.foldOver (folded.f) folder == Foldl.fold (handles f folder)

Foldl.foldOver folded == Foldl.fold

newtype EndoM m a Source #

instance Monad m => Monoid (EndoM m a) where
    mempty = EndoM return
    mappend (EndoM f) (EndoM g) = EndoM (f <=< g)

Constructors

EndoM
Fields appEndoM :: a -> m a

Instances

Instances details

Monad m => Monoid (EndoM m a) Source #
Instance details Defined in Control.Foldl Methods mempty :: EndoM m a # mappend :: EndoM m a -> EndoM m a -> EndoM m a # mconcat :: [EndoM m a] -> EndoM m a #
Monad m => Semigroup (EndoM m a) Source #
Instance details Defined in Control.Foldl Methods (<>) :: EndoM m a -> EndoM m a -> EndoM m a # sconcat :: NonEmpty (EndoM m a) -> EndoM m a # stimes :: Integral b => b -> EndoM m a -> EndoM m a #

type HandlerM m a b = forall x. (b -> Const (Dual (EndoM m x)) b) -> a -> Const (Dual (EndoM m x)) a Source #

A Handler for the upstream input of FoldM

Any lens, traversal, or prism will type-check as a HandlerM

handlesM :: HandlerM m a b -> FoldM m b r -> FoldM m a r Source #

(handlesM t folder) transforms the input of a FoldM using a lens, traversal, or prism:

handlesM _1       :: FoldM m a r -> FoldM (a, b) r
handlesM _Left    :: FoldM m a r -> FoldM (Either a b) r
handlesM traverse :: Traversable t => FoldM m a r -> FoldM m (t a) r
handlesM folded   :: Foldable    t => FoldM m a r -> FoldM m (t a) r

handlesM obeys these laws:

handlesM id = id

handlesM (f . g) = handlesM f . handlesM g

handlesM t (pure r) = pure r

handlesM t (f <*> x) = handlesM t f <*> handlesM t x

foldOverM :: Monad m => HandlerM m s a -> FoldM m a b -> s -> m b Source #

(foldOverM f folder xs) folds all values from a Lens, Traversal, Prism or Fold monadically with the given folder

Foldl.foldOverM (folded.f) folder == Foldl.foldM (handlesM f folder)

Foldl.foldOverM folded == Foldl.foldM

folded :: (Contravariant f, Applicative f, Foldable t) => (a -> f a) -> t a -> f (t a) Source #

folded :: Foldable t => Fold (t a) a

handles folded :: Foldable t => Fold a r -> Fold (t a) r

filtered :: Monoid m => (a -> Bool) -> (a -> m) -> a -> m Source #

>>> fold (handles (filtered even) sum) [1..10]
30

>>> foldM (handlesM (filtered even) (Foldl.mapM_ print)) [1..10]
2
4
6
8
10

groupBy :: Ord g => (a -> g) -> Fold a r -> Fold a (Map g r) Source #

Perform a Fold while grouping the data according to a specified group projection function. Returns the folded result grouped as a map keyed by the group.

either :: Fold a1 b1 -> Fold a2 b2 -> Fold (Either a1 a2) (b1, b2) Source #

Combine two folds into a fold over inputs for either of them.

eitherM :: Monad m => FoldM m a1 b1 -> FoldM m a2 b2 -> FoldM m (Either a1 a2) (b1, b2) Source #

Combine two monadic folds into a fold over inputs for either of them.

nest :: Applicative f => Fold a b -> Fold (f a) (f b) Source #

Nest a fold in an applicative.

Re-exports

Control.Monad.Primitive re-exports the PrimMonad type class

Data.Foldable re-exports the Foldable type class

Data.Vector.Generic re-exports the Vector type class

data RealWorld #

RealWorld is deeply magical. It is primitive, but it is not unlifted (hence ptrArg). We never manipulate values of type RealWorld; it's only used in the type system, to parameterise State#.

class Monad m => PrimMonad (m :: Type -> Type) #

Class of monads which can perform primitive state-transformer actions.

Minimal complete definition

primitive

Instances

Instances details

PrimMonad IO
Instance details Defined in Control.Monad.Primitive Associated Types type PrimState IO # Methods primitive :: (State# (PrimState IO) -> (# State# (PrimState IO), a #)) -> IO a #
PrimMonad (ST s)
Instance details Defined in Control.Monad.Primitive Associated Types type PrimState (ST s) # Methods primitive :: (State# (PrimState (ST s)) -> (# State# (PrimState (ST s)), a #)) -> ST s a #
PrimMonad (ST s)
Instance details Defined in Control.Monad.Primitive Associated Types type PrimState (ST s) # Methods primitive :: (State# (PrimState (ST s)) -> (# State# (PrimState (ST s)), a #)) -> ST s a #
PrimMonad m => PrimMonad (ListT m)
Instance details Defined in Control.Monad.Primitive Associated Types type PrimState (ListT m) # Methods primitive :: (State# (PrimState (ListT m)) -> (# State# (PrimState (ListT m)), a #)) -> ListT m a #
PrimMonad m => PrimMonad (MaybeT m)
Instance details Defined in Control.Monad.Primitive Associated Types type PrimState (MaybeT m) # Methods primitive :: (State# (PrimState (MaybeT m)) -> (# State# (PrimState (MaybeT m)), a #)) -> MaybeT m a #
(Monoid w, PrimMonad m) => PrimMonad (AccumT w m)	Since: primitive-0.6.3.0
Instance details Defined in Control.Monad.Primitive Associated Types type PrimState (AccumT w m) # Methods primitive :: (State# (PrimState (AccumT w m)) -> (# State# (PrimState (AccumT w m)), a #)) -> AccumT w m a #
(Error e, PrimMonad m) => PrimMonad (ErrorT e m)
Instance details Defined in Control.Monad.Primitive Associated Types type PrimState (ErrorT e m) # Methods primitive :: (State# (PrimState (ErrorT e m)) -> (# State# (PrimState (ErrorT e m)), a #)) -> ErrorT e m a #
PrimMonad m => PrimMonad (ExceptT e m)
Instance details Defined in Control.Monad.Primitive Associated Types type PrimState (ExceptT e m) # Methods primitive :: (State# (PrimState (ExceptT e m)) -> (# State# (PrimState (ExceptT e m)), a #)) -> ExceptT e m a #
PrimMonad m => PrimMonad (IdentityT m)
Instance details Defined in Control.Monad.Primitive Associated Types type PrimState (IdentityT m) # Methods primitive :: (State# (PrimState (IdentityT m)) -> (# State# (PrimState (IdentityT m)), a #)) -> IdentityT m a #
PrimMonad m => PrimMonad (ReaderT r m)
Instance details Defined in Control.Monad.Primitive Associated Types type PrimState (ReaderT r m) # Methods primitive :: (State# (PrimState (ReaderT r m)) -> (# State# (PrimState (ReaderT r m)), a #)) -> ReaderT r m a #
PrimMonad m => PrimMonad (SelectT r m)
Instance details Defined in Control.Monad.Primitive Associated Types type PrimState (SelectT r m) # Methods primitive :: (State# (PrimState (SelectT r m)) -> (# State# (PrimState (SelectT r m)), a #)) -> SelectT r m a #
PrimMonad m => PrimMonad (StateT s m)
Instance details Defined in Control.Monad.Primitive Associated Types type PrimState (StateT s m) # Methods primitive :: (State# (PrimState (StateT s m)) -> (# State# (PrimState (StateT s m)), a #)) -> StateT s m a #
PrimMonad m => PrimMonad (StateT s m)
Instance details Defined in Control.Monad.Primitive Associated Types type PrimState (StateT s m) # Methods primitive :: (State# (PrimState (StateT s m)) -> (# State# (PrimState (StateT s m)), a #)) -> StateT s m a #
(Monoid w, PrimMonad m) => PrimMonad (WriterT w m)
Instance details Defined in Control.Monad.Primitive Associated Types type PrimState (WriterT w m) # Methods primitive :: (State# (PrimState (WriterT w m)) -> (# State# (PrimState (WriterT w m)), a #)) -> WriterT w m a #
(Monoid w, PrimMonad m) => PrimMonad (WriterT w m)
Instance details Defined in Control.Monad.Primitive Associated Types type PrimState (WriterT w m) # Methods primitive :: (State# (PrimState (WriterT w m)) -> (# State# (PrimState (WriterT w m)), a #)) -> WriterT w m a #
(Monoid w, PrimMonad m) => PrimMonad (WriterT w m)
Instance details Defined in Control.Monad.Primitive Associated Types type PrimState (WriterT w m) # Methods primitive :: (State# (PrimState (WriterT w m)) -> (# State# (PrimState (WriterT w m)), a #)) -> WriterT w m a #
PrimMonad m => PrimMonad (ContT r m)	Since: primitive-0.6.3.0
Instance details Defined in Control.Monad.Primitive Associated Types type PrimState (ContT r m) # Methods primitive :: (State# (PrimState (ContT r m)) -> (# State# (PrimState (ContT r m)), a #)) -> ContT r m a #
(Monoid w, PrimMonad m) => PrimMonad (RWST r w s m)
Instance details Defined in Control.Monad.Primitive Associated Types type PrimState (RWST r w s m) # Methods primitive :: (State# (PrimState (RWST r w s m)) -> (# State# (PrimState (RWST r w s m)), a #)) -> RWST r w s m a #
(Monoid w, PrimMonad m) => PrimMonad (RWST r w s m)
Instance details Defined in Control.Monad.Primitive Associated Types type PrimState (RWST r w s m) # Methods primitive :: (State# (PrimState (RWST r w s m)) -> (# State# (PrimState (RWST r w s m)), a #)) -> RWST r w s m a #
(Monoid w, PrimMonad m) => PrimMonad (RWST r w s m)
Instance details Defined in Control.Monad.Primitive Associated Types type PrimState (RWST r w s m) # Methods primitive :: (State# (PrimState (RWST r w s m)) -> (# State# (PrimState (RWST r w s m)), a #)) -> RWST r w s m a #

class Foldable (t :: TYPE LiftedRep -> Type) #

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.

Minimal complete definition

foldMap | foldr

Instances

Instances details

Foldable ZipList	Since: base-4.9.0.0
Instance details Defined in Control.Applicative Methods fold :: Monoid m => ZipList m -> m # foldMap :: Monoid m => (a -> m) -> ZipList a -> m # foldMap' :: Monoid m => (a -> m) -> ZipList a -> m # foldr :: (a -> b -> b) -> b -> ZipList a -> b # foldr' :: (a -> b -> b) -> b -> ZipList a -> b # foldl :: (b -> a -> b) -> b -> ZipList a -> b # foldl' :: (b -> a -> b) -> b -> ZipList a -> b # foldr1 :: (a -> a -> a) -> ZipList a -> a # foldl1 :: (a -> a -> a) -> ZipList a -> a # toList :: ZipList a -> [a] # null :: ZipList a -> Bool # length :: ZipList a -> Int # elem :: Eq a => a -> ZipList a -> Bool # maximum :: Ord a => ZipList a -> a # minimum :: Ord a => ZipList a -> a # sum :: Num a => ZipList a -> a # product :: Num a => ZipList a -> a #
Foldable Complex	Since: base-4.9.0.0
Instance details Defined in Data.Complex Methods fold :: Monoid m => Complex m -> m # foldMap :: Monoid m => (a -> m) -> Complex a -> m # foldMap' :: Monoid m => (a -> m) -> Complex a -> m # foldr :: (a -> b -> b) -> b -> Complex a -> b # foldr' :: (a -> b -> b) -> b -> Complex a -> b # foldl :: (b -> a -> b) -> b -> Complex a -> b # foldl' :: (b -> a -> b) -> b -> Complex a -> b # foldr1 :: (a -> a -> a) -> Complex a -> a # foldl1 :: (a -> a -> a) -> Complex a -> a # toList :: Complex a -> [a] # null :: Complex a -> Bool # length :: Complex a -> Int # elem :: Eq a => a -> Complex a -> Bool # maximum :: Ord a => Complex a -> a # minimum :: Ord a => Complex a -> a # sum :: Num a => Complex a -> a # product :: Num a => Complex a -> a #
Foldable Identity	Since: base-4.8.0.0
Instance details Defined in Data.Functor.Identity Methods fold :: Monoid m => Identity m -> m # foldMap :: Monoid m => (a -> m) -> Identity a -> m # foldMap' :: Monoid m => (a -> m) -> Identity a -> m # foldr :: (a -> b -> b) -> b -> Identity a -> b # foldr' :: (a -> b -> b) -> b -> Identity a -> b # foldl :: (b -> a -> b) -> b -> Identity a -> b # foldl' :: (b -> a -> b) -> b -> Identity a -> b # foldr1 :: (a -> a -> a) -> Identity a -> a # foldl1 :: (a -> a -> a) -> Identity a -> a # toList :: Identity a -> [a] # null :: Identity a -> Bool # length :: Identity a -> Int # elem :: Eq a => a -> Identity a -> Bool # maximum :: Ord a => Identity a -> a # minimum :: Ord a => Identity a -> a # sum :: Num a => Identity a -> a # product :: Num a => Identity a -> a #
Foldable First	Since: base-4.8.0.0
Instance details Defined in Data.Foldable Methods fold :: Monoid m => First m -> m # foldMap :: Monoid m => (a -> m) -> First a -> m # foldMap' :: Monoid m => (a -> m) -> First a -> m # foldr :: (a -> b -> b) -> b -> First a -> b # foldr' :: (a -> b -> b) -> b -> First a -> b # foldl :: (b -> a -> b) -> b -> First a -> b # foldl' :: (b -> a -> b) -> b -> First a -> b # foldr1 :: (a -> a -> a) -> First a -> a # foldl1 :: (a -> a -> a) -> First a -> a # toList :: First a -> [a] # null :: First a -> Bool # length :: First a -> Int # elem :: Eq a => a -> First a -> Bool # maximum :: Ord a => First a -> a # minimum :: Ord a => First a -> a # sum :: Num a => First a -> a # product :: Num a => First a -> a #
Foldable Last	Since: base-4.8.0.0
Instance details Defined in Data.Foldable Methods fold :: Monoid m => Last m -> m # foldMap :: Monoid m => (a -> m) -> Last a -> m # foldMap' :: Monoid m => (a -> m) -> Last a -> m # foldr :: (a -> b -> b) -> b -> Last a -> b # foldr' :: (a -> b -> b) -> b -> Last a -> b # foldl :: (b -> a -> b) -> b -> Last a -> b # foldl' :: (b -> a -> b) -> b -> Last a -> b # foldr1 :: (a -> a -> a) -> Last a -> a # foldl1 :: (a -> a -> a) -> Last a -> a # toList :: Last a -> [a] # null :: Last a -> Bool # length :: Last a -> Int # elem :: Eq a => a -> Last a -> Bool # maximum :: Ord a => Last a -> a # minimum :: Ord a => Last a -> a # sum :: Num a => Last a -> a # product :: Num a => Last a -> a #
Foldable Down	Since: base-4.12.0.0
Instance details Defined in Data.Foldable Methods fold :: Monoid m => Down m -> m # foldMap :: Monoid m => (a -> m) -> Down a -> m # foldMap' :: Monoid m => (a -> m) -> Down a -> m # foldr :: (a -> b -> b) -> b -> Down a -> b # foldr' :: (a -> b -> b) -> b -> Down a -> b # foldl :: (b -> a -> b) -> b -> Down a -> b # foldl' :: (b -> a -> b) -> b -> Down a -> b # foldr1 :: (a -> a -> a) -> Down a -> a # foldl1 :: (a -> a -> a) -> Down a -> a # toList :: Down a -> [a] # null :: Down a -> Bool # length :: Down a -> Int # elem :: Eq a => a -> Down a -> Bool # maximum :: Ord a => Down a -> a # minimum :: Ord a => Down a -> a # sum :: Num a => Down a -> a # product :: Num a => Down a -> a #
Foldable First	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods fold :: Monoid m => First m -> m # foldMap :: Monoid m => (a -> m) -> First a -> m # foldMap' :: Monoid m => (a -> m) -> First a -> m # foldr :: (a -> b -> b) -> b -> First a -> b # foldr' :: (a -> b -> b) -> b -> First a -> b # foldl :: (b -> a -> b) -> b -> First a -> b # foldl' :: (b -> a -> b) -> b -> First a -> b # foldr1 :: (a -> a -> a) -> First a -> a # foldl1 :: (a -> a -> a) -> First a -> a # toList :: First a -> [a] # null :: First a -> Bool # length :: First a -> Int # elem :: Eq a => a -> First a -> Bool # maximum :: Ord a => First a -> a # minimum :: Ord a => First a -> a # sum :: Num a => First a -> a # product :: Num a => First a -> a #
Foldable Last	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods fold :: Monoid m => Last m -> m # foldMap :: Monoid m => (a -> m) -> Last a -> m # foldMap' :: Monoid m => (a -> m) -> Last a -> m # foldr :: (a -> b -> b) -> b -> Last a -> b # foldr' :: (a -> b -> b) -> b -> Last a -> b # foldl :: (b -> a -> b) -> b -> Last a -> b # foldl' :: (b -> a -> b) -> b -> Last a -> b # foldr1 :: (a -> a -> a) -> Last a -> a # foldl1 :: (a -> a -> a) -> Last a -> a # toList :: Last a -> [a] # null :: Last a -> Bool # length :: Last a -> Int # elem :: Eq a => a -> Last a -> Bool # maximum :: Ord a => Last a -> a # minimum :: Ord a => Last a -> a # sum :: Num a => Last a -> a # product :: Num a => Last a -> a #
Foldable Max	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods fold :: Monoid m => Max m -> m # foldMap :: Monoid m => (a -> m) -> Max a -> m # foldMap' :: Monoid m => (a -> m) -> Max a -> m # foldr :: (a -> b -> b) -> b -> Max a -> b # foldr' :: (a -> b -> b) -> b -> Max a -> b # foldl :: (b -> a -> b) -> b -> Max a -> b # foldl' :: (b -> a -> b) -> b -> Max a -> b # foldr1 :: (a -> a -> a) -> Max a -> a # foldl1 :: (a -> a -> a) -> Max a -> a # toList :: Max a -> [a] # null :: Max a -> Bool # length :: Max a -> Int # elem :: Eq a => a -> Max a -> Bool # maximum :: Ord a => Max a -> a # minimum :: Ord a => Max a -> a # sum :: Num a => Max a -> a # product :: Num a => Max a -> a #
Foldable Min	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods fold :: Monoid m => Min m -> m # foldMap :: Monoid m => (a -> m) -> Min a -> m # foldMap' :: Monoid m => (a -> m) -> Min a -> m # foldr :: (a -> b -> b) -> b -> Min a -> b # foldr' :: (a -> b -> b) -> b -> Min a -> b # foldl :: (b -> a -> b) -> b -> Min a -> b # foldl' :: (b -> a -> b) -> b -> Min a -> b # foldr1 :: (a -> a -> a) -> Min a -> a # foldl1 :: (a -> a -> a) -> Min a -> a # toList :: Min a -> [a] # null :: Min a -> Bool # length :: Min a -> Int # elem :: Eq a => a -> Min a -> Bool # maximum :: Ord a => Min a -> a # minimum :: Ord a => Min a -> a # sum :: Num a => Min a -> a # product :: Num a => Min a -> a #
Foldable Dual	Since: base-4.8.0.0
Instance details Defined in Data.Foldable Methods fold :: Monoid m => Dual m -> m # foldMap :: Monoid m => (a -> m) -> Dual a -> m # foldMap' :: Monoid m => (a -> m) -> Dual a -> m # foldr :: (a -> b -> b) -> b -> Dual a -> b # foldr' :: (a -> b -> b) -> b -> Dual a -> b # foldl :: (b -> a -> b) -> b -> Dual a -> b # foldl' :: (b -> a -> b) -> b -> Dual a -> b # foldr1 :: (a -> a -> a) -> Dual a -> a # foldl1 :: (a -> a -> a) -> Dual a -> a # toList :: Dual a -> [a] # null :: Dual a -> Bool # length :: Dual a -> Int # elem :: Eq a => a -> Dual a -> Bool # maximum :: Ord a => Dual a -> a # minimum :: Ord a => Dual a -> a # sum :: Num a => Dual a -> a # product :: Num a => Dual a -> a #
Foldable Product	Since: base-4.8.0.0
Instance details Defined in Data.Foldable Methods fold :: Monoid m => Product m -> m # foldMap :: Monoid m => (a -> m) -> Product a -> m # foldMap' :: Monoid m => (a -> m) -> Product a -> m # foldr :: (a -> b -> b) -> b -> Product a -> b # foldr' :: (a -> b -> b) -> b -> Product a -> b # foldl :: (b -> a -> b) -> b -> Product a -> b # foldl' :: (b -> a -> b) -> b -> Product a -> b # foldr1 :: (a -> a -> a) -> Product a -> a # foldl1 :: (a -> a -> a) -> Product a -> a # toList :: Product a -> [a] # null :: Product a -> Bool # length :: Product a -> Int # elem :: Eq a => a -> Product a -> Bool # maximum :: Ord a => Product a -> a # minimum :: Ord a => Product a -> a # sum :: Num a => Product a -> a # product :: Num a => Product a -> a #
Foldable Sum	Since: base-4.8.0.0
Instance details Defined in Data.Foldable Methods fold :: Monoid m => Sum m -> m # foldMap :: Monoid m => (a -> m) -> Sum a -> m # foldMap' :: Monoid m => (a -> m) -> Sum a -> m # foldr :: (a -> b -> b) -> b -> Sum a -> b # foldr' :: (a -> b -> b) -> b -> Sum a -> b # foldl :: (b -> a -> b) -> b -> Sum a -> b # foldl' :: (b -> a -> b) -> b -> Sum a -> b # foldr1 :: (a -> a -> a) -> Sum a -> a # foldl1 :: (a -> a -> a) -> Sum a -> a # toList :: Sum a -> [a] # null :: Sum a -> Bool # length :: Sum a -> Int # elem :: Eq a => a -> Sum a -> Bool # maximum :: Ord a => Sum a -> a # minimum :: Ord a => Sum a -> a # sum :: Num a => Sum a -> a # product :: Num a => Sum a -> a #
Foldable Par1	Since: base-4.9.0.0
Instance details Defined in Data.Foldable Methods fold :: Monoid m => Par1 m -> m # foldMap :: Monoid m => (a -> m) -> Par1 a -> m # foldMap' :: Monoid m => (a -> m) -> Par1 a -> m # foldr :: (a -> b -> b) -> b -> Par1 a -> b # foldr' :: (a -> b -> b) -> b -> Par1 a -> b # foldl :: (b -> a -> b) -> b -> Par1 a -> b # foldl' :: (b -> a -> b) -> b -> Par1 a -> b # foldr1 :: (a -> a -> a) -> Par1 a -> a # foldl1 :: (a -> a -> a) -> Par1 a -> a # toList :: Par1 a -> [a] # null :: Par1 a -> Bool # length :: Par1 a -> Int # elem :: Eq a => a -> Par1 a -> Bool # maximum :: Ord a => Par1 a -> a # minimum :: Ord a => Par1 a -> a # sum :: Num a => Par1 a -> a # product :: Num a => Par1 a -> a #
Foldable IntMap	Folds in order of increasing key.
Instance details 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 # toList :: IntMap a -> [a] # null :: IntMap a -> Bool # length :: IntMap a -> Int # elem :: Eq a => a -> IntMap a -> Bool # maximum :: Ord a => IntMap a -> a # minimum :: Ord a => IntMap a -> a # sum :: Num a => IntMap a -> a # product :: Num a => IntMap a -> a #
Foldable Digit
Instance details 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 # toList :: Digit a -> [a] # null :: Digit a -> Bool # length :: Digit a -> Int # elem :: Eq a => a -> Digit a -> Bool # maximum :: Ord a => Digit a -> a # minimum :: Ord a => Digit a -> a # sum :: Num a => Digit a -> a # product :: Num a => Digit a -> a #
Foldable Elem
Instance details 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 # toList :: Elem a -> [a] # null :: Elem a -> Bool # length :: Elem a -> Int # elem :: Eq a => a -> Elem a -> Bool # maximum :: Ord a => Elem a -> a # minimum :: Ord a => Elem a -> a # sum :: Num a => Elem a -> a # product :: Num a => Elem a -> a #
Foldable FingerTree
Instance details 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
Instance details 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 # toList :: Node a -> [a] # null :: Node a -> Bool # length :: Node a -> Int # elem :: Eq a => a -> Node a -> Bool # maximum :: Ord a => Node a -> a # minimum :: Ord a => Node a -> a # sum :: Num a => Node a -> a # product :: Num a => Node a -> a #
Foldable Seq
Instance details 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 # toList :: Seq a -> [a] # null :: Seq a -> Bool # length :: Seq a -> Int # elem :: Eq a => a -> Seq a -> Bool # maximum :: Ord a => Seq a -> a # minimum :: Ord a => Seq a -> a # sum :: Num a => Seq a -> a # product :: Num a => Seq a -> a #
Foldable ViewL
Instance details 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 # toList :: ViewL a -> [a] # null :: ViewL a -> Bool # length :: ViewL a -> Int # elem :: Eq a => a -> ViewL a -> Bool # maximum :: Ord a => ViewL a -> a # minimum :: Ord a => ViewL a -> a # sum :: Num a => ViewL a -> a # product :: Num a => ViewL a -> a #
Foldable ViewR
Instance details 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 # toList :: ViewR a -> [a] # null :: ViewR a -> Bool # length :: ViewR a -> Int # elem :: Eq a => a -> ViewR a -> Bool # maximum :: Ord a => ViewR a -> a # minimum :: Ord a => ViewR a -> a # sum :: Num a => ViewR a -> a # product :: Num a => ViewR a -> a #
Foldable Set	Folds in order of increasing key.
Instance details 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 # toList :: Set a -> [a] # null :: Set a -> Bool # length :: Set a -> Int # elem :: Eq a => a -> Set a -> Bool # maximum :: Ord a => Set a -> a # minimum :: Ord a => Set a -> a # sum :: Num a => Set a -> a # product :: Num a => Set a -> a #
Foldable Tree
Instance details 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 # toList :: Tree a -> [a] # null :: Tree a -> Bool # length :: Tree a -> Int # elem :: Eq a => a -> Tree a -> Bool # maximum :: Ord a => Tree a -> a # minimum :: Ord a => Tree a -> a # sum :: Num a => Tree a -> a # product :: Num a => Tree a -> a #
Foldable Hashed
Instance details 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 # toList :: Hashed a -> [a] # null :: Hashed a -> Bool # length :: Hashed a -> Int # elem :: Eq a => a -> Hashed a -> Bool # maximum :: Ord a => Hashed a -> a # minimum :: Ord a => Hashed a -> a # sum :: Num a => Hashed a -> a # product :: Num a => Hashed a -> a #
Foldable HashSet
Instance details 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 # toList :: HashSet a -> [a] # null :: HashSet a -> Bool # length :: HashSet a -> Int # elem :: Eq a => a -> HashSet a -> Bool # maximum :: Ord a => HashSet a -> a # minimum :: Ord a => HashSet a -> a # sum :: Num a => HashSet a -> a # product :: Num a => HashSet a -> a #
Foldable NonEmpty	Since: base-4.9.0.0
Instance details Defined in Data.Foldable Methods fold :: Monoid m => NonEmpty m -> m # foldMap :: Monoid m => (a -> m) -> NonEmpty a -> m # foldMap' :: Monoid m => (a -> m) -> NonEmpty a -> m # foldr :: (a -> b -> b) -> b -> NonEmpty a -> b # foldr' :: (a -> b -> b) -> b -> NonEmpty a -> b # foldl :: (b -> a -> b) -> b -> NonEmpty a -> b # foldl' :: (b -> a -> b) -> b -> NonEmpty a -> b # foldr1 :: (a -> a -> a) -> NonEmpty a -> a # foldl1 :: (a -> a -> a) -> NonEmpty a -> a # toList :: NonEmpty a -> [a] # null :: NonEmpty a -> Bool # length :: NonEmpty a -> Int # elem :: Eq a => a -> NonEmpty a -> Bool # maximum :: Ord a => NonEmpty a -> a # minimum :: Ord a => NonEmpty a -> a # sum :: Num a => NonEmpty a -> a # product :: Num a => NonEmpty a -> a #
Foldable Maybe	Since: base-2.1
Instance details Defined in Data.Foldable Methods fold :: Monoid m => Maybe m -> m # foldMap :: Monoid m => (a -> m) -> Maybe a -> m # foldMap' :: Monoid m => (a -> m) -> Maybe a -> m # foldr :: (a -> b -> b) -> b -> Maybe a -> b # foldr' :: (a -> b -> b) -> b -> Maybe a -> b # foldl :: (b -> a -> b) -> b -> Maybe a -> b # foldl' :: (b -> a -> b) -> b -> Maybe a -> b # foldr1 :: (a -> a -> a) -> Maybe a -> a # foldl1 :: (a -> a -> a) -> Maybe a -> a # toList :: Maybe a -> [a] # null :: Maybe a -> Bool # length :: Maybe a -> Int # elem :: Eq a => a -> Maybe a -> Bool # maximum :: Ord a => Maybe a -> a # minimum :: Ord a => Maybe a -> a # sum :: Num a => Maybe a -> a # product :: Num a => Maybe a -> a #
Foldable Solo	Since: base-4.15
Instance details 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 # toList :: Solo a -> [a] # null :: Solo a -> Bool # length :: Solo a -> Int # elem :: Eq a => a -> Solo a -> Bool # maximum :: Ord a => Solo a -> a # minimum :: Ord a => Solo a -> a # sum :: Num a => Solo a -> a # product :: Num a => Solo a -> a #
Foldable []	Since: base-2.1
Instance details 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 # toList :: [a] -> [a] # null :: [a] -> Bool # length :: [a] -> Int # elem :: Eq a => a -> [a] -> Bool # maximum :: Ord a => [a] -> a # minimum :: Ord a => [a] -> a # sum :: Num a => [a] -> a # product :: Num a => [a] -> a #
Foldable (Either a)	Since: base-4.7.0.0
Instance details Defined in Data.Foldable Methods fold :: Monoid m => Either a m -> m # foldMap :: Monoid m => (a0 -> m) -> Either a a0 -> m # foldMap' :: Monoid m => (a0 -> m) -> Either a a0 -> m # foldr :: (a0 -> b -> b) -> b -> Either a a0 -> b # foldr' :: (a0 -> b -> b) -> b -> Either a a0 -> b # foldl :: (b -> a0 -> b) -> b -> Either a a0 -> b # foldl' :: (b -> a0 -> b) -> b -> Either a a0 -> b # foldr1 :: (a0 -> a0 -> a0) -> Either a a0 -> a0 # foldl1 :: (a0 -> a0 -> a0) -> Either a a0 -> a0 # toList :: Either a a0 -> [a0] # null :: Either a a0 -> Bool # length :: Either a a0 -> Int # elem :: Eq a0 => a0 -> Either a a0 -> Bool # maximum :: Ord a0 => Either a a0 -> a0 # minimum :: Ord a0 => Either a a0 -> a0 # sum :: Num a0 => Either a a0 -> a0 # product :: Num a0 => Either a a0 -> a0 #
Foldable (Proxy :: TYPE LiftedRep -> Type)	Since: base-4.7.0.0
Instance details Defined in Data.Foldable Methods fold :: Monoid m => Proxy m -> m # foldMap :: Monoid m => (a -> m) -> Proxy a -> m # foldMap' :: Monoid m => (a -> m) -> Proxy a -> m # foldr :: (a -> b -> b) -> b -> Proxy a -> b # foldr' :: (a -> b -> b) -> b -> Proxy a -> b # foldl :: (b -> a -> b) -> b -> Proxy a -> b # foldl' :: (b -> a -> b) -> b -> Proxy a -> b # foldr1 :: (a -> a -> a) -> Proxy a -> a # foldl1 :: (a -> a -> a) -> Proxy a -> a # toList :: Proxy a -> [a] # null :: Proxy a -> Bool # length :: Proxy a -> Int # elem :: Eq a => a -> Proxy a -> Bool # maximum :: Ord a => Proxy a -> a # minimum :: Ord a => Proxy a -> a # sum :: Num a => Proxy a -> a # product :: Num a => Proxy a -> a #
Foldable (Arg a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods fold :: Monoid m => Arg a m -> m # foldMap :: Monoid m => (a0 -> m) -> Arg a a0 -> m # foldMap' :: Monoid m => (a0 -> m) -> Arg a a0 -> m # foldr :: (a0 -> b -> b) -> b -> Arg a a0 -> b # foldr' :: (a0 -> b -> b) -> b -> Arg a a0 -> b # foldl :: (b -> a0 -> b) -> b -> Arg a a0 -> b # foldl' :: (b -> a0 -> b) -> b -> Arg a a0 -> b # foldr1 :: (a0 -> a0 -> a0) -> Arg a a0 -> a0 # foldl1 :: (a0 -> a0 -> a0) -> Arg a a0 -> a0 # toList :: Arg a a0 -> [a0] # null :: Arg a a0 -> Bool # length :: Arg a a0 -> Int # elem :: Eq a0 => a0 -> Arg a a0 -> Bool # maximum :: Ord a0 => Arg a a0 -> a0 # minimum :: Ord a0 => Arg a a0 -> a0 # sum :: Num a0 => Arg a a0 -> a0 # product :: Num a0 => Arg a a0 -> a0 #
Foldable (Array i)	Since: base-4.8.0.0
Instance details Defined in Data.Foldable Methods fold :: Monoid m => Array i m -> m # foldMap :: Monoid m => (a -> m) -> Array i a -> m # foldMap' :: Monoid m => (a -> m) -> Array i a -> m # foldr :: (a -> b -> b) -> b -> Array i a -> b # foldr' :: (a -> b -> b) -> b -> Array i a -> b # foldl :: (b -> a -> b) -> b -> Array i a -> b # foldl' :: (b -> a -> b) -> b -> Array i a -> b # foldr1 :: (a -> a -> a) -> Array i a -> a # foldl1 :: (a -> a -> a) -> Array i a -> a # toList :: Array i a -> [a] # null :: Array i a -> Bool # length :: Array i a -> Int # elem :: Eq a => a -> Array i a -> Bool # maximum :: Ord a => Array i a -> a # minimum :: Ord a => Array i a -> a # sum :: Num a => Array i a -> a # product :: Num a => Array i a -> a #
Foldable (U1 :: TYPE LiftedRep -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Foldable Methods fold :: Monoid m => U1 m -> m # foldMap :: Monoid m => (a -> m) -> U1 a -> m # foldMap' :: Monoid m => (a -> m) -> U1 a -> m # foldr :: (a -> b -> b) -> b -> U1 a -> b # foldr' :: (a -> b -> b) -> b -> U1 a -> b # foldl :: (b -> a -> b) -> b -> U1 a -> b # foldl' :: (b -> a -> b) -> b -> U1 a -> b # foldr1 :: (a -> a -> a) -> U1 a -> a # foldl1 :: (a -> a -> a) -> U1 a -> a # toList :: U1 a -> [a] # null :: U1 a -> Bool # length :: U1 a -> Int # elem :: Eq a => a -> U1 a -> Bool # maximum :: Ord a => U1 a -> a # minimum :: Ord a => U1 a -> a # sum :: Num a => U1 a -> a # product :: Num a => U1 a -> a #
Foldable (UAddr :: TYPE LiftedRep -> Type)	Since: base-4.9.0.0
Instance details 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 # toList :: UAddr a -> [a] # null :: UAddr a -> Bool # length :: UAddr a -> Int # elem :: Eq a => a -> UAddr a -> Bool # maximum :: Ord a => UAddr a -> a # minimum :: Ord a => UAddr a -> a # sum :: Num a => UAddr a -> a # product :: Num a => UAddr a -> a #
Foldable (UChar :: TYPE LiftedRep -> Type)	Since: base-4.9.0.0
Instance details 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 # toList :: UChar a -> [a] # null :: UChar a -> Bool # length :: UChar a -> Int # elem :: Eq a => a -> UChar a -> Bool # maximum :: Ord a => UChar a -> a # minimum :: Ord a => UChar a -> a # sum :: Num a => UChar a -> a # product :: Num a => UChar a -> a #
Foldable (UDouble :: TYPE LiftedRep -> Type)	Since: base-4.9.0.0
Instance details 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 # toList :: UDouble a -> [a] # null :: UDouble a -> Bool # length :: UDouble a -> Int # elem :: Eq a => a -> UDouble a -> Bool # maximum :: Ord a => UDouble a -> a # minimum :: Ord a => UDouble a -> a # sum :: Num a => UDouble a -> a # product :: Num a => UDouble a -> a #
Foldable (UFloat :: TYPE LiftedRep -> Type)	Since: base-4.9.0.0
Instance details 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 # toList :: UFloat a -> [a] # null :: UFloat a -> Bool # length :: UFloat a -> Int # elem :: Eq a => a -> UFloat a -> Bool # maximum :: Ord a => UFloat a -> a # minimum :: Ord a => UFloat a -> a # sum :: Num a => UFloat a -> a # product :: Num a => UFloat a -> a #
Foldable (UInt :: TYPE LiftedRep -> Type)	Since: base-4.9.0.0
Instance details 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 # toList :: UInt a -> [a] # null :: UInt a -> Bool # length :: UInt a -> Int # elem :: Eq a => a -> UInt a -> Bool # maximum :: Ord a => UInt a -> a # minimum :: Ord a => UInt a -> a # sum :: Num a => UInt a -> a # product :: Num a => UInt a -> a #
Foldable (UWord :: TYPE LiftedRep -> Type)	Since: base-4.9.0.0
Instance details 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 # toList :: UWord a -> [a] # null :: UWord a -> Bool # length :: UWord a -> Int # elem :: Eq a => a -> UWord a -> Bool # maximum :: Ord a => UWord a -> a # minimum :: Ord a => UWord a -> a # sum :: Num a => UWord a -> a # product :: Num a => UWord a -> a #
Foldable (V1 :: TYPE LiftedRep -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Foldable Methods fold :: Monoid m => V1 m -> m # foldMap :: Monoid m => (a -> m) -> V1 a -> m # foldMap' :: Monoid m => (a -> m) -> V1 a -> m # foldr :: (a -> b -> b) -> b -> V1 a -> b # foldr' :: (a -> b -> b) -> b -> V1 a -> b # foldl :: (b -> a -> b) -> b -> V1 a -> b # foldl' :: (b -> a -> b) -> b -> V1 a -> b # foldr1 :: (a -> a -> a) -> V1 a -> a # foldl1 :: (a -> a -> a) -> V1 a -> a # toList :: V1 a -> [a] # null :: V1 a -> Bool # length :: V1 a -> Int # elem :: Eq a => a -> V1 a -> Bool # maximum :: Ord a => V1 a -> a # minimum :: Ord a => V1 a -> a # sum :: Num a => V1 a -> a # product :: Num a => V1 a -> a #
Foldable (Map k)	Folds in order of increasing key.
Instance details 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 # toList :: Map k a -> [a] # null :: Map k a -> Bool # length :: Map k a -> Int # elem :: Eq a => a -> Map k a -> Bool # maximum :: Ord a => Map k a -> a # minimum :: Ord a => Map k a -> a # sum :: Num a => Map k a -> a # product :: Num a => Map k a -> a #
Foldable f => Foldable (ListT f)
Instance details Defined in Control.Monad.Trans.List Methods fold :: Monoid m => ListT f m -> m # foldMap :: Monoid m => (a -> m) -> ListT f a -> m # foldMap' :: Monoid m => (a -> m) -> ListT f a -> m # foldr :: (a -> b -> b) -> b -> ListT f a -> b # foldr' :: (a -> b -> b) -> b -> ListT f a -> b # foldl :: (b -> a -> b) -> b -> ListT f a -> b # foldl' :: (b -> a -> b) -> b -> ListT f a -> b # foldr1 :: (a -> a -> a) -> ListT f a -> a # foldl1 :: (a -> a -> a) -> ListT f a -> a # toList :: ListT f a -> [a] # null :: ListT f a -> Bool # length :: ListT f a -> Int # elem :: Eq a => a -> ListT f a -> Bool # maximum :: Ord a => ListT f a -> a # minimum :: Ord a => ListT f a -> a # sum :: Num a => ListT f a -> a # product :: Num a => ListT f a -> a #
Foldable f => Foldable (MaybeT f)
Instance details Defined in Control.Monad.Trans.Maybe Methods fold :: Monoid m => MaybeT f m -> m # foldMap :: Monoid m => (a -> m) -> MaybeT f a -> m # foldMap' :: Monoid m => (a -> m) -> MaybeT f a -> m # foldr :: (a -> b -> b) -> b -> MaybeT f a -> b # foldr' :: (a -> b -> b) -> b -> MaybeT f a -> b # foldl :: (b -> a -> b) -> b -> MaybeT f a -> b # foldl' :: (b -> a -> b) -> b -> MaybeT f a -> b # foldr1 :: (a -> a -> a) -> MaybeT f a -> a # foldl1 :: (a -> a -> a) -> MaybeT f a -> a # toList :: MaybeT f a -> [a] # null :: MaybeT f a -> Bool # length :: MaybeT f a -> Int # elem :: Eq a => a -> MaybeT f a -> Bool # maximum :: Ord a => MaybeT f a -> a # minimum :: Ord a => MaybeT f a -> a # sum :: Num a => MaybeT f a -> a # product :: Num a => MaybeT f a -> a #
Foldable (HashMap k)
Instance details 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] # null :: HashMap k a -> Bool # 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 # sum :: Num a => HashMap k a -> a # product :: Num a => HashMap k a -> a #
Foldable ((,) a)	Since: base-4.7.0.0
Instance details Defined in Data.Foldable Methods fold :: Monoid m => (a, m) -> m # foldMap :: Monoid m => (a0 -> m) -> (a, a0) -> m # foldMap' :: Monoid m => (a0 -> m) -> (a, a0) -> m # foldr :: (a0 -> b -> b) -> b -> (a, a0) -> b # foldr' :: (a0 -> b -> b) -> b -> (a, a0) -> b # foldl :: (b -> a0 -> b) -> b -> (a, a0) -> b # foldl' :: (b -> a0 -> b) -> b -> (a, a0) -> b # foldr1 :: (a0 -> a0 -> a0) -> (a, a0) -> a0 # foldl1 :: (a0 -> a0 -> a0) -> (a, a0) -> a0 # toList :: (a, a0) -> [a0] # null :: (a, a0) -> Bool # length :: (a, a0) -> Int # elem :: Eq a0 => a0 -> (a, a0) -> Bool # maximum :: Ord a0 => (a, a0) -> a0 # minimum :: Ord a0 => (a, a0) -> a0 # sum :: Num a0 => (a, a0) -> a0 # product :: Num a0 => (a, a0) -> a0 #
Foldable (Const m :: TYPE LiftedRep -> Type)	Since: base-4.7.0.0
Instance details Defined in Data.Functor.Const Methods fold :: Monoid m0 => Const m m0 -> m0 # foldMap :: Monoid m0 => (a -> m0) -> Const m a -> m0 # foldMap' :: Monoid m0 => (a -> m0) -> Const m a -> m0 # foldr :: (a -> b -> b) -> b -> Const m a -> b # foldr' :: (a -> b -> b) -> b -> Const m a -> b # foldl :: (b -> a -> b) -> b -> Const m a -> b # foldl' :: (b -> a -> b) -> b -> Const m a -> b # foldr1 :: (a -> a -> a) -> Const m a -> a # foldl1 :: (a -> a -> a) -> Const m a -> a # toList :: Const m a -> [a] # null :: Const m a -> Bool # length :: Const m a -> Int # elem :: Eq a => a -> Const m a -> Bool # maximum :: Ord a => Const m a -> a # minimum :: Ord a => Const m a -> a # sum :: Num a => Const m a -> a # product :: Num a => Const m a -> a #
Foldable f => Foldable (Ap f)	Since: base-4.12.0.0
Instance details Defined in Data.Foldable Methods fold :: Monoid m => Ap f m -> m # foldMap :: Monoid m => (a -> m) -> Ap f a -> m # foldMap' :: Monoid m => (a -> m) -> Ap f a -> m # foldr :: (a -> b -> b) -> b -> Ap f a -> b # foldr' :: (a -> b -> b) -> b -> Ap f a -> b # foldl :: (b -> a -> b) -> b -> Ap f a -> b # foldl' :: (b -> a -> b) -> b -> Ap f a -> b # foldr1 :: (a -> a -> a) -> Ap f a -> a # foldl1 :: (a -> a -> a) -> Ap f a -> a # toList :: Ap f a -> [a] # null :: Ap f a -> Bool # length :: Ap f a -> Int # elem :: Eq a => a -> Ap f a -> Bool # maximum :: Ord a => Ap f a -> a # minimum :: Ord a => Ap f a -> a # sum :: Num a => Ap f a -> a # product :: Num a => Ap f a -> a #
Foldable f => Foldable (Alt f)	Since: base-4.12.0.0
Instance details Defined in Data.Foldable Methods fold :: Monoid m => Alt f m -> m # foldMap :: Monoid m => (a -> m) -> Alt f a -> m # foldMap' :: Monoid m => (a -> m) -> Alt f a -> m # foldr :: (a -> b -> b) -> b -> Alt f a -> b # foldr' :: (a -> b -> b) -> b -> Alt f a -> b # foldl :: (b -> a -> b) -> b -> Alt f a -> b # foldl' :: (b -> a -> b) -> b -> Alt f a -> b # foldr1 :: (a -> a -> a) -> Alt f a -> a # foldl1 :: (a -> a -> a) -> Alt f a -> a # toList :: Alt f a -> [a] # null :: Alt f a -> Bool # length :: Alt f a -> Int # elem :: Eq a => a -> Alt f a -> Bool # maximum :: Ord a => Alt f a -> a # minimum :: Ord a => Alt f a -> a # sum :: Num a => Alt f a -> a # product :: Num a => Alt f a -> a #
Foldable f => Foldable (Rec1 f)	Since: base-4.9.0.0
Instance details Defined in Data.Foldable Methods fold :: Monoid m => Rec1 f m -> m # foldMap :: Monoid m => (a -> m) -> Rec1 f a -> m # foldMap' :: Monoid m => (a -> m) -> Rec1 f a -> m # foldr :: (a -> b -> b) -> b -> Rec1 f a -> b # foldr' :: (a -> b -> b) -> b -> Rec1 f a -> b # foldl :: (b -> a -> b) -> b -> Rec1 f a -> b # foldl' :: (b -> a -> b) -> b -> Rec1 f a -> b # foldr1 :: (a -> a -> a) -> Rec1 f a -> a # foldl1 :: (a -> a -> a) -> Rec1 f a -> a # toList :: Rec1 f a -> [a] # null :: Rec1 f a -> Bool # length :: Rec1 f a -> Int # elem :: Eq a => a -> Rec1 f a -> Bool # maximum :: Ord a => Rec1 f a -> a # minimum :: Ord a => Rec1 f a -> a # sum :: Num a => Rec1 f a -> a # product :: Num a => Rec1 f a -> a #
Bifoldable p => Foldable (Join p)
Instance details 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 # toList :: Join p a -> [a] # null :: Join p a -> Bool # length :: Join p a -> Int # elem :: Eq a => a -> Join p a -> Bool # maximum :: Ord a => Join p a -> a # minimum :: Ord a => Join p a -> a # sum :: Num a => Join p a -> a # product :: Num a => Join p a -> a #
Foldable (Tagged s)
Instance details 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 # toList :: Tagged s a -> [a] # null :: Tagged s a -> Bool # length :: Tagged s a -> Int # elem :: Eq a => a -> Tagged s a -> Bool # maximum :: Ord a => Tagged s a -> a # minimum :: Ord a => Tagged s a -> a # sum :: Num a => Tagged s a -> a # product :: Num a => Tagged s a -> a #
Foldable f => Foldable (ErrorT e f)
Instance details Defined in Control.Monad.Trans.Error Methods fold :: Monoid m => ErrorT e f m -> m # foldMap :: Monoid m => (a -> m) -> ErrorT e f a -> m # foldMap' :: Monoid m => (a -> m) -> ErrorT e f a -> m # foldr :: (a -> b -> b) -> b -> ErrorT e f a -> b # foldr' :: (a -> b -> b) -> b -> ErrorT e f a -> b # foldl :: (b -> a -> b) -> b -> ErrorT e f a -> b # foldl' :: (b -> a -> b) -> b -> ErrorT e f a -> b # foldr1 :: (a -> a -> a) -> ErrorT e f a -> a # foldl1 :: (a -> a -> a) -> ErrorT e f a -> a # toList :: ErrorT e f a -> [a] # null :: ErrorT e f a -> Bool # length :: ErrorT e f a -> Int # elem :: Eq a => a -> ErrorT e f a -> Bool # maximum :: Ord a => ErrorT e f a -> a # minimum :: Ord a => ErrorT e f a -> a # sum :: Num a => ErrorT e f a -> a # product :: Num a => ErrorT e f a -> a #
Foldable f => Foldable (ExceptT e f)
Instance details Defined in Control.Monad.Trans.Except Methods fold :: Monoid m => ExceptT e f m -> m # foldMap :: Monoid m => (a -> m) -> ExceptT e f a -> m # foldMap' :: Monoid m => (a -> m) -> ExceptT e f a -> m # foldr :: (a -> b -> b) -> b -> ExceptT e f a -> b # foldr' :: (a -> b -> b) -> b -> ExceptT e f a -> b # foldl :: (b -> a -> b) -> b -> ExceptT e f a -> b # foldl' :: (b -> a -> b) -> b -> ExceptT e f a -> b # foldr1 :: (a -> a -> a) -> ExceptT e f a -> a # foldl1 :: (a -> a -> a) -> ExceptT e f a -> a # toList :: ExceptT e f a -> [a] # null :: ExceptT e f a -> Bool # length :: ExceptT e f a -> Int # elem :: Eq a => a -> ExceptT e f a -> Bool # maximum :: Ord a => ExceptT e f a -> a # minimum :: Ord a => ExceptT e f a -> a # sum :: Num a => ExceptT e f a -> a # product :: Num a => ExceptT e f a -> a #
Foldable f => Foldable (IdentityT f)
Instance details Defined in Control.Monad.Trans.Identity Methods fold :: Monoid m => IdentityT f m -> m # foldMap :: Monoid m => (a -> m) -> IdentityT f a -> m # foldMap' :: Monoid m => (a -> m) -> IdentityT f a -> m # foldr :: (a -> b -> b) -> b -> IdentityT f a -> b # foldr' :: (a -> b -> b) -> b -> IdentityT f a -> b # foldl :: (b -> a -> b) -> b -> IdentityT f a -> b # foldl' :: (b -> a -> b) -> b -> IdentityT f a -> b # foldr1 :: (a -> a -> a) -> IdentityT f a -> a # foldl1 :: (a -> a -> a) -> IdentityT f a -> a # toList :: IdentityT f a -> [a] # null :: IdentityT f a -> Bool # length :: IdentityT f a -> Int # elem :: Eq a => a -> IdentityT f a -> Bool # maximum :: Ord a => IdentityT f a -> a # minimum :: Ord a => IdentityT f a -> a # sum :: Num a => IdentityT f a -> a # product :: Num a => IdentityT f a -> a #
Foldable f => Foldable (WriterT w f)
Instance details Defined in Control.Monad.Trans.Writer.Lazy Methods fold :: Monoid m => WriterT w f m -> m # foldMap :: Monoid m => (a -> m) -> WriterT w f a -> m # foldMap' :: Monoid m => (a -> m) -> WriterT w f a -> m # foldr :: (a -> b -> b) -> b -> WriterT w f a -> b # foldr' :: (a -> b -> b) -> b -> WriterT w f a -> b # foldl :: (b -> a -> b) -> b -> WriterT w f a -> b # foldl' :: (b -> a -> b) -> b -> WriterT w f a -> b # foldr1 :: (a -> a -> a) -> WriterT w f a -> a # foldl1 :: (a -> a -> a) -> WriterT w f a -> a # toList :: WriterT w f a -> [a] # null :: WriterT w f a -> Bool # length :: WriterT w f a -> Int # elem :: Eq a => a -> WriterT w f a -> Bool # maximum :: Ord a => WriterT w f a -> a # minimum :: Ord a => WriterT w f a -> a # sum :: Num a => WriterT w f a -> a # product :: Num a => WriterT w f a -> a #
Foldable f => Foldable (WriterT w f)
Instance details Defined in Control.Monad.Trans.Writer.Strict Methods fold :: Monoid m => WriterT w f m -> m # foldMap :: Monoid m => (a -> m) -> WriterT w f a -> m # foldMap' :: Monoid m => (a -> m) -> WriterT w f a -> m # foldr :: (a -> b -> b) -> b -> WriterT w f a -> b # foldr' :: (a -> b -> b) -> b -> WriterT w f a -> b # foldl :: (b -> a -> b) -> b -> WriterT w f a -> b # foldl' :: (b -> a -> b) -> b -> WriterT w f a -> b # foldr1 :: (a -> a -> a) -> WriterT w f a -> a # foldl1 :: (a -> a -> a) -> WriterT w f a -> a # toList :: WriterT w f a -> [a] # null :: WriterT w f a -> Bool # length :: WriterT w f a -> Int # elem :: Eq a => a -> WriterT w f a -> Bool # maximum :: Ord a => WriterT w f a -> a # minimum :: Ord a => WriterT w f a -> a # sum :: Num a => WriterT w f a -> a # product :: Num a => WriterT w f a -> a #
(Foldable f, Foldable g) => Foldable (Product f g)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Product Methods fold :: Monoid m => Product f g m -> m # foldMap :: Monoid m => (a -> m) -> Product f g a -> m # foldMap' :: Monoid m => (a -> m) -> Product f g a -> m # foldr :: (a -> b -> b) -> b -> Product f g a -> b # foldr' :: (a -> b -> b) -> b -> Product f g a -> b # foldl :: (b -> a -> b) -> b -> Product f g a -> b # foldl' :: (b -> a -> b) -> b -> Product f g a -> b # foldr1 :: (a -> a -> a) -> Product f g a -> a # foldl1 :: (a -> a -> a) -> Product f g a -> a # toList :: Product f g a -> [a] # null :: Product f g a -> Bool # length :: Product f g a -> Int # elem :: Eq a => a -> Product f g a -> Bool # maximum :: Ord a => Product f g a -> a # minimum :: Ord a => Product f g a -> a # sum :: Num a => Product f g a -> a # product :: Num a => Product f g a -> a #
(Foldable f, Foldable g) => Foldable (Sum f g)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Sum Methods fold :: Monoid m => Sum f g m -> m # foldMap :: Monoid m => (a -> m) -> Sum f g a -> m # foldMap' :: Monoid m => (a -> m) -> Sum f g a -> m # foldr :: (a -> b -> b) -> b -> Sum f g a -> b # foldr' :: (a -> b -> b) -> b -> Sum f g a -> b # foldl :: (b -> a -> b) -> b -> Sum f g a -> b # foldl' :: (b -> a -> b) -> b -> Sum f g a -> b # foldr1 :: (a -> a -> a) -> Sum f g a -> a # foldl1 :: (a -> a -> a) -> Sum f g a -> a # toList :: Sum f g a -> [a] # null :: Sum f g a -> Bool # length :: Sum f g a -> Int # elem :: Eq a => a -> Sum f g a -> Bool # maximum :: Ord a => Sum f g a -> a # minimum :: Ord a => Sum f g a -> a # sum :: Num a => Sum f g a -> a # product :: Num a => Sum f g a -> a #
(Foldable f, Foldable g) => Foldable (f :*: g)	Since: base-4.9.0.0
Instance details Defined in Data.Foldable Methods fold :: Monoid m => (f :: g) m -> m # foldMap :: Monoid m => (a -> m) -> (f :: g) a -> m # foldMap' :: Monoid m => (a -> m) -> (f :: g) a -> m # foldr :: (a -> b -> b) -> b -> (f :: g) a -> b # foldr' :: (a -> b -> b) -> b -> (f :: g) a -> b # foldl :: (b -> a -> b) -> b -> (f :: g) a -> b # foldl' :: (b -> a -> b) -> b -> (f :: g) a -> b # foldr1 :: (a -> a -> a) -> (f :: g) a -> a # foldl1 :: (a -> a -> a) -> (f :: g) a -> a # toList :: (f :: g) a -> [a] # null :: (f :: g) a -> Bool # length :: (f :: g) a -> Int # elem :: Eq a => a -> (f :: g) a -> Bool # maximum :: Ord a => (f :: g) a -> a # minimum :: Ord a => (f :: g) a -> a # sum :: Num a => (f :: g) a -> a # product :: Num a => (f :*: g) a -> a #
(Foldable f, Foldable g) => Foldable (f :+: g)	Since: base-4.9.0.0
Instance details Defined in Data.Foldable Methods fold :: Monoid m => (f :+: g) m -> m # foldMap :: Monoid m => (a -> m) -> (f :+: g) a -> m # foldMap' :: Monoid m => (a -> m) -> (f :+: g) a -> m # foldr :: (a -> b -> b) -> b -> (f :+: g) a -> b # foldr' :: (a -> b -> b) -> b -> (f :+: g) a -> b # foldl :: (b -> a -> b) -> b -> (f :+: g) a -> b # foldl' :: (b -> a -> b) -> b -> (f :+: g) a -> b # foldr1 :: (a -> a -> a) -> (f :+: g) a -> a # foldl1 :: (a -> a -> a) -> (f :+: g) a -> a # toList :: (f :+: g) a -> [a] # null :: (f :+: g) a -> Bool # length :: (f :+: g) a -> Int # elem :: Eq a => a -> (f :+: g) a -> Bool # maximum :: Ord a => (f :+: g) a -> a # minimum :: Ord a => (f :+: g) a -> a # sum :: Num a => (f :+: g) a -> a # product :: Num a => (f :+: g) a -> a #
Foldable (K1 i c :: TYPE LiftedRep -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Foldable Methods fold :: Monoid m => K1 i c m -> m # foldMap :: Monoid m => (a -> m) -> K1 i c a -> m # foldMap' :: Monoid m => (a -> m) -> K1 i c a -> m # foldr :: (a -> b -> b) -> b -> K1 i c a -> b # foldr' :: (a -> b -> b) -> b -> K1 i c a -> b # foldl :: (b -> a -> b) -> b -> K1 i c a -> b # foldl' :: (b -> a -> b) -> b -> K1 i c a -> b # foldr1 :: (a -> a -> a) -> K1 i c a -> a # foldl1 :: (a -> a -> a) -> K1 i c a -> a # toList :: K1 i c a -> [a] # null :: K1 i c a -> Bool # length :: K1 i c a -> Int # elem :: Eq a => a -> K1 i c a -> Bool # maximum :: Ord a => K1 i c a -> a # minimum :: Ord a => K1 i c a -> a # sum :: Num a => K1 i c a -> a # product :: Num a => K1 i c a -> a #
Foldable (Forget r a :: TYPE LiftedRep -> TYPE LiftedRep)
Instance details Defined in Data.Profunctor.Types Methods fold :: Monoid m => Forget r a m -> m # foldMap :: Monoid m => (a0 -> m) -> Forget r a a0 -> m # foldMap' :: Monoid m => (a0 -> m) -> Forget r a a0 -> m # foldr :: (a0 -> b -> b) -> b -> Forget r a a0 -> b # foldr' :: (a0 -> b -> b) -> b -> Forget r a a0 -> b # foldl :: (b -> a0 -> b) -> b -> Forget r a a0 -> b # foldl' :: (b -> a0 -> b) -> b -> Forget r a a0 -> b # foldr1 :: (a0 -> a0 -> a0) -> Forget r a a0 -> a0 # foldl1 :: (a0 -> a0 -> a0) -> Forget r a a0 -> a0 # toList :: Forget r a a0 -> [a0] # null :: Forget r a a0 -> Bool # length :: Forget r a a0 -> Int # elem :: Eq a0 => a0 -> Forget r a a0 -> Bool # maximum :: Ord a0 => Forget r a a0 -> a0 # minimum :: Ord a0 => Forget r a a0 -> a0 # sum :: Num a0 => Forget r a a0 -> a0 # product :: Num a0 => Forget r a a0 -> a0 #
(Foldable f, Foldable g) => Foldable (Compose f g)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Compose Methods fold :: Monoid m => Compose f g m -> m # foldMap :: Monoid m => (a -> m) -> Compose f g a -> m # foldMap' :: Monoid m => (a -> m) -> Compose f g a -> m # foldr :: (a -> b -> b) -> b -> Compose f g a -> b # foldr' :: (a -> b -> b) -> b -> Compose f g a -> b # foldl :: (b -> a -> b) -> b -> Compose f g a -> b # foldl' :: (b -> a -> b) -> b -> Compose f g a -> b # foldr1 :: (a -> a -> a) -> Compose f g a -> a # foldl1 :: (a -> a -> a) -> Compose f g a -> a # toList :: Compose f g a -> [a] # null :: Compose f g a -> Bool # length :: Compose f g a -> Int # elem :: Eq a => a -> Compose f g a -> Bool # maximum :: Ord a => Compose f g a -> a # minimum :: Ord a => Compose f g a -> a # sum :: Num a => Compose f g a -> a # product :: Num a => Compose f g a -> a #
(Foldable f, Foldable g) => Foldable (f :.: g)	Since: base-4.9.0.0
Instance details Defined in Data.Foldable Methods fold :: Monoid m => (f :.: g) m -> m # foldMap :: Monoid m => (a -> m) -> (f :.: g) a -> m # foldMap' :: Monoid m => (a -> m) -> (f :.: g) a -> m # foldr :: (a -> b -> b) -> b -> (f :.: g) a -> b # foldr' :: (a -> b -> b) -> b -> (f :.: g) a -> b # foldl :: (b -> a -> b) -> b -> (f :.: g) a -> b # foldl' :: (b -> a -> b) -> b -> (f :.: g) a -> b # foldr1 :: (a -> a -> a) -> (f :.: g) a -> a # foldl1 :: (a -> a -> a) -> (f :.: g) a -> a # toList :: (f :.: g) a -> [a] # null :: (f :.: g) a -> Bool # length :: (f :.: g) a -> Int # elem :: Eq a => a -> (f :.: g) a -> Bool # maximum :: Ord a => (f :.: g) a -> a # minimum :: Ord a => (f :.: g) a -> a # sum :: Num a => (f :.: g) a -> a # product :: Num a => (f :.: g) a -> a #
Foldable f => Foldable (M1 i c f)	Since: base-4.9.0.0
Instance details Defined in Data.Foldable Methods fold :: Monoid m => M1 i c f m -> m # foldMap :: Monoid m => (a -> m) -> M1 i c f a -> m # foldMap' :: Monoid m => (a -> m) -> M1 i c f a -> m # foldr :: (a -> b -> b) -> b -> M1 i c f a -> b # foldr' :: (a -> b -> b) -> b -> M1 i c f a -> b # foldl :: (b -> a -> b) -> b -> M1 i c f a -> b # foldl' :: (b -> a -> b) -> b -> M1 i c f a -> b # foldr1 :: (a -> a -> a) -> M1 i c f a -> a # foldl1 :: (a -> a -> a) -> M1 i c f a -> a # toList :: M1 i c f a -> [a] # null :: M1 i c f a -> Bool # length :: M1 i c f a -> Int # elem :: Eq a => a -> M1 i c f a -> Bool # maximum :: Ord a => M1 i c f a -> a # minimum :: Ord a => M1 i c f a -> a # sum :: Num a => M1 i c f a -> a # product :: Num a => M1 i c f a -> a #
Foldable (Clown f a :: TYPE LiftedRep -> Type)
Instance details 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 # sum :: Num a0 => Clown f a a0 -> a0 # product :: Num a0 => Clown f a a0 -> a0 #
Bifoldable p => Foldable (Flip p a)
Instance details 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] # null :: Flip p a a0 -> Bool # 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 # sum :: Num a0 => Flip p a a0 -> a0 # product :: Num a0 => Flip p a a0 -> a0 #
Foldable g => Foldable (Joker g a)
Instance details 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 # sum :: Num a0 => Joker g a a0 -> a0 # product :: Num a0 => Joker g a a0 -> a0 #
Bifoldable p => Foldable (WrappedBifunctor p a)
Instance details 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, Bifoldable p) => Foldable (Tannen f p a)
Instance details 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 # sum :: Num a0 => Tannen f p a a0 -> a0 # product :: Num a0 => Tannen f p a a0 -> a0 #
(Bifoldable p, Foldable g) => Foldable (Biff p f g a)
Instance details 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 # sum :: Num a0 => Biff p f g a a0 -> a0 # product :: Num a0 => Biff p f g a a0 -> a0 #

type family Mutable (v :: Type -> Type) = (mv :: Type -> Type -> Type) | mv -> v #

Mutable v s a is the mutable version of the immutable vector type v a with the state token s. It is injective on GHC 8 and newer.

class MVector (Mutable v) a => Vector (v :: Type -> Type) a #

Class of immutable vectors. Every immutable vector is associated with its mutable version through the Mutable type family. Methods of this class should not be used directly. Instead, Data.Vector.Generic and other Data.Vector modules provide safe and fusible wrappers.

Minimum complete implementation:

Minimal complete definition

basicUnsafeFreeze, basicUnsafeThaw, basicLength, basicUnsafeSlice, basicUnsafeIndexM