{-# LANGUAGE DeriveFoldable #-}{-# LANGUAGE FlexibleInstances #-}{-# LANGUAGE NoImplicitPrelude #-}{-# LANGUAGE ScopedTypeVariables #-}{-# LANGUAGE StandaloneDeriving #-}{-# LANGUAGE Trustworthy #-}{-# LANGUAGE TypeOperators #-}------------------------------------------------------------------------------- |-- Module : Data.Foldable-- Copyright : Ross Paterson 2005-- License : BSD-style (see the LICENSE file in the distribution)---- Maintainer : libraries@haskell.org-- Stability : experimental-- Portability : portable---- Class of data structures that can be folded to a summary value.-------------------------------------------------------------------------------moduleData.Foldable(Foldable (..),-- * Special biased foldsfoldrM ,foldlM ,-- * Folding actions-- ** Applicative actionstraverse_ ,for_ ,sequenceA_ ,asum ,-- ** Monadic actionsmapM_ ,forM_ ,sequence_ ,msum ,-- * Specialized foldsconcat ,concatMap ,and ,or ,any ,all ,maximumBy ,minimumBy ,-- * SearchesnotElem ,find )whereimportData.Bool importData.Either importData.Eq importData.Functor.Utils (Max (..),Min (..),(#.) )importqualifiedGHC.List asListimportData.Maybe importData.Monoid importData.Ord importData.Proxy importGHC.Arr (Array (..),elems ,numElements ,foldlElems ,foldrElems ,foldlElems' ,foldrElems' ,foldl1Elems ,foldr1Elems )importGHC.Base hiding(foldr )importGHC.Generics importGHC.Num (Num (..))infix4`elem` ,`notElem` -- | Data structures that can be folded.---- For example, given a data type---- > data Tree a = Empty | Leaf a | Node (Tree a) a (Tree a)---- a suitable instance would be---- > instance Foldable Tree where-- > foldMap f Empty = mempty-- > foldMap f (Leaf x) = f x-- > foldMap f (Node l k r) = foldMap f l `mappend` f k `mappend` foldMap f r---- This is suitable even for abstract types, as the monoid is assumed-- to satisfy the monoid laws. Alternatively, one could define @foldr@:---- > instance Foldable Tree where-- > foldr f z Empty = z-- > foldr f z (Leaf x) = f x z-- > foldr f z (Node l k r) = foldr f (f k (foldr f z r)) l---- @Foldable@ instances are expected to satisfy the following laws:---- > foldr f z t = appEndo (foldMap (Endo . f) t ) z---- > foldl f z t = appEndo (getDual (foldMap (Dual . Endo . flip f) t)) z---- > fold = foldMap id---- > length = getSum . foldMap (Sum . const 1)---- @sum@, @product@, @maximum@, and @minimum@ should all be essentially-- equivalent to @foldMap@ forms, such as---- > sum = getSum . foldMap Sum---- but may be less defined.---- If the type is also a 'Functor' instance, it should satisfy---- > foldMap f = fold . fmap f---- which implies that---- > foldMap f . fmap g = foldMap (f . g)classFoldable t where{-# MINIMALfoldMap |foldr #-}-- | Combine the elements of a structure using a monoid.fold ::Monoid m =>t m ->m fold =(m -> m) -> t m -> m
forall (t :: * -> *) m a.
(Foldable t, Monoid m) =>
(a -> m) -> t a -> m
foldMap m -> m
forall a. a -> a
id -- | Map each element of the structure to a monoid,-- and combine the results.foldMap ::Monoid m =>(a ->m )->t a ->m {-# INLINEfoldMap #-}-- This INLINE allows more list functions to fuse. See Trac #9848.foldMap f :: a -> m
f =(a -> m -> m) -> m -> t a -> m
forall (t :: * -> *) a b.
Foldable t =>
(a -> b -> b) -> b -> t a -> b
foldr (m -> m -> m
forall a. Monoid a => a -> a -> a
mappend (m -> m -> m) -> (a -> m) -> a -> m -> m
forall b c a. (b -> c) -> (a -> b) -> a -> c
. a -> m
f )m
forall a. Monoid a => a
mempty -- | A variant of 'foldMap' that is strict in the accumulator.---- @since 4.13.0.0foldMap' ::Monoid m =>(a ->m )->t a ->m foldMap' f :: a -> m
f =(m -> a -> m) -> m -> t a -> m
forall (t :: * -> *) b a.
Foldable t =>
(b -> a -> b) -> b -> t a -> b
foldl' (\acc :: m
acc a :: a
a ->m
acc m -> m -> m
forall a. Semigroup a => a -> a -> a
<> a -> m
f a
a )m
forall a. Monoid a => a
mempty -- | Right-associative fold of a structure.---- In the case of lists, 'foldr', when applied to a binary operator, a-- starting value (typically the right-identity of the operator), and a-- list, reduces the list using the binary operator, from right to left:---- > foldr f z [x1, x2, ..., xn] == x1 `f` (x2 `f` ... (xn `f` z)...)---- Note that, since the head of the resulting expression is produced by-- an application of the operator to the first element of the list,-- 'foldr' can produce a terminating expression from an infinite list.---- For a general 'Foldable' structure this should be semantically identical-- to,---- @foldr f z = 'List.foldr' f z . 'toList'@--foldr ::(a ->b ->b )->b ->t a ->b foldr f :: a -> b -> b
f z :: b
z t :: t a
t =Endo b -> b -> b
forall a. Endo a -> a -> a
appEndo ((a -> Endo b) -> t a -> Endo b
forall (t :: * -> *) m a.
(Foldable t, Monoid m) =>
(a -> m) -> t a -> m
foldMap ((b -> b) -> Endo b
forall a. (a -> a) -> Endo a
Endo ((b -> b) -> Endo b) -> (a -> b -> b) -> a -> Endo b
forall b c a. Coercible b c => (b -> c) -> (a -> b) -> a -> c
#. a -> b -> b
f )t a
t )b
z -- | Right-associative fold of a structure, but with strict application of-- the operator.---- @since 4.6.0.0foldr' ::(a ->b ->b )->b ->t a ->b foldr' f :: a -> b -> b
f z0 :: b
z0 xs :: t a
xs =((b -> b) -> a -> b -> b) -> (b -> b) -> t a -> b -> b
forall (t :: * -> *) b a.
Foldable t =>
(b -> a -> b) -> b -> t a -> b
foldl (b -> b) -> a -> b -> b
forall b. (b -> b) -> a -> b -> b
f' b -> b
forall a. a -> a
id t a
xs b
z0 wheref' :: (b -> b) -> a -> b -> b
f' k :: b -> b
k x :: a
x z :: b
z =b -> b
k (b -> b) -> b -> b
forall a b. (a -> b) -> a -> b
$! a -> b -> b
f a
x b
z -- | Left-associative fold of a structure.---- In the case of lists, 'foldl', when applied to a binary-- operator, a starting value (typically the left-identity of the operator),-- and a list, reduces the list using the binary operator, from left to-- right:---- > foldl f z [x1, x2, ..., xn] == (...((z `f` x1) `f` x2) `f`...) `f` xn---- Note that to produce the outermost application of the operator the-- entire input list must be traversed. This means that 'foldl'' will-- diverge if given an infinite list.---- Also note that if you want an efficient left-fold, you probably want to-- use 'foldl'' instead of 'foldl'. The reason for this is that latter does-- not force the "inner" results (e.g. @z \`f\` x1@ in the above example)-- before applying them to the operator (e.g. to @(\`f\` x2)@). This results-- in a thunk chain @O(n)@ elements long, which then must be evaluated from-- the outside-in.---- For a general 'Foldable' structure this should be semantically identical-- to,---- @foldl f z = 'List.foldl' f z . 'toList'@--foldl ::(b ->a ->b )->b ->t a ->b foldl f :: b -> a -> b
f z :: b
z t :: t a
t =Endo b -> b -> b
forall a. Endo a -> a -> a
appEndo (Dual (Endo b) -> Endo b
forall a. Dual a -> a
getDual ((a -> Dual (Endo b)) -> t a -> Dual (Endo b)
forall (t :: * -> *) m a.
(Foldable t, Monoid m) =>
(a -> m) -> t a -> m
foldMap (Endo b -> Dual (Endo b)
forall a. a -> Dual a
Dual (Endo b -> Dual (Endo b)) -> (a -> Endo b) -> a -> Dual (Endo b)
forall b c a. (b -> c) -> (a -> b) -> a -> c
. (b -> b) -> Endo b
forall a. (a -> a) -> Endo a
Endo ((b -> b) -> Endo b) -> (a -> b -> b) -> a -> Endo b
forall b c a. (b -> c) -> (a -> b) -> a -> c
. (b -> a -> b) -> a -> b -> b
forall a b c. (a -> b -> c) -> b -> a -> c
flip b -> a -> b
f )t a
t ))b
z -- There's no point mucking around with coercions here,-- because flip forces us to build a new function anyway.-- | Left-associative fold of a structure but with strict application of-- the operator.---- This ensures that each step of the fold is forced to weak head normal-- form before being applied, avoiding the collection of thunks that would-- otherwise occur. This is often what you want to strictly reduce a finite-- list to a single, monolithic result (e.g. 'length').---- For a general 'Foldable' structure this should be semantically identical-- to,---- @foldl' f z = 'List.foldl'' f z . 'toList'@---- @since 4.6.0.0foldl' ::(b ->a ->b )->b ->t a ->b foldl' f :: b -> a -> b
f z0 :: b
z0 xs :: t a
xs =(a -> (b -> b) -> b -> b) -> (b -> b) -> t a -> b -> b
forall (t :: * -> *) a b.
Foldable t =>
(a -> b -> b) -> b -> t a -> b
foldr a -> (b -> b) -> b -> b
forall b. a -> (b -> b) -> b -> b
f' b -> b
forall a. a -> a
id t a
xs b
z0 wheref' :: a -> (b -> b) -> b -> b
f' x :: a
x k :: b -> b
k z :: b
z =b -> b
k (b -> b) -> b -> b
forall a b. (a -> b) -> a -> b
$! b -> a -> b
f b
z a
x -- | A variant of 'foldr' that has no base case,-- and thus may only be applied to non-empty structures.---- @'foldr1' f = 'List.foldr1' f . 'toList'@foldr1 ::(a ->a ->a )->t a ->a foldr1 f :: a -> a -> a
f xs :: t a
xs =a -> Maybe a -> a
forall a. a -> Maybe a -> a
fromMaybe ([Char] -> a
forall a. [Char] -> a
errorWithoutStackTrace "foldr1: empty structure")((a -> Maybe a -> Maybe a) -> Maybe a -> t a -> Maybe a
forall (t :: * -> *) a b.
Foldable t =>
(a -> b -> b) -> b -> t a -> b
foldr a -> Maybe a -> Maybe a
mf Maybe a
forall a. Maybe a
Nothing t a
xs )wheremf :: a -> Maybe a -> Maybe a
mf x :: a
x m :: Maybe a
m =a -> Maybe a
forall a. a -> Maybe a
Just (caseMaybe a
m ofNothing ->a
x Just y :: a
y ->a -> a -> a
f a
x a
y )-- | A variant of 'foldl' that has no base case,-- and thus may only be applied to non-empty structures.---- @'foldl1' f = 'List.foldl1' f . 'toList'@foldl1 ::(a ->a ->a )->t a ->a foldl1 f :: a -> a -> a
f xs :: t a
xs =a -> Maybe a -> a
forall a. a -> Maybe a -> a
fromMaybe ([Char] -> a
forall a. [Char] -> a
errorWithoutStackTrace "foldl1: empty structure")((Maybe a -> a -> Maybe a) -> Maybe a -> t a -> Maybe a
forall (t :: * -> *) b a.
Foldable t =>
(b -> a -> b) -> b -> t a -> b
foldl Maybe a -> a -> Maybe a
mf Maybe a
forall a. Maybe a
Nothing t a
xs )wheremf :: Maybe a -> a -> Maybe a
mf m :: Maybe a
m y :: a
y =a -> Maybe a
forall a. a -> Maybe a
Just (caseMaybe a
m ofNothing ->a
y Just x :: a
x ->a -> a -> a
f a
x a
y )-- | List of elements of a structure, from left to right.---- @since 4.8.0.0toList ::t a ->[a ]{-# INLINEtoList #-}toList t :: t a
t =(forall b. (a -> b -> b) -> b -> b) -> [a]
forall a. (forall b. (a -> b -> b) -> b -> b) -> [a]
build (\c :: a -> b -> b
c n :: b
n ->(a -> b -> b) -> b -> t a -> b
forall (t :: * -> *) a b.
Foldable t =>
(a -> b -> b) -> b -> t a -> b
foldr a -> b -> b
c b
n t a
t )-- | Test whether the structure is empty. The default implementation is-- optimized for structures that are similar to cons-lists, because there-- is no general way to do better.---- @since 4.8.0.0null ::t a ->Boolnull =(a -> Bool -> Bool) -> Bool -> t a -> Bool
forall (t :: * -> *) a b.
Foldable t =>
(a -> b -> b) -> b -> t a -> b
foldr (\__->Bool
False)Bool
True-- | Returns the size/length of a finite structure as an 'Int'. The-- default implementation is optimized for structures that are similar to-- cons-lists, because there is no general way to do better.---- @since 4.8.0.0length ::t a ->Intlength =(Int -> a -> Int) -> Int -> t a -> Int
forall (t :: * -> *) b a.
Foldable t =>
(b -> a -> b) -> b -> t a -> b
foldl' (\c :: Int
c _->Int
c Int -> Int -> Int
forall a. Num a => a -> a -> a
+ 1)0-- | Does the element occur in the structure?---- @since 4.8.0.0elem ::Eqa =>a ->t a ->Boolelem =(a -> Bool) -> t a -> Bool
forall (t :: * -> *) a. Foldable t => (a -> Bool) -> t a -> Bool
any ((a -> Bool) -> t a -> Bool)
-> (a -> a -> Bool) -> a -> t a -> Bool
forall b c a. (b -> c) -> (a -> b) -> a -> c
. a -> a -> Bool
forall a. Eq a => a -> a -> Bool
(==)-- | The largest element of a non-empty structure.---- @since 4.8.0.0maximum ::foralla .Orda =>t a ->a maximum =a -> Maybe a -> a
forall a. a -> Maybe a -> a
fromMaybe ([Char] -> a
forall a. [Char] -> a
errorWithoutStackTrace "maximum: empty structure")(Maybe a -> a) -> (t a -> Maybe a) -> t a -> a
forall b c a. (b -> c) -> (a -> b) -> a -> c
. Max a -> Maybe a
forall a. Max a -> Maybe a
getMax (Max a -> Maybe a) -> (t a -> Max a) -> t a -> Maybe a
forall b c a. (b -> c) -> (a -> b) -> a -> c
. (a -> Max a) -> t a -> Max a
forall (t :: * -> *) m a.
(Foldable t, Monoid m) =>
(a -> m) -> t a -> m
foldMap (Maybe a -> Max a
forall a. Maybe a -> Max a
Max (Maybe a -> Max a) -> (a -> Maybe a) -> a -> Max a
forall b c a. Coercible b c => (b -> c) -> (a -> b) -> a -> c
#. (a -> Maybe a
forall a. a -> Maybe a
Just ::a ->Maybe a ))-- | The least element of a non-empty structure.---- @since 4.8.0.0minimum ::foralla .Orda =>t a ->a minimum =a -> Maybe a -> a
forall a. a -> Maybe a -> a
fromMaybe ([Char] -> a
forall a. [Char] -> a
errorWithoutStackTrace "minimum: empty structure")(Maybe a -> a) -> (t a -> Maybe a) -> t a -> a
forall b c a. (b -> c) -> (a -> b) -> a -> c
. Min a -> Maybe a
forall a. Min a -> Maybe a
getMin (Min a -> Maybe a) -> (t a -> Min a) -> t a -> Maybe a
forall b c a. (b -> c) -> (a -> b) -> a -> c
. (a -> Min a) -> t a -> Min a
forall (t :: * -> *) m a.
(Foldable t, Monoid m) =>
(a -> m) -> t a -> m
foldMap (Maybe a -> Min a
forall a. Maybe a -> Min a
Min (Maybe a -> Min a) -> (a -> Maybe a) -> a -> Min a
forall b c a. Coercible b c => (b -> c) -> (a -> b) -> a -> c
#. (a -> Maybe a
forall a. a -> Maybe a
Just ::a ->Maybe a ))-- | The 'sum' function computes the sum of the numbers of a structure.---- @since 4.8.0.0sum ::Num a =>t a ->a sum =Sum a -> a
forall a. Sum a -> a
getSum (Sum a -> a) -> (t a -> Sum a) -> t a -> a
forall b c a. Coercible b c => (b -> c) -> (a -> b) -> a -> c
#. (a -> Sum a) -> t a -> Sum a
forall (t :: * -> *) m a.
(Foldable t, Monoid m) =>
(a -> m) -> t a -> m
foldMap a -> Sum a
forall a. a -> Sum a
Sum -- | The 'product' function computes the product of the numbers of a-- structure.---- @since 4.8.0.0product ::Num a =>t a ->a product =Product a -> a
forall a. Product a -> a
getProduct (Product a -> a) -> (t a -> Product a) -> t a -> a
forall b c a. Coercible b c => (b -> c) -> (a -> b) -> a -> c
#. (a -> Product a) -> t a -> Product a
forall (t :: * -> *) m a.
(Foldable t, Monoid m) =>
(a -> m) -> t a -> m
foldMap a -> Product a
forall a. a -> Product a
Product -- instances for Prelude types-- | @since 2.01instanceFoldable Maybe wherefoldMap :: (a -> m) -> Maybe a -> m
foldMap =m -> (a -> m) -> Maybe a -> m
forall b a. b -> (a -> b) -> Maybe a -> b
maybe m
forall a. Monoid a => a
mempty foldr :: (a -> b -> b) -> b -> Maybe a -> b
foldr _z :: b
z Nothing =b
z foldr f :: a -> b -> b
f z :: b
z (Just x :: a
x )=a -> b -> b
f a
x b
z foldl :: (b -> a -> b) -> b -> Maybe a -> b
foldl _z :: b
z Nothing =b
z foldl f :: b -> a -> b
f z :: b
z (Just x :: a
x )=b -> a -> b
f b
z a
x -- | @since 2.01instanceFoldable []whereelem :: a -> [a] -> Bool
elem =a -> [a] -> Bool
forall a. Eq a => a -> [a] -> Bool
List.elem foldl :: (b -> a -> b) -> b -> [a] -> b
foldl =(b -> a -> b) -> b -> [a] -> b
forall a b. (b -> a -> b) -> b -> [a] -> b
List.foldl foldl' :: (b -> a -> b) -> b -> [a] -> b
foldl' =(b -> a -> b) -> b -> [a] -> b
forall a b. (b -> a -> b) -> b -> [a] -> b
List.foldl' foldl1 :: (a -> a -> a) -> [a] -> a
foldl1 =(a -> a -> a) -> [a] -> a
forall a. (a -> a -> a) -> [a] -> a
List.foldl1 foldr :: (a -> b -> b) -> b -> [a] -> b
foldr =(a -> b -> b) -> b -> [a] -> b
forall a b. (a -> b -> b) -> b -> [a] -> b
List.foldr foldr1 :: (a -> a -> a) -> [a] -> a
foldr1 =(a -> a -> a) -> [a] -> a
forall a. (a -> a -> a) -> [a] -> a
List.foldr1 length :: [a] -> Int
length =[a] -> Int
forall a. [a] -> Int
List.length maximum :: [a] -> a
maximum =[a] -> a
forall a. Ord a => [a] -> a
List.maximum minimum :: [a] -> a
minimum =[a] -> a
forall a. Ord a => [a] -> a
List.minimum null :: [a] -> Bool
null =[a] -> Bool
forall a. [a] -> Bool
List.null product :: [a] -> a
product =[a] -> a
forall a. Num a => [a] -> a
List.product sum :: [a] -> a
sum =[a] -> a
forall a. Num a => [a] -> a
List.sum toList :: [a] -> [a]
toList =[a] -> [a]
forall a. a -> a
id -- | @since 4.9.0.0instanceFoldable NonEmpty wherefoldr :: (a -> b -> b) -> b -> NonEmpty a -> b
foldr f :: a -> b -> b
f z :: b
z ~(a :: a
a :| as :: [a]
as )=a -> b -> b
f a
a ((a -> b -> b) -> b -> [a] -> b
forall a b. (a -> b -> b) -> b -> [a] -> b
List.foldr a -> b -> b
f b
z [a]
as )foldl :: (b -> a -> b) -> b -> NonEmpty a -> b
foldl f :: b -> a -> b
f z :: b
z (a :: a
a :| as :: [a]
as )=(b -> a -> b) -> b -> [a] -> b
forall a b. (b -> a -> b) -> b -> [a] -> b
List.foldl b -> a -> b
f (b -> a -> b
f b
z a
a )[a]
as foldl1 :: (a -> a -> a) -> NonEmpty a -> a
foldl1 f :: a -> a -> a
f (a :: a
a :| as :: [a]
as )=(a -> a -> a) -> a -> [a] -> a
forall a b. (b -> a -> b) -> b -> [a] -> b
List.foldl a -> a -> a
f a
a [a]
as -- GHC isn't clever enough to transform the default definition-- into anything like this, so we'd end up shuffling a bunch of-- Maybes around.foldr1 :: (a -> a -> a) -> NonEmpty a -> a
foldr1 f :: a -> a -> a
f (p :: a
p :| ps :: [a]
ps )=(a -> (a -> a) -> a -> a) -> (a -> a) -> [a] -> a -> a
forall (t :: * -> *) a b.
Foldable t =>
(a -> b -> b) -> b -> t a -> b
foldr a -> (a -> a) -> a -> a
forall t. t -> (t -> a) -> a -> a
go a -> a
forall a. a -> a
id [a]
ps a
p wherego :: t -> (t -> a) -> a -> a
go x :: t
x r :: t -> a
r prev :: a
prev =a -> a -> a
f a
prev (t -> a
r t
x )-- We used to say---- length (_ :| as) = 1 + length as---- but the default definition is better, counting from 1.---- The default definition also works great for null and foldl'.-- As usual for cons lists, foldr' is basically hopeless.foldMap :: (a -> m) -> NonEmpty a -> m
foldMap f :: a -> m
f ~(a :: a
a :| as :: [a]
as )=a -> m
f a
a m -> m -> m
forall a. Monoid a => a -> a -> a
`mappend` (a -> m) -> [a] -> m
forall (t :: * -> *) m a.
(Foldable t, Monoid m) =>
(a -> m) -> t a -> m
foldMap a -> m
f [a]
as fold :: NonEmpty m -> m
fold ~(m :: m
m :| ms :: [m]
ms )=m
m m -> m -> m
forall a. Monoid a => a -> a -> a
`mappend` [m] -> m
forall (t :: * -> *) m. (Foldable t, Monoid m) => t m -> m
fold [m]
ms toList :: NonEmpty a -> [a]
toList ~(a :: a
a :| as :: [a]
as )=a
a a -> [a] -> [a]
forall a. a -> [a] -> [a]
:[a]
as -- | @since 4.7.0.0instanceFoldable (Either a )wherefoldMap :: (a -> m) -> Either a a -> m
foldMap _(Left _)=m
forall a. Monoid a => a
mempty foldMap f :: a -> m
f (Right y :: a
y )=a -> m
f a
y foldr :: (a -> b -> b) -> b -> Either a a -> b
foldr _z :: b
z (Left _)=b
z foldr f :: a -> b -> b
f z :: b
z (Right y :: a
y )=a -> b -> b
f a
y b
z length :: Either a a -> Int
length (Left _)=0length (Right _)=1null :: Either a a -> Bool
null =Either a a -> Bool
forall a a. Either a a -> Bool
isLeft -- | @since 4.7.0.0instanceFoldable ((,)a )wherefoldMap :: (a -> m) -> (a, a) -> m
foldMap f :: a -> m
f (_,y :: a
y )=a -> m
f a
y foldr :: (a -> b -> b) -> b -> (a, a) -> b
foldr f :: a -> b -> b
f z :: b
z (_,y :: a
y )=a -> b -> b
f a
y b
z -- | @since 4.8.0.0instanceFoldable (Array i )wherefoldr :: (a -> b -> b) -> b -> Array i a -> b
foldr =(a -> b -> b) -> b -> Array i a -> b
forall a b i. (a -> b -> b) -> b -> Array i a -> b
foldrElems foldl :: (b -> a -> b) -> b -> Array i a -> b
foldl =(b -> a -> b) -> b -> Array i a -> b
forall b a i. (b -> a -> b) -> b -> Array i a -> b
foldlElems foldl' :: (b -> a -> b) -> b -> Array i a -> b
foldl' =(b -> a -> b) -> b -> Array i a -> b
forall b a i. (b -> a -> b) -> b -> Array i a -> b
foldlElems' foldr' :: (a -> b -> b) -> b -> Array i a -> b
foldr' =(a -> b -> b) -> b -> Array i a -> b
forall a b i. (a -> b -> b) -> b -> Array i a -> b
foldrElems' foldl1 :: (a -> a -> a) -> Array i a -> a
foldl1 =(a -> a -> a) -> Array i a -> a
forall a i. (a -> a -> a) -> Array i a -> a
foldl1Elems foldr1 :: (a -> a -> a) -> Array i a -> a
foldr1 =(a -> a -> a) -> Array i a -> a
forall a i. (a -> a -> a) -> Array i a -> a
foldr1Elems toList :: Array i a -> [a]
toList =Array i a -> [a]
forall i a. Array i a -> [a]
elems length :: Array i a -> Int
length =Array i a -> Int
forall i a. Array i a -> Int
numElements null :: Array i a -> Bool
null a :: Array i a
a =Array i a -> Int
forall i a. Array i a -> Int
numElements Array i a
a Int -> Int -> Bool
forall a. Eq a => a -> a -> Bool
==0-- | @since 4.7.0.0instanceFoldable Proxy wherefoldMap :: (a -> m) -> Proxy a -> m
foldMap __=m
forall a. Monoid a => a
mempty {-# INLINEfoldMap #-}fold :: Proxy m -> m
fold _=m
forall a. Monoid a => a
mempty {-# INLINEfold #-}foldr :: (a -> b -> b) -> b -> Proxy a -> b
foldr _z :: b
z _=b
z {-# INLINEfoldr #-}foldl :: (b -> a -> b) -> b -> Proxy a -> b
foldl _z :: b
z _=b
z {-# INLINEfoldl #-}foldl1 :: (a -> a -> a) -> Proxy a -> a
foldl1 __=[Char] -> a
forall a. [Char] -> a
errorWithoutStackTrace "foldl1: Proxy"foldr1 :: (a -> a -> a) -> Proxy a -> a
foldr1 __=[Char] -> a
forall a. [Char] -> a
errorWithoutStackTrace "foldr1: Proxy"length :: Proxy a -> Int
length _=0null :: Proxy a -> Bool
null _=Bool
Trueelem :: a -> Proxy a -> Bool
elem __=Bool
Falsesum :: Proxy a -> a
sum _=0product :: Proxy a -> a
product _=1-- | @since 4.8.0.0instanceFoldable Dual wherefoldMap :: (a -> m) -> Dual a -> m
foldMap =(a -> m) -> Dual a -> m
forall a b. Coercible a b => a -> b
coerceelem :: a -> Dual a -> Bool
elem =((a -> Bool) -> (Dual a -> a) -> Dual a -> Bool
forall b c a. (b -> c) -> (a -> b) -> a -> c
. Dual a -> a
forall a. Dual a -> a
getDual )((a -> Bool) -> Dual a -> Bool)
-> (a -> a -> Bool) -> a -> Dual a -> Bool
forall b c a. Coercible b c => (b -> c) -> (a -> b) -> a -> c
#. a -> a -> Bool
forall a. Eq a => a -> a -> Bool
(==)foldl :: (b -> a -> b) -> b -> Dual a -> b
foldl =(b -> a -> b) -> b -> Dual a -> b
forall a b. Coercible a b => a -> b
coercefoldl' :: (b -> a -> b) -> b -> Dual a -> b
foldl' =(b -> a -> b) -> b -> Dual a -> b
forall a b. Coercible a b => a -> b
coercefoldl1 :: (a -> a -> a) -> Dual a -> a
foldl1 _=Dual a -> a
forall a. Dual a -> a
getDual foldr :: (a -> b -> b) -> b -> Dual a -> b
foldr f :: a -> b -> b
f z :: b
z (Dual x :: a
x )=a -> b -> b
f a
x b
z foldr' :: (a -> b -> b) -> b -> Dual a -> b
foldr' =(a -> b -> b) -> b -> Dual a -> b
forall (t :: * -> *) a b.
Foldable t =>
(a -> b -> b) -> b -> t a -> b
foldr foldr1 :: (a -> a -> a) -> Dual a -> a
foldr1 _=Dual a -> a
forall a. Dual a -> a
getDual length :: Dual a -> Int
length _=1maximum :: Dual a -> a
maximum =Dual a -> a
forall a. Dual a -> a
getDual minimum :: Dual a -> a
minimum =Dual a -> a
forall a. Dual a -> a
getDual null :: Dual a -> Bool
null _=Bool
Falseproduct :: Dual a -> a
product =Dual a -> a
forall a. Dual a -> a
getDual sum :: Dual a -> a
sum =Dual a -> a
forall a. Dual a -> a
getDual toList :: Dual a -> [a]
toList (Dual x :: a
x )=[a
x ]-- | @since 4.8.0.0instanceFoldable Sum wherefoldMap :: (a -> m) -> Sum a -> m
foldMap =(a -> m) -> Sum a -> m
forall a b. Coercible a b => a -> b
coerceelem :: a -> Sum a -> Bool
elem =((a -> Bool) -> (Sum a -> a) -> Sum a -> Bool
forall b c a. (b -> c) -> (a -> b) -> a -> c
. Sum a -> a
forall a. Sum a -> a
getSum )((a -> Bool) -> Sum a -> Bool)
-> (a -> a -> Bool) -> a -> Sum a -> Bool
forall b c a. Coercible b c => (b -> c) -> (a -> b) -> a -> c
#. a -> a -> Bool
forall a. Eq a => a -> a -> Bool
(==)foldl :: (b -> a -> b) -> b -> Sum a -> b
foldl =(b -> a -> b) -> b -> Sum a -> b
forall a b. Coercible a b => a -> b
coercefoldl' :: (b -> a -> b) -> b -> Sum a -> b
foldl' =(b -> a -> b) -> b -> Sum a -> b
forall a b. Coercible a b => a -> b
coercefoldl1 :: (a -> a -> a) -> Sum a -> a
foldl1 _=Sum a -> a
forall a. Sum a -> a
getSum foldr :: (a -> b -> b) -> b -> Sum a -> b
foldr f :: a -> b -> b
f z :: b
z (Sum x :: a
x )=a -> b -> b
f a
x b
z foldr' :: (a -> b -> b) -> b -> Sum a -> b
foldr' =(a -> b -> b) -> b -> Sum a -> b
forall (t :: * -> *) a b.
Foldable t =>
(a -> b -> b) -> b -> t a -> b
foldr foldr1 :: (a -> a -> a) -> Sum a -> a
foldr1 _=Sum a -> a
forall a. Sum a -> a
getSum length :: Sum a -> Int
length _=1maximum :: Sum a -> a
maximum =Sum a -> a
forall a. Sum a -> a
getSum minimum :: Sum a -> a
minimum =Sum a -> a
forall a. Sum a -> a
getSum null :: Sum a -> Bool
null _=Bool
Falseproduct :: Sum a -> a
product =Sum a -> a
forall a. Sum a -> a
getSum sum :: Sum a -> a
sum =Sum a -> a
forall a. Sum a -> a
getSum toList :: Sum a -> [a]
toList (Sum x :: a
x )=[a
x ]-- | @since 4.8.0.0instanceFoldable Product wherefoldMap :: (a -> m) -> Product a -> m
foldMap =(a -> m) -> Product a -> m
forall a b. Coercible a b => a -> b
coerceelem :: a -> Product a -> Bool
elem =((a -> Bool) -> (Product a -> a) -> Product a -> Bool
forall b c a. (b -> c) -> (a -> b) -> a -> c
. Product a -> a
forall a. Product a -> a
getProduct )((a -> Bool) -> Product a -> Bool)
-> (a -> a -> Bool) -> a -> Product a -> Bool
forall b c a. Coercible b c => (b -> c) -> (a -> b) -> a -> c
#. a -> a -> Bool
forall a. Eq a => a -> a -> Bool
(==)foldl :: (b -> a -> b) -> b -> Product a -> b
foldl =(b -> a -> b) -> b -> Product a -> b
forall a b. Coercible a b => a -> b
coercefoldl' :: (b -> a -> b) -> b -> Product a -> b
foldl' =(b -> a -> b) -> b -> Product a -> b
forall a b. Coercible a b => a -> b
coercefoldl1 :: (a -> a -> a) -> Product a -> a
foldl1 _=Product a -> a
forall a. Product a -> a
getProduct foldr :: (a -> b -> b) -> b -> Product a -> b
foldr f :: a -> b -> b
f z :: b
z (Product x :: a
x )=a -> b -> b
f a
x b
z foldr' :: (a -> b -> b) -> b -> Product a -> b
foldr' =(a -> b -> b) -> b -> Product a -> b
forall (t :: * -> *) a b.
Foldable t =>
(a -> b -> b) -> b -> t a -> b
foldr foldr1 :: (a -> a -> a) -> Product a -> a
foldr1 _=Product a -> a
forall a. Product a -> a
getProduct length :: Product a -> Int
length _=1maximum :: Product a -> a
maximum =Product a -> a
forall a. Product a -> a
getProduct minimum :: Product a -> a
minimum =Product a -> a
forall a. Product a -> a
getProduct null :: Product a -> Bool
null _=Bool
Falseproduct :: Product a -> a
product =Product a -> a
forall a. Product a -> a
getProduct sum :: Product a -> a
sum =Product a -> a
forall a. Product a -> a
getProduct toList :: Product a -> [a]
toList (Product x :: a
x )=[a
x ]-- | @since 4.8.0.0instanceFoldable First wherefoldMap :: (a -> m) -> First a -> m
foldMap f :: a -> m
f =(a -> m) -> Maybe a -> m
forall (t :: * -> *) m a.
(Foldable t, Monoid m) =>
(a -> m) -> t a -> m
foldMap a -> m
f (Maybe a -> m) -> (First a -> Maybe a) -> First a -> m
forall b c a. (b -> c) -> (a -> b) -> a -> c
. First a -> Maybe a
forall a. First a -> Maybe a
getFirst -- | @since 4.8.0.0instanceFoldable Last wherefoldMap :: (a -> m) -> Last a -> m
foldMap f :: a -> m
f =(a -> m) -> Maybe a -> m
forall (t :: * -> *) m a.
(Foldable t, Monoid m) =>
(a -> m) -> t a -> m
foldMap a -> m
f (Maybe a -> m) -> (Last a -> Maybe a) -> Last a -> m
forall b c a. (b -> c) -> (a -> b) -> a -> c
. Last a -> Maybe a
forall a. Last a -> Maybe a
getLast -- | @since 4.12.0.0instance(Foldable f )=>Foldable (Alt f )wherefoldMap :: (a -> m) -> Alt f a -> m
foldMap f :: a -> m
f =(a -> m) -> f a -> m
forall (t :: * -> *) m a.
(Foldable t, Monoid m) =>
(a -> m) -> t a -> m
foldMap a -> m
f (f a -> m) -> (Alt f a -> f a) -> Alt f a -> m
forall b c a. (b -> c) -> (a -> b) -> a -> c
. Alt f a -> f a
forall k (f :: k -> *) (a :: k). Alt f a -> f a
getAlt -- | @since 4.12.0.0instance(Foldable f )=>Foldable (Ap f )wherefoldMap :: (a -> m) -> Ap f a -> m
foldMap f :: a -> m
f =(a -> m) -> f a -> m
forall (t :: * -> *) m a.
(Foldable t, Monoid m) =>
(a -> m) -> t a -> m
foldMap a -> m
f (f a -> m) -> (Ap f a -> f a) -> Ap f a -> m
forall b c a. (b -> c) -> (a -> b) -> a -> c
. Ap f a -> f a
forall k (f :: k -> *) (a :: k). Ap f a -> f a
getAp -- Instances for GHC.Generics-- | @since 4.9.0.0instanceFoldable U1 wherefoldMap :: (a -> m) -> U1 a -> m
foldMap __=m
forall a. Monoid a => a
mempty {-# INLINEfoldMap #-}fold :: U1 m -> m
fold _=m
forall a. Monoid a => a
mempty {-# INLINEfold #-}foldr :: (a -> b -> b) -> b -> U1 a -> b
foldr _z :: b
z _=b
z {-# INLINEfoldr #-}foldl :: (b -> a -> b) -> b -> U1 a -> b
foldl _z :: b
z _=b
z {-# INLINEfoldl #-}foldl1 :: (a -> a -> a) -> U1 a -> a
foldl1 __=[Char] -> a
forall a. [Char] -> a
errorWithoutStackTrace "foldl1: U1"foldr1 :: (a -> a -> a) -> U1 a -> a
foldr1 __=[Char] -> a
forall a. [Char] -> a
errorWithoutStackTrace "foldr1: U1"length :: U1 a -> Int
length _=0null :: U1 a -> Bool
null _=Bool
Trueelem :: a -> U1 a -> Bool
elem __=Bool
Falsesum :: U1 a -> a
sum _=0product :: U1 a -> a
product _=1-- | @since 4.9.0.0derivinginstanceFoldable V1 -- | @since 4.9.0.0derivinginstanceFoldable Par1 -- | @since 4.9.0.0derivinginstanceFoldable f =>Foldable (Rec1 f )-- | @since 4.9.0.0derivinginstanceFoldable (K1 i c )-- | @since 4.9.0.0derivinginstanceFoldable f =>Foldable (M1 i c f )-- | @since 4.9.0.0derivinginstance(Foldable f ,Foldable g )=>Foldable (f :+: g )-- | @since 4.9.0.0derivinginstance(Foldable f ,Foldable g )=>Foldable (f :*: g )-- | @since 4.9.0.0derivinginstance(Foldable f ,Foldable g )=>Foldable (f :.: g )-- | @since 4.9.0.0derivinginstanceFoldable UAddr -- | @since 4.9.0.0derivinginstanceFoldable UChar -- | @since 4.9.0.0derivinginstanceFoldable UDouble -- | @since 4.9.0.0derivinginstanceFoldable UFloat -- | @since 4.9.0.0derivinginstanceFoldable UInt -- | @since 4.9.0.0derivinginstanceFoldable UWord -- Instances for Data.Ord-- | @since 4.12.0.0derivinginstanceFoldable Down -- | Monadic fold over the elements of a structure,-- associating to the right, i.e. from right to left.foldrM ::(Foldable t ,Monad m )=>(a ->b ->m b )->b ->t a ->m b foldrM :: (a -> b -> m b) -> b -> t a -> m b
foldrM f :: a -> b -> m b
f z0 :: b
z0 xs :: t a
xs =((b -> m b) -> a -> b -> m b) -> (b -> m b) -> t a -> b -> m b
forall (t :: * -> *) b a.
Foldable t =>
(b -> a -> b) -> b -> t a -> b
foldl (b -> m b) -> a -> b -> m b
forall b. (b -> m b) -> a -> b -> m b
c b -> m b
forall (m :: * -> *) a. Monad m => a -> m a
return t a
xs b
z0 -- See Note [List fusion and continuations in 'c']wherec :: (b -> m b) -> a -> b -> m b
c k :: b -> m b
k x :: a
x z :: b
z =a -> b -> m b
f a
x b
z m b -> (b -> m b) -> m b
forall (m :: * -> *) a b. Monad m => m a -> (a -> m b) -> m b
>>= b -> m b
k {-# INLINEc #-}-- | Monadic fold over the elements of a structure,-- associating to the left, i.e. from left to right.foldlM ::(Foldable t ,Monad m )=>(b ->a ->m b )->b ->t a ->m b foldlM :: (b -> a -> m b) -> b -> t a -> m b
foldlM f :: b -> a -> m b
f z0 :: b
z0 xs :: t a
xs =(a -> (b -> m b) -> b -> m b) -> (b -> m b) -> t a -> b -> m b
forall (t :: * -> *) a b.
Foldable t =>
(a -> b -> b) -> b -> t a -> b
foldr a -> (b -> m b) -> b -> m b
forall b. a -> (b -> m b) -> b -> m b
c b -> m b
forall (m :: * -> *) a. Monad m => a -> m a
return t a
xs b
z0 -- See Note [List fusion and continuations in 'c']wherec :: a -> (b -> m b) -> b -> m b
c x :: a
x k :: b -> m b
k z :: b
z =b -> a -> m b
f b
z a
x m b -> (b -> m b) -> m b
forall (m :: * -> *) a b. Monad m => m a -> (a -> m b) -> m b
>>= b -> m b
k {-# INLINEc #-}-- | Map each element of a structure to an action, evaluate these-- actions from left to right, and ignore the results. For a version-- that doesn't ignore the results see 'Data.Traversable.traverse'.traverse_ ::(Foldable t ,Applicative f )=>(a ->f b )->t a ->f ()traverse_ :: (a -> f b) -> t a -> f ()
traverse_ f :: a -> f b
f =(a -> f () -> f ()) -> f () -> t a -> f ()
forall (t :: * -> *) a b.
Foldable t =>
(a -> b -> b) -> b -> t a -> b
foldr a -> f () -> f ()
forall b. a -> f b -> f b
c (() -> f ()
forall (f :: * -> *) a. Applicative f => a -> f a
pure ())-- See Note [List fusion and continuations in 'c']wherec :: a -> f b -> f b
c x :: a
x k :: f b
k =a -> f b
f a
x f b -> f b -> f b
forall (f :: * -> *) a b. Applicative f => f a -> f b -> f b
*> f b
k {-# INLINEc #-}-- | 'for_' is 'traverse_' with its arguments flipped. For a version-- that doesn't ignore the results see 'Data.Traversable.for'.---- >>> for_ [1..4] print-- 1-- 2-- 3-- 4for_ ::(Foldable t ,Applicative f )=>t a ->(a ->f b )->f (){-# INLINEfor_ #-}for_ :: t a -> (a -> f b) -> f ()
for_ =((a -> f b) -> t a -> f ()) -> t a -> (a -> f b) -> f ()
forall a b c. (a -> b -> c) -> b -> a -> c
flip (a -> f b) -> t a -> f ()
forall (t :: * -> *) (f :: * -> *) a b.
(Foldable t, Applicative f) =>
(a -> f b) -> t a -> f ()
traverse_ -- | Map each element of a structure to a monadic action, evaluate-- these actions from left to right, and ignore the results. For a-- version that doesn't ignore the results see-- 'Data.Traversable.mapM'.---- As of base 4.8.0.0, 'mapM_' is just 'traverse_', specialized to-- 'Monad'.mapM_ ::(Foldable t ,Monad m )=>(a ->m b )->t a ->m ()mapM_ :: (a -> m b) -> t a -> m ()
mapM_ f :: a -> m b
f =(a -> m () -> m ()) -> m () -> t a -> m ()
forall (t :: * -> *) a b.
Foldable t =>
(a -> b -> b) -> b -> t a -> b
foldr a -> m () -> m ()
forall b. a -> m b -> m b
c (() -> m ()
forall (m :: * -> *) a. Monad m => a -> m a
return ())-- See Note [List fusion and continuations in 'c']wherec :: a -> m b -> m b
c x :: a
x k :: m b
k =a -> m b
f a
x m b -> m b -> m b
forall (m :: * -> *) a b. Monad m => m a -> m b -> m b
>> m b
k {-# INLINEc #-}-- | 'forM_' is 'mapM_' with its arguments flipped. For a version that-- doesn't ignore the results see 'Data.Traversable.forM'.---- As of base 4.8.0.0, 'forM_' is just 'for_', specialized to 'Monad'.forM_ ::(Foldable t ,Monad m )=>t a ->(a ->m b )->m (){-# INLINEforM_ #-}forM_ :: t a -> (a -> m b) -> m ()
forM_ =((a -> m b) -> t a -> m ()) -> t a -> (a -> m b) -> m ()
forall a b c. (a -> b -> c) -> b -> a -> c
flip (a -> m b) -> t a -> m ()
forall (t :: * -> *) (m :: * -> *) a b.
(Foldable t, Monad m) =>
(a -> m b) -> t a -> m ()
mapM_ -- | Evaluate each action in the structure from left to right, and-- ignore the results. For a version that doesn't ignore the results-- see 'Data.Traversable.sequenceA'.sequenceA_ ::(Foldable t ,Applicative f )=>t (f a )->f ()sequenceA_ :: t (f a) -> f ()
sequenceA_ =(f a -> f () -> f ()) -> f () -> t (f a) -> f ()
forall (t :: * -> *) a b.
Foldable t =>
(a -> b -> b) -> b -> t a -> b
foldr f a -> f () -> f ()
forall (f :: * -> *) a b. Applicative f => f a -> f b -> f b
c (() -> f ()
forall (f :: * -> *) a. Applicative f => a -> f a
pure ())-- See Note [List fusion and continuations in 'c']wherec :: f a -> f b -> f b
c m :: f a
m k :: f b
k =f a
m f a -> f b -> f b
forall (f :: * -> *) a b. Applicative f => f a -> f b -> f b
*> f b
k {-# INLINEc #-}-- | Evaluate each monadic action in the structure from left to right,-- and ignore the results. For a version that doesn't ignore the-- results see 'Data.Traversable.sequence'.---- As of base 4.8.0.0, 'sequence_' is just 'sequenceA_', specialized-- to 'Monad'.sequence_ ::(Foldable t ,Monad m )=>t (m a )->m ()sequence_ :: t (m a) -> m ()
sequence_ =(m a -> m () -> m ()) -> m () -> t (m a) -> m ()
forall (t :: * -> *) a b.
Foldable t =>
(a -> b -> b) -> b -> t a -> b
foldr m a -> m () -> m ()
forall (m :: * -> *) a b. Monad m => m a -> m b -> m b
c (() -> m ()
forall (m :: * -> *) a. Monad m => a -> m a
return ())-- See Note [List fusion and continuations in 'c']wherec :: m a -> m b -> m b
c m :: m a
m k :: m b
k =m a
m m a -> m b -> m b
forall (m :: * -> *) a b. Monad m => m a -> m b -> m b
>> m b
k {-# INLINEc #-}-- | The sum of a collection of actions, generalizing 'concat'.---- >>> asum [Just "Hello", Nothing, Just "World"]-- Just "Hello"asum ::(Foldable t ,Alternative f )=>t (f a )->f a {-# INLINEasum #-}asum :: t (f a) -> f a
asum =(f a -> f a -> f a) -> f a -> t (f a) -> f a
forall (t :: * -> *) a b.
Foldable t =>
(a -> b -> b) -> b -> t a -> b
foldr f a -> f a -> f a
forall (f :: * -> *) a. Alternative f => f a -> f a -> f a
(<|>) f a
forall (f :: * -> *) a. Alternative f => f a
empty -- | The sum of a collection of actions, generalizing 'concat'.-- As of base 4.8.0.0, 'msum' is just 'asum', specialized to 'MonadPlus'.msum ::(Foldable t ,MonadPlus m )=>t (m a )->m a {-# INLINEmsum #-}msum :: t (m a) -> m a
msum =t (m a) -> m a
forall (t :: * -> *) (f :: * -> *) a.
(Foldable t, Alternative f) =>
t (f a) -> f a
asum -- | The concatenation of all the elements of a container of lists.concat ::Foldable t =>t [a ]->[a ]concat :: t [a] -> [a]
concat xs :: t [a]
xs =(forall b. (a -> b -> b) -> b -> b) -> [a]
forall a. (forall b. (a -> b -> b) -> b -> b) -> [a]
build (\c :: a -> b -> b
c n :: b
n ->([a] -> b -> b) -> b -> t [a] -> b
forall (t :: * -> *) a b.
Foldable t =>
(a -> b -> b) -> b -> t a -> b
foldr (\x :: [a]
x y :: b
y ->(a -> b -> b) -> b -> [a] -> b
forall (t :: * -> *) a b.
Foldable t =>
(a -> b -> b) -> b -> t a -> b
foldr a -> b -> b
c b
y [a]
x )b
n t [a]
xs ){-# INLINEconcat #-}-- | Map a function over all the elements of a container and concatenate-- the resulting lists.concatMap ::Foldable t =>(a ->[b ])->t a ->[b ]concatMap :: (a -> [b]) -> t a -> [b]
concatMap f :: a -> [b]
f xs :: t a
xs =(forall b. (b -> b -> b) -> b -> b) -> [b]
forall a. (forall b. (a -> b -> b) -> b -> b) -> [a]
build (\c :: b -> b -> b
c n :: b
n ->(a -> b -> b) -> b -> t a -> b
forall (t :: * -> *) a b.
Foldable t =>
(a -> b -> b) -> b -> t a -> b
foldr (\x :: a
x b :: b
b ->(b -> b -> b) -> b -> [b] -> b
forall (t :: * -> *) a b.
Foldable t =>
(a -> b -> b) -> b -> t a -> b
foldr b -> b -> b
c b
b (a -> [b]
f a
x ))b
n t a
xs ){-# INLINEconcatMap #-}-- These use foldr rather than foldMap to avoid repeated concatenation.-- | 'and' returns the conjunction of a container of Bools. For the-- result to be 'True', the container must be finite; 'False', however,-- results from a 'False' value finitely far from the left end.and ::Foldable t =>t Bool->Booland :: t Bool -> Bool
and =All -> Bool
getAll (All -> Bool) -> (t Bool -> All) -> t Bool -> Bool
forall b c a. Coercible b c => (b -> c) -> (a -> b) -> a -> c
#. (Bool -> All) -> t Bool -> All
forall (t :: * -> *) m a.
(Foldable t, Monoid m) =>
(a -> m) -> t a -> m
foldMap Bool -> All
All -- | 'or' returns the disjunction of a container of Bools. For the-- result to be 'False', the container must be finite; 'True', however,-- results from a 'True' value finitely far from the left end.or ::Foldable t =>t Bool->Boolor :: t Bool -> Bool
or =Any -> Bool
getAny (Any -> Bool) -> (t Bool -> Any) -> t Bool -> Bool
forall b c a. Coercible b c => (b -> c) -> (a -> b) -> a -> c
#. (Bool -> Any) -> t Bool -> Any
forall (t :: * -> *) m a.
(Foldable t, Monoid m) =>
(a -> m) -> t a -> m
foldMap Bool -> Any
Any -- | Determines whether any element of the structure satisfies the predicate.any ::Foldable t =>(a ->Bool)->t a ->Boolany :: (a -> Bool) -> t a -> Bool
any p :: a -> Bool
p =Any -> Bool
getAny (Any -> Bool) -> (t a -> Any) -> t a -> Bool
forall b c a. Coercible b c => (b -> c) -> (a -> b) -> a -> c
#. (a -> Any) -> t a -> Any
forall (t :: * -> *) m a.
(Foldable t, Monoid m) =>
(a -> m) -> t a -> m
foldMap (Bool -> Any
Any (Bool -> Any) -> (a -> Bool) -> a -> Any
forall b c a. Coercible b c => (b -> c) -> (a -> b) -> a -> c
#. a -> Bool
p )-- | Determines whether all elements of the structure satisfy the predicate.all ::Foldable t =>(a ->Bool)->t a ->Boolall :: (a -> Bool) -> t a -> Bool
all p :: a -> Bool
p =All -> Bool
getAll (All -> Bool) -> (t a -> All) -> t a -> Bool
forall b c a. Coercible b c => (b -> c) -> (a -> b) -> a -> c
#. (a -> All) -> t a -> All
forall (t :: * -> *) m a.
(Foldable t, Monoid m) =>
(a -> m) -> t a -> m
foldMap (Bool -> All
All (Bool -> All) -> (a -> Bool) -> a -> All
forall b c a. Coercible b c => (b -> c) -> (a -> b) -> a -> c
#. a -> Bool
p )-- | The largest element of a non-empty structure with respect to the-- given comparison function.-- See Note [maximumBy/minimumBy space usage]maximumBy ::Foldable t =>(a ->a ->Ordering)->t a ->a maximumBy :: (a -> a -> Ordering) -> t a -> a
maximumBy cmp :: a -> a -> Ordering
cmp =(a -> a -> a) -> t a -> a
forall (t :: * -> *) a. Foldable t => (a -> a -> a) -> t a -> a
foldl1 a -> a -> a
max' wheremax' :: a -> a -> a
max' x :: a
x y :: a
y =casea -> a -> Ordering
cmp a
x a
y ofGT->a
x _->a
y -- | The least element of a non-empty structure with respect to the-- given comparison function.-- See Note [maximumBy/minimumBy space usage]minimumBy ::Foldable t =>(a ->a ->Ordering)->t a ->a minimumBy :: (a -> a -> Ordering) -> t a -> a
minimumBy cmp :: a -> a -> Ordering
cmp =(a -> a -> a) -> t a -> a
forall (t :: * -> *) a. Foldable t => (a -> a -> a) -> t a -> a
foldl1 a -> a -> a
min' wheremin' :: a -> a -> a
min' x :: a
x y :: a
y =casea -> a -> Ordering
cmp a
x a
y ofGT->a
y _->a
x -- | 'notElem' is the negation of 'elem'.notElem ::(Foldable t ,Eqa )=>a ->t a ->BoolnotElem :: a -> t a -> Bool
notElem x :: a
x =Bool -> Bool
not(Bool -> Bool) -> (t a -> Bool) -> t a -> Bool
forall b c a. (b -> c) -> (a -> b) -> a -> c
. a -> t a -> Bool
forall (t :: * -> *) a. (Foldable t, Eq a) => a -> t a -> Bool
elem a
x -- | The 'find' function takes a predicate and a structure and returns-- the leftmost element of the structure matching the predicate, or-- 'Nothing' if there is no such element.find ::Foldable t =>(a ->Bool)->t a ->Maybe a find :: (a -> Bool) -> t a -> Maybe a
find p :: a -> Bool
p =First a -> Maybe a
forall a. First a -> Maybe a
getFirst (First a -> Maybe a) -> (t a -> First a) -> t a -> Maybe a
forall b c a. (b -> c) -> (a -> b) -> a -> c
. (a -> First a) -> t a -> First a
forall (t :: * -> *) m a.
(Foldable t, Monoid m) =>
(a -> m) -> t a -> m
foldMap (\x :: a
x ->Maybe a -> First a
forall a. Maybe a -> First a
First (ifa -> Bool
p a
x thena -> Maybe a
forall a. a -> Maybe a
Just a
x elseMaybe a
forall a. Maybe a
Nothing )){-
Note [List fusion and continuations in 'c']
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Suppose we define
 mapM_ f = foldr ((>>) . f) (return ())
(this is the way it used to be).
Now suppose we want to optimise the call
 mapM_ <big> (build g)
 where
 g c n = ...(c x1 y1)...(c x2 y2)....n...
GHC used to proceed like this:
 mapM_ <big> (build g)
 = { Definition of mapM_ }
 foldr ((>>) . <big>) (return ()) (build g)
 = { foldr/build rule }
 g ((>>) . <big>) (return ())
 = { Inline g }
 let c = (>>) . <big>
 n = return ()
 in ...(c x1 y1)...(c x2 y2)....n...
The trouble is that `c`, being big, will not be inlined. And that can
be absolutely terrible for performance, as we saw in Trac #8763.
It's much better to define
 mapM_ f = foldr c (return ())
 where
 c x k = f x >> k
 {-# INLINE c #-}
Now we get
 mapM_ <big> (build g)
 = { inline mapM_ }
 foldr c (return ()) (build g)
 where c x k = f x >> k
 {-# INLINE c #-}
 f = <big>
Notice that `f` does not inline into the RHS of `c`,
because the INLINE pragma stops it; see
Note [Simplifying inside stable unfoldings] in SimplUtils.
Continuing:
 = { foldr/build rule }
 g c (return ())
 where ...
 c x k = f x >> k
 {-# INLINE c #-}
 f = <big>
 = { inline g }
 ...(c x1 y1)...(c x2 y2)....n...
 where c x k = f x >> k
 {-# INLINE c #-}
 f = <big>
 n = return ()
 Now, crucially, `c` does inline
 = { inline c }
 ...(f x1 >> y1)...(f x2 >> y2)....n...
 where f = <big>
 n = return ()
And all is well! The key thing is that the fragment
`(f x1 >> y1)` is inlined into the body of the builder
`g`.
-}{-
Note [maximumBy/minimumBy space usage]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
When the type signatures of maximumBy and minimumBy were generalized to work
over any Foldable instance (instead of just lists), they were defined using
foldr1. This was problematic for space usage, as the semantics of maximumBy
and minimumBy essentially require that they examine every element of the
data structure. Using foldr1 to examine every element results in space usage
proportional to the size of the data structure. For the common case of lists,
this could be particularly bad (see Trac #10830).
For the common case of lists, switching the implementations of maximumBy and
minimumBy to foldl1 solves the issue, as GHC's strictness analysis can then
make these functions only use O(1) stack space. It is perhaps not the optimal
way to fix this problem, as there are other conceivable data structures
(besides lists) which might benefit from specialized implementations for
maximumBy and minimumBy (see
https://ghc.haskell.org/trac/ghc/ticket/10830#comment:26 for a further
discussion). But using foldl1 is at least always better than using foldr1, so
GHC has chosen to adopt that approach for now.
-}