foldl-1.4.15: Composable, streaming, and efficient left folds

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

`Fold`s are `Applicative`s, 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 -> Type)
- class MVector (Mutable v) a => Vector (v :: Type -> Type) a
- type family Mutable (v :: Type -> Type) = (mv :: Type -> Type -> Type) | mv -> v

# 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) Source # right' :: Fold a b -> Fold (Either c a) (Either c b) Source #
Costrong Fold Source # |
Instance details Defined in Control.Foldl Methods unfirst :: Fold (a, d) (b, d) -> Fold a b Source # unsecond :: Fold (d, a) (d, b) -> Fold a b Source #
Profunctor Fold Source # |
Instance details Defined in Control.Foldl Methods dimap :: (a -> b) -> (c -> d) -> Fold b c -> Fold a d Source # lmap :: (a -> b) -> Fold b c -> Fold a c Source # rmap :: (b -> c) -> Fold a b -> Fold a c Source # (#.) :: forall a b c q. Coercible c b => q b c -> Fold a b -> Fold a c Source # (.#) :: forall a b c q. Coercible b a => Fold b c -> q a b -> Fold a c Source #
Cosieve Fold [] Source # |
Instance details Defined in Control.Foldl Methods cosieve :: Fold a b -> [a] -> b Source #
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 Source #
Applicative (Fold a) Source # |
Instance details Defined in Control.Foldl Methods pure :: a0 -> Fold a a0 Source # (<*>) :: Fold a (a0 -> b) -> Fold a a0 -> Fold a b Source # liftA2 :: (a0 -> b -> c) -> Fold a a0 -> Fold a b -> Fold a c Source # (*>) :: Fold a a0 -> Fold a b -> Fold a b Source # (<*) :: Fold a a0 -> Fold a b -> Fold a a0 Source #
Functor (Fold a) Source # |
Instance details Defined in Control.Foldl Methods fmap :: (a0 -> b) -> Fold a a0 -> Fold a b Source # (<$) :: a0 -> Fold a b -> Fold a a0 Source #
Comonad (Fold a) Source # |
Instance details Defined in Control.Foldl Methods extract :: Fold a a0 -> a0 Source # duplicate :: Fold a a0 -> Fold a (Fold a a0) Source # extend :: (Fold a a0 -> b) -> Fold a a0 -> Fold a b Source #
Extend (Fold a) Source # |
Instance details Defined in Control.Foldl Methods duplicated :: Fold a a0 -> Fold a (Fold a a0) Source # extended :: (Fold a a0 -> b) -> Fold a a0 -> Fold a b Source #
Monoid b => Monoid (Fold a b) Source # |
Instance details Defined in Control.Foldl Methods mempty :: Fold a b Source # mappend :: Fold a b -> Fold a b -> Fold a b Source # mconcat :: [Fold a b] -> Fold a b Source #
Semigroup b => Semigroup (Fold a b) Source # |
Instance details Defined in Control.Foldl Methods (<>) :: Fold a b -> Fold a b -> Fold a b Source # sconcat :: NonEmpty (Fold a b) -> Fold a b Source # stimes :: Integral b0 => b0 -> Fold a b -> Fold a b Source #
Floating b => Floating (Fold a b) Source # |

Instance details

Defined in Control.Foldl

Methods

pi :: Fold a b Source #

exp :: Fold a b -> Fold a b Source #

log :: Fold a b -> Fold a b Source #

sqrt :: Fold a b -> Fold a b Source #

(**) :: Fold a b -> Fold a b -> Fold a b Source #

logBase :: Fold a b -> Fold a b -> Fold a b Source #

sin :: Fold a b -> Fold a b Source #

cos :: Fold a b -> Fold a b Source #

tan :: Fold a b -> Fold a b Source #

asin :: Fold a b -> Fold a b Source #

acos :: Fold a b -> Fold a b Source #

atan :: Fold a b -> Fold a b Source #

sinh :: Fold a b -> Fold a b Source #

cosh :: Fold a b -> Fold a b Source #

tanh :: Fold a b -> Fold a b Source #

asinh :: Fold a b -> Fold a b Source #

acosh :: Fold a b -> Fold a b Source #

atanh :: Fold a b -> Fold a b Source #

log1p :: Fold a b -> Fold a b Source #

expm1 :: Fold a b -> Fold a b Source #

log1pexp :: Fold a b -> Fold a b Source #

log1mexp :: Fold a b -> Fold a b Source #

Num b => Num (Fold a b) Source # |
Instance details Defined in Control.Foldl Methods (+) :: Fold a b -> Fold a b -> Fold a b Source # (-) :: Fold a b -> Fold a b -> Fold a b Source # (*) :: Fold a b -> Fold a b -> Fold a b Source # negate :: Fold a b -> Fold a b Source # abs :: Fold a b -> Fold a b Source # signum :: Fold a b -> Fold a b Source # fromInteger :: Integer -> Fold a b Source #
Fractional b => Fractional (Fold a b) Source # |
Instance details Defined in Control.Foldl Methods (/) :: Fold a b -> Fold a b -> Fold a b Source # recip :: Fold a b -> Fold a b Source # fromRational :: Rational -> Fold a b Source #

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 Source #

lmap :: (a -> b) -> FoldM m b c -> FoldM m a c Source #

rmap :: (b -> c) -> FoldM m a b -> FoldM m a c Source #

(#.) :: forall a b c q. Coercible c b => q b c -> FoldM m a b -> FoldM m a c Source #

(.#) :: forall a b c q. Coercible b a => FoldM m b c -> q a b -> FoldM m a c Source #

Applicative m => Applicative (FoldM m a) Source # |
Instance details Defined in Control.Foldl Methods pure :: a0 -> FoldM m a a0 Source # (<*>) :: FoldM m a (a0 -> b) -> FoldM m a a0 -> FoldM m a b Source # liftA2 :: (a0 -> b -> c) -> FoldM m a a0 -> FoldM m a b -> FoldM m a c Source # (*>) :: FoldM m a a0 -> FoldM m a b -> FoldM m a b Source # (<*) :: FoldM m a a0 -> FoldM m a b -> FoldM m a a0 Source #
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 Source # (<$) :: a0 -> FoldM m a b -> FoldM m a a0 Source #
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) Source # extended :: (FoldM m a a0 -> b) -> FoldM m a a0 -> FoldM m a b Source #
(Monoid b, Monad m) => Monoid (FoldM m a b) Source # |
Instance details Defined in Control.Foldl Methods mempty :: FoldM m a b Source # mappend :: FoldM m a b -> FoldM m a b -> FoldM m a b Source # mconcat :: [FoldM m a b] -> FoldM m a b Source #
(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 Source # sconcat :: NonEmpty (FoldM m a b) -> FoldM m a b Source # stimes :: Integral b0 => b0 -> FoldM m a b -> FoldM m a b Source #
(Monad m, Floating b) => Floating (FoldM m a b) Source # |

Instance details

Defined in Control.Foldl

Methods

pi :: FoldM m a b Source #

exp :: FoldM m a b -> FoldM m a b Source #

log :: FoldM m a b -> FoldM m a b Source #

sqrt :: FoldM m a b -> FoldM m a b Source #

(**) :: FoldM m a b -> FoldM m a b -> FoldM m a b Source #

logBase :: FoldM m a b -> FoldM m a b -> FoldM m a b Source #

sin :: FoldM m a b -> FoldM m a b Source #

cos :: FoldM m a b -> FoldM m a b Source #

tan :: FoldM m a b -> FoldM m a b Source #

asin :: FoldM m a b -> FoldM m a b Source #

acos :: FoldM m a b -> FoldM m a b Source #

atan :: FoldM m a b -> FoldM m a b Source #

sinh :: FoldM m a b -> FoldM m a b Source #

cosh :: FoldM m a b -> FoldM m a b Source #

tanh :: FoldM m a b -> FoldM m a b Source #

asinh :: FoldM m a b -> FoldM m a b Source #

acosh :: FoldM m a b -> FoldM m a b Source #

atanh :: FoldM m a b -> FoldM m a b Source #

log1p :: FoldM m a b -> FoldM m a b Source #

expm1 :: FoldM m a b -> FoldM m a b Source #

log1pexp :: FoldM m a b -> FoldM m a b Source #

log1mexp :: FoldM m a b -> FoldM m a b Source #

(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 Source #

(-) :: FoldM m a b -> FoldM m a b -> FoldM m a b Source #

(*) :: FoldM m a b -> FoldM m a b -> FoldM m a b Source #

negate :: FoldM m a b -> FoldM m a b Source #

abs :: FoldM m a b -> FoldM m a b Source #

signum :: FoldM m a b -> FoldM m a b Source #

fromInteger :: Integer -> FoldM m a b Source #

(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 Source # recip :: FoldM m a b -> FoldM m a b Source # fromRational :: Rational -> FoldM m a b Source #

# 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 `n`th 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 `Fold`s, 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.

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

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 Source #

`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) Source #

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

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

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 Source #

foldMap :: Monoid m => (a -> m) -> ZipList a -> m Source #

foldMap' :: Monoid m => (a -> m) -> ZipList a -> m Source #

foldr :: (a -> b -> b) -> b -> ZipList a -> b Source #

foldr' :: (a -> b -> b) -> b -> ZipList a -> b Source #

foldl :: (b -> a -> b) -> b -> ZipList a -> b Source #

foldl' :: (b -> a -> b) -> b -> ZipList a -> b Source #

foldr1 :: (a -> a -> a) -> ZipList a -> a Source #

foldl1 :: (a -> a -> a) -> ZipList a -> a Source #

toList :: ZipList a -> [a] Source #

null :: ZipList a -> Bool Source #

length :: ZipList a -> Int Source #

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

maximum :: Ord a => ZipList a -> a Source #

minimum :: Ord a => ZipList a -> a Source #

sum :: Num a => ZipList a -> a Source #

product :: Num a => ZipList a -> a Source #

Foldable Identity | Since: base-4.8.0.0

Instance details

Defined in Data.Functor.Identity

Methods

fold :: Monoid m => Identity m -> m Source #

foldMap :: Monoid m => (a -> m) -> Identity a -> m Source #

foldMap' :: Monoid m => (a -> m) -> Identity a -> m Source #

foldr :: (a -> b -> b) -> b -> Identity a -> b Source #

foldr' :: (a -> b -> b) -> b -> Identity a -> b Source #

foldl :: (b -> a -> b) -> b -> Identity a -> b Source #

foldl' :: (b -> a -> b) -> b -> Identity a -> b Source #

foldr1 :: (a -> a -> a) -> Identity a -> a Source #

foldl1 :: (a -> a -> a) -> Identity a -> a Source #

toList :: Identity a -> [a] Source #

null :: Identity a -> Bool Source #

length :: Identity a -> Int Source #

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

maximum :: Ord a => Identity a -> a Source #

minimum :: Ord a => Identity a -> a Source #

sum :: Num a => Identity a -> a Source #

product :: Num a => Identity a -> a Source #

Foldable First | Since: base-4.8.0.0

Instance details

Defined in Data.Foldable

Methods

fold :: Monoid m => First m -> m Source #

foldMap :: Monoid m => (a -> m) -> First a -> m Source #

foldMap' :: Monoid m => (a -> m) -> First a -> m Source #

foldr :: (a -> b -> b) -> b -> First a -> b Source #

foldr' :: (a -> b -> b) -> b -> First a -> b Source #

foldl :: (b -> a -> b) -> b -> First a -> b Source #

foldl' :: (b -> a -> b) -> b -> First a -> b Source #

foldr1 :: (a -> a -> a) -> First a -> a Source #

foldl1 :: (a -> a -> a) -> First a -> a Source #

toList :: First a -> [a] Source #

null :: First a -> Bool Source #

length :: First a -> Int Source #

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

maximum :: Ord a => First a -> a Source #

minimum :: Ord a => First a -> a Source #

sum :: Num a => First a -> a Source #

product :: Num a => First a -> a Source #

Foldable Last | Since: base-4.8.0.0

Instance details

Defined in Data.Foldable

Methods

fold :: Monoid m => Last m -> m Source #

foldMap :: Monoid m => (a -> m) -> Last a -> m Source #

foldMap' :: Monoid m => (a -> m) -> Last a -> m Source #

foldr :: (a -> b -> b) -> b -> Last a -> b Source #

foldr' :: (a -> b -> b) -> b -> Last a -> b Source #

foldl :: (b -> a -> b) -> b -> Last a -> b Source #

foldl' :: (b -> a -> b) -> b -> Last a -> b Source #

foldr1 :: (a -> a -> a) -> Last a -> a Source #

foldl1 :: (a -> a -> a) -> Last a -> a Source #

toList :: Last a -> [a] Source #

null :: Last a -> Bool Source #

length :: Last a -> Int Source #

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

maximum :: Ord a => Last a -> a Source #

minimum :: Ord a => Last a -> a Source #

sum :: Num a => Last a -> a Source #

product :: Num a => Last a -> a Source #

Foldable Down | Since: base-4.12.0.0

Instance details

Defined in Data.Foldable

Methods

fold :: Monoid m => Down m -> m Source #

foldMap :: Monoid m => (a -> m) -> Down a -> m Source #

foldMap' :: Monoid m => (a -> m) -> Down a -> m Source #

foldr :: (a -> b -> b) -> b -> Down a -> b Source #

foldr' :: (a -> b -> b) -> b -> Down a -> b Source #

foldl :: (b -> a -> b) -> b -> Down a -> b Source #

foldl' :: (b -> a -> b) -> b -> Down a -> b Source #

foldr1 :: (a -> a -> a) -> Down a -> a Source #

foldl1 :: (a -> a -> a) -> Down a -> a Source #

toList :: Down a -> [a] Source #

null :: Down a -> Bool Source #

length :: Down a -> Int Source #

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

maximum :: Ord a => Down a -> a Source #

minimum :: Ord a => Down a -> a Source #

sum :: Num a => Down a -> a Source #

product :: Num a => Down a -> a Source #

Foldable First | Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

fold :: Monoid m => First m -> m Source #

foldMap :: Monoid m => (a -> m) -> First a -> m Source #

foldMap' :: Monoid m => (a -> m) -> First a -> m Source #

foldr :: (a -> b -> b) -> b -> First a -> b Source #

foldr' :: (a -> b -> b) -> b -> First a -> b Source #

foldl :: (b -> a -> b) -> b -> First a -> b Source #

foldl' :: (b -> a -> b) -> b -> First a -> b Source #

foldr1 :: (a -> a -> a) -> First a -> a Source #

foldl1 :: (a -> a -> a) -> First a -> a Source #

toList :: First a -> [a] Source #

null :: First a -> Bool Source #

length :: First a -> Int Source #

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

maximum :: Ord a => First a -> a Source #

minimum :: Ord a => First a -> a Source #

sum :: Num a => First a -> a Source #

product :: Num a => First a -> a Source #

Foldable Last | Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

fold :: Monoid m => Last m -> m Source #

foldMap :: Monoid m => (a -> m) -> Last a -> m Source #

foldMap' :: Monoid m => (a -> m) -> Last a -> m Source #

foldr :: (a -> b -> b) -> b -> Last a -> b Source #

foldr' :: (a -> b -> b) -> b -> Last a -> b Source #

foldl :: (b -> a -> b) -> b -> Last a -> b Source #

foldl' :: (b -> a -> b) -> b -> Last a -> b Source #

foldr1 :: (a -> a -> a) -> Last a -> a Source #

foldl1 :: (a -> a -> a) -> Last a -> a Source #

toList :: Last a -> [a] Source #

null :: Last a -> Bool Source #

length :: Last a -> Int Source #

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

maximum :: Ord a => Last a -> a Source #

minimum :: Ord a => Last a -> a Source #

sum :: Num a => Last a -> a Source #

product :: Num a => Last a -> a Source #

Foldable Max | Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

fold :: Monoid m => Max m -> m Source #

foldMap :: Monoid m => (a -> m) -> Max a -> m Source #

foldMap' :: Monoid m => (a -> m) -> Max a -> m Source #

foldr :: (a -> b -> b) -> b -> Max a -> b Source #

foldr' :: (a -> b -> b) -> b -> Max a -> b Source #

foldl :: (b -> a -> b) -> b -> Max a -> b Source #

foldl' :: (b -> a -> b) -> b -> Max a -> b Source #

foldr1 :: (a -> a -> a) -> Max a -> a Source #

foldl1 :: (a -> a -> a) -> Max a -> a Source #

toList :: Max a -> [a] Source #

null :: Max a -> Bool Source #

length :: Max a -> Int Source #

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

maximum :: Ord a => Max a -> a Source #

minimum :: Ord a => Max a -> a Source #

sum :: Num a => Max a -> a Source #

product :: Num a => Max a -> a Source #

Foldable Min | Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

fold :: Monoid m => Min m -> m Source #

foldMap :: Monoid m => (a -> m) -> Min a -> m Source #

foldMap' :: Monoid m => (a -> m) -> Min a -> m Source #

foldr :: (a -> b -> b) -> b -> Min a -> b Source #

foldr' :: (a -> b -> b) -> b -> Min a -> b Source #

foldl :: (b -> a -> b) -> b -> Min a -> b Source #

foldl' :: (b -> a -> b) -> b -> Min a -> b Source #

foldr1 :: (a -> a -> a) -> Min a -> a Source #

foldl1 :: (a -> a -> a) -> Min a -> a Source #

toList :: Min a -> [a] Source #

null :: Min a -> Bool Source #

length :: Min a -> Int Source #

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

maximum :: Ord a => Min a -> a Source #

minimum :: Ord a => Min a -> a Source #

sum :: Num a => Min a -> a Source #

product :: Num a => Min a -> a Source #

Foldable Dual | Since: base-4.8.0.0

Instance details

Defined in Data.Foldable

Methods

fold :: Monoid m => Dual m -> m Source #

foldMap :: Monoid m => (a -> m) -> Dual a -> m Source #

foldMap' :: Monoid m => (a -> m) -> Dual a -> m Source #

foldr :: (a -> b -> b) -> b -> Dual a -> b Source #

foldr' :: (a -> b -> b) -> b -> Dual a -> b Source #

foldl :: (b -> a -> b) -> b -> Dual a -> b Source #

foldl' :: (b -> a -> b) -> b -> Dual a -> b Source #

foldr1 :: (a -> a -> a) -> Dual a -> a Source #

foldl1 :: (a -> a -> a) -> Dual a -> a Source #

toList :: Dual a -> [a] Source #

null :: Dual a -> Bool Source #

length :: Dual a -> Int Source #

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

maximum :: Ord a => Dual a -> a Source #

minimum :: Ord a => Dual a -> a Source #

sum :: Num a => Dual a -> a Source #

product :: Num a => Dual a -> a Source #

Foldable Product | Since: base-4.8.0.0

Instance details

Defined in Data.Foldable

Methods

fold :: Monoid m => Product m -> m Source #

foldMap :: Monoid m => (a -> m) -> Product a -> m Source #

foldMap' :: Monoid m => (a -> m) -> Product a -> m Source #

foldr :: (a -> b -> b) -> b -> Product a -> b Source #

foldr' :: (a -> b -> b) -> b -> Product a -> b Source #

foldl :: (b -> a -> b) -> b -> Product a -> b Source #

foldl' :: (b -> a -> b) -> b -> Product a -> b Source #

foldr1 :: (a -> a -> a) -> Product a -> a Source #

foldl1 :: (a -> a -> a) -> Product a -> a Source #

toList :: Product a -> [a] Source #

null :: Product a -> Bool Source #

length :: Product a -> Int Source #

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

maximum :: Ord a => Product a -> a Source #

minimum :: Ord a => Product a -> a Source #

sum :: Num a => Product a -> a Source #

product :: Num a => Product a -> a Source #

Foldable Sum | Since: base-4.8.0.0

Instance details

Defined in Data.Foldable

Methods

fold :: Monoid m => Sum m -> m Source #

foldMap :: Monoid m => (a -> m) -> Sum a -> m Source #

foldMap' :: Monoid m => (a -> m) -> Sum a -> m Source #

foldr :: (a -> b -> b) -> b -> Sum a -> b Source #

foldr' :: (a -> b -> b) -> b -> Sum a -> b Source #

foldl :: (b -> a -> b) -> b -> Sum a -> b Source #

foldl' :: (b -> a -> b) -> b -> Sum a -> b Source #

foldr1 :: (a -> a -> a) -> Sum a -> a Source #

foldl1 :: (a -> a -> a) -> Sum a -> a Source #

toList :: Sum a -> [a] Source #

null :: Sum a -> Bool Source #

length :: Sum a -> Int Source #

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

maximum :: Ord a => Sum a -> a Source #

minimum :: Ord a => Sum a -> a Source #

sum :: Num a => Sum a -> a Source #

product :: Num a => Sum a -> a Source #

Foldable Par1 | Since: base-4.9.0.0

Instance details

Defined in Data.Foldable

Methods

fold :: Monoid m => Par1 m -> m Source #

foldMap :: Monoid m => (a -> m) -> Par1 a -> m Source #

foldMap' :: Monoid m => (a -> m) -> Par1 a -> m Source #

foldr :: (a -> b -> b) -> b -> Par1 a -> b Source #

foldr' :: (a -> b -> b) -> b -> Par1 a -> b Source #

foldl :: (b -> a -> b) -> b -> Par1 a -> b Source #

foldl' :: (b -> a -> b) -> b -> Par1 a -> b Source #

foldr1 :: (a -> a -> a) -> Par1 a -> a Source #

foldl1 :: (a -> a -> a) -> Par1 a -> a Source #

toList :: Par1 a -> [a] Source #

null :: Par1 a -> Bool Source #

length :: Par1 a -> Int Source #

elem :: Eq a => a -> Par1 a -> Bool Source #

maximum :: Ord a => Par1 a -> a Source #

minimum :: Ord a => Par1 a -> a Source #

sum :: Num a => Par1 a -> a Source #

product :: Num a => Par1 a -> a Source #

Foldable IntMap | Folds in order of increasing key.

Instance details

Defined in Data.IntMap.Internal

Methods

fold :: Monoid m => IntMap m -> m Source #

foldMap :: Monoid m => (a -> m) -> IntMap a -> m Source #

foldMap' :: Monoid m => (a -> m) -> IntMap a -> m Source #

foldr :: (a -> b -> b) -> b -> IntMap a -> b Source #

foldr' :: (a -> b -> b) -> b -> IntMap a -> b Source #

foldl :: (b -> a -> b) -> b -> IntMap a -> b Source #

foldl' :: (b -> a -> b) -> b -> IntMap a -> b Source #

foldr1 :: (a -> a -> a) -> IntMap a -> a Source #

foldl1 :: (a -> a -> a) -> IntMap a -> a Source #

toList :: IntMap a -> [a] Source #

null :: IntMap a -> Bool Source #

length :: IntMap a -> Int Source #

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

maximum :: Ord a => IntMap a -> a Source #

minimum :: Ord a => IntMap a -> a Source #

sum :: Num a => IntMap a -> a Source #

product :: Num a => IntMap a -> a Source #

Foldable Digit |

Instance details

Defined in Data.Sequence.Internal

Methods

fold :: Monoid m => Digit m -> m Source #

foldMap :: Monoid m => (a -> m) -> Digit a -> m Source #

foldMap' :: Monoid m => (a -> m) -> Digit a -> m Source #

foldr :: (a -> b -> b) -> b -> Digit a -> b Source #

foldr' :: (a -> b -> b) -> b -> Digit a -> b Source #

foldl :: (b -> a -> b) -> b -> Digit a -> b Source #

foldl' :: (b -> a -> b) -> b -> Digit a -> b Source #

foldr1 :: (a -> a -> a) -> Digit a -> a Source #

foldl1 :: (a -> a -> a) -> Digit a -> a Source #

toList :: Digit a -> [a] Source #

null :: Digit a -> Bool Source #

length :: Digit a -> Int Source #

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

maximum :: Ord a => Digit a -> a Source #

minimum :: Ord a => Digit a -> a Source #

sum :: Num a => Digit a -> a Source #

product :: Num a => Digit a -> a Source #

Foldable Elem |

Instance details

Defined in Data.Sequence.Internal

Methods

fold :: Monoid m => Elem m -> m Source #

foldMap :: Monoid m => (a -> m) -> Elem a -> m Source #

foldMap' :: Monoid m => (a -> m) -> Elem a -> m Source #

foldr :: (a -> b -> b) -> b -> Elem a -> b Source #

foldr' :: (a -> b -> b) -> b -> Elem a -> b Source #

foldl :: (b -> a -> b) -> b -> Elem a -> b Source #

foldl' :: (b -> a -> b) -> b -> Elem a -> b Source #

foldr1 :: (a -> a -> a) -> Elem a -> a Source #

foldl1 :: (a -> a -> a) -> Elem a -> a Source #

toList :: Elem a -> [a] Source #

null :: Elem a -> Bool Source #

length :: Elem a -> Int Source #

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

maximum :: Ord a => Elem a -> a Source #

minimum :: Ord a => Elem a -> a Source #

sum :: Num a => Elem a -> a Source #

product :: Num a => Elem a -> a Source #

Foldable FingerTree |

Instance details

Defined in Data.Sequence.Internal

Methods

fold :: Monoid m => FingerTree m -> m Source #

foldMap :: Monoid m => (a -> m) -> FingerTree a -> m Source #

foldMap' :: Monoid m => (a -> m) -> FingerTree a -> m Source #

foldr :: (a -> b -> b) -> b -> FingerTree a -> b Source #

foldr' :: (a -> b -> b) -> b -> FingerTree a -> b Source #

foldl :: (b -> a -> b) -> b -> FingerTree a -> b Source #

foldl' :: (b -> a -> b) -> b -> FingerTree a -> b Source #

foldr1 :: (a -> a -> a) -> FingerTree a -> a Source #

foldl1 :: (a -> a -> a) -> FingerTree a -> a Source #

toList :: FingerTree a -> [a] Source #

null :: FingerTree a -> Bool Source #

length :: FingerTree a -> Int Source #

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

maximum :: Ord a => FingerTree a -> a Source #

minimum :: Ord a => FingerTree a -> a Source #

sum :: Num a => FingerTree a -> a Source #

product :: Num a => FingerTree a -> a Source #

Foldable Node |

Instance details

Defined in Data.Sequence.Internal

Methods

fold :: Monoid m => Node m -> m Source #

foldMap :: Monoid m => (a -> m) -> Node a -> m Source #

foldMap' :: Monoid m => (a -> m) -> Node a -> m Source #

foldr :: (a -> b -> b) -> b -> Node a -> b Source #

foldr' :: (a -> b -> b) -> b -> Node a -> b Source #

foldl :: (b -> a -> b) -> b -> Node a -> b Source #

foldl' :: (b -> a -> b) -> b -> Node a -> b Source #

foldr1 :: (a -> a -> a) -> Node a -> a Source #

foldl1 :: (a -> a -> a) -> Node a -> a Source #

toList :: Node a -> [a] Source #

null :: Node a -> Bool Source #

length :: Node a -> Int Source #

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

maximum :: Ord a => Node a -> a Source #

minimum :: Ord a => Node a -> a Source #

sum :: Num a => Node a -> a Source #

product :: Num a => Node a -> a Source #

Foldable Seq |

Instance details

Defined in Data.Sequence.Internal

Methods

fold :: Monoid m => Seq m -> m Source #

foldMap :: Monoid m => (a -> m) -> Seq a -> m Source #

foldMap' :: Monoid m => (a -> m) -> Seq a -> m Source #

foldr :: (a -> b -> b) -> b -> Seq a -> b Source #

foldr' :: (a -> b -> b) -> b -> Seq a -> b Source #

foldl :: (b -> a -> b) -> b -> Seq a -> b Source #

foldl' :: (b -> a -> b) -> b -> Seq a -> b Source #

foldr1 :: (a -> a -> a) -> Seq a -> a Source #

foldl1 :: (a -> a -> a) -> Seq a -> a Source #

toList :: Seq a -> [a] Source #

null :: Seq a -> Bool Source #

length :: Seq a -> Int Source #

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

maximum :: Ord a => Seq a -> a Source #

minimum :: Ord a => Seq a -> a Source #

sum :: Num a => Seq a -> a Source #

product :: Num a => Seq a -> a Source #

Foldable ViewL |

Instance details

Defined in Data.Sequence.Internal

Methods

fold :: Monoid m => ViewL m -> m Source #

foldMap :: Monoid m => (a -> m) -> ViewL a -> m Source #

foldMap' :: Monoid m => (a -> m) -> ViewL a -> m Source #

foldr :: (a -> b -> b) -> b -> ViewL a -> b Source #

foldr' :: (a -> b -> b) -> b -> ViewL a -> b Source #

foldl :: (b -> a -> b) -> b -> ViewL a -> b Source #

foldl' :: (b -> a -> b) -> b -> ViewL a -> b Source #

foldr1 :: (a -> a -> a) -> ViewL a -> a Source #

foldl1 :: (a -> a -> a) -> ViewL a -> a Source #

toList :: ViewL a -> [a] Source #

null :: ViewL a -> Bool Source #

length :: ViewL a -> Int Source #

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

maximum :: Ord a => ViewL a -> a Source #

minimum :: Ord a => ViewL a -> a Source #

sum :: Num a => ViewL a -> a Source #

product :: Num a => ViewL a -> a Source #

Foldable ViewR |

Instance details

Defined in Data.Sequence.Internal

Methods

fold :: Monoid m => ViewR m -> m Source #

foldMap :: Monoid m => (a -> m) -> ViewR a -> m Source #

foldMap' :: Monoid m => (a -> m) -> ViewR a -> m Source #

foldr :: (a -> b -> b) -> b -> ViewR a -> b Source #

foldr' :: (a -> b -> b) -> b -> ViewR a -> b Source #

foldl :: (b -> a -> b) -> b -> ViewR a -> b Source #

foldl' :: (b -> a -> b) -> b -> ViewR a -> b Source #

foldr1 :: (a -> a -> a) -> ViewR a -> a Source #

foldl1 :: (a -> a -> a) -> ViewR a -> a Source #

toList :: ViewR a -> [a] Source #

null :: ViewR a -> Bool Source #

length :: ViewR a -> Int Source #

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

maximum :: Ord a => ViewR a -> a Source #

minimum :: Ord a => ViewR a -> a Source #

sum :: Num a => ViewR a -> a Source #

product :: Num a => ViewR a -> a Source #

Foldable Set | Folds in order of increasing key.

Instance details

Defined in Data.Set.Internal

Methods

fold :: Monoid m => Set m -> m Source #

foldMap :: Monoid m => (a -> m) -> Set a -> m Source #

foldMap' :: Monoid m => (a -> m) -> Set a -> m Source #

foldr :: (a -> b -> b) -> b -> Set a -> b Source #

foldr' :: (a -> b -> b) -> b -> Set a -> b Source #

foldl :: (b -> a -> b) -> b -> Set a -> b Source #

foldl' :: (b -> a -> b) -> b -> Set a -> b Source #

foldr1 :: (a -> a -> a) -> Set a -> a Source #

foldl1 :: (a -> a -> a) -> Set a -> a Source #

toList :: Set a -> [a] Source #

null :: Set a -> Bool Source #

length :: Set a -> Int Source #

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

maximum :: Ord a => Set a -> a Source #

minimum :: Ord a => Set a -> a Source #

sum :: Num a => Set a -> a Source #

product :: Num a => Set a -> a Source #

Foldable Tree | Folds in preorder

Instance details

Defined in Data.Tree

Methods

fold :: Monoid m => Tree m -> m Source #

foldMap :: Monoid m => (a -> m) -> Tree a -> m Source #

foldMap' :: Monoid m => (a -> m) -> Tree a -> m Source #

foldr :: (a -> b -> b) -> b -> Tree a -> b Source #

foldr' :: (a -> b -> b) -> b -> Tree a -> b Source #

foldl :: (b -> a -> b) -> b -> Tree a -> b Source #

foldl' :: (b -> a -> b) -> b -> Tree a -> b Source #

foldr1 :: (a -> a -> a) -> Tree a -> a Source #

foldl1 :: (a -> a -> a) -> Tree a -> a Source #

toList :: Tree a -> [a] Source #

null :: Tree a -> Bool Source #

length :: Tree a -> Int Source #

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

maximum :: Ord a => Tree a -> a Source #

minimum :: Ord a => Tree a -> a Source #

sum :: Num a => Tree a -> a Source #

product :: Num a => Tree a -> a Source #

Foldable Hashed |

Instance details

Defined in Data.Hashable.Class

Methods

fold :: Monoid m => Hashed m -> m Source #

foldMap :: Monoid m => (a -> m) -> Hashed a -> m Source #

foldMap' :: Monoid m => (a -> m) -> Hashed a -> m Source #

foldr :: (a -> b -> b) -> b -> Hashed a -> b Source #

foldr' :: (a -> b -> b) -> b -> Hashed a -> b Source #

foldl :: (b -> a -> b) -> b -> Hashed a -> b Source #

foldl' :: (b -> a -> b) -> b -> Hashed a -> b Source #

foldr1 :: (a -> a -> a) -> Hashed a -> a Source #

foldl1 :: (a -> a -> a) -> Hashed a -> a Source #

toList :: Hashed a -> [a] Source #

null :: Hashed a -> Bool Source #

length :: Hashed a -> Int Source #

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

maximum :: Ord a => Hashed a -> a Source #

minimum :: Ord a => Hashed a -> a Source #

sum :: Num a => Hashed a -> a Source #

product :: Num a => Hashed a -> a Source #

Foldable HashSet |

Instance details

Defined in Data.HashSet.Internal

Methods

fold :: Monoid m => HashSet m -> m Source #

foldMap :: Monoid m => (a -> m) -> HashSet a -> m Source #

foldMap' :: Monoid m => (a -> m) -> HashSet a -> m Source #

foldr :: (a -> b -> b) -> b -> HashSet a -> b Source #

foldr' :: (a -> b -> b) -> b -> HashSet a -> b Source #

foldl :: (b -> a -> b) -> b -> HashSet a -> b Source #

foldl' :: (b -> a -> b) -> b -> HashSet a -> b Source #

foldr1 :: (a -> a -> a) -> HashSet a -> a Source #

foldl1 :: (a -> a -> a) -> HashSet a -> a Source #

toList :: HashSet a -> [a] Source #

null :: HashSet a -> Bool Source #

length :: HashSet a -> Int Source #

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

maximum :: Ord a => HashSet a -> a Source #

minimum :: Ord a => HashSet a -> a Source #

sum :: Num a => HashSet a -> a Source #

product :: Num a => HashSet a -> a Source #

Foldable NonEmpty | Since: base-4.9.0.0

Instance details

Defined in Data.Foldable

Methods

fold :: Monoid m => NonEmpty m -> m Source #

foldMap :: Monoid m => (a -> m) -> NonEmpty a -> m Source #

foldMap' :: Monoid m => (a -> m) -> NonEmpty a -> m Source #

foldr :: (a -> b -> b) -> b -> NonEmpty a -> b Source #

foldr' :: (a -> b -> b) -> b -> NonEmpty a -> b Source #

foldl :: (b -> a -> b) -> b -> NonEmpty a -> b Source #

foldl' :: (b -> a -> b) -> b -> NonEmpty a -> b Source #

foldr1 :: (a -> a -> a) -> NonEmpty a -> a Source #

foldl1 :: (a -> a -> a) -> NonEmpty a -> a Source #

toList :: NonEmpty a -> [a] Source #

null :: NonEmpty a -> Bool Source #

length :: NonEmpty a -> Int Source #

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

maximum :: Ord a => NonEmpty a -> a Source #

minimum :: Ord a => NonEmpty a -> a Source #

sum :: Num a => NonEmpty a -> a Source #

product :: Num a => NonEmpty a -> a Source #

Foldable Maybe | Since: base-2.1

Instance details

Defined in Data.Foldable

Methods

fold :: Monoid m => Maybe m -> m Source #

foldMap :: Monoid m => (a -> m) -> Maybe a -> m Source #

foldMap' :: Monoid m => (a -> m) -> Maybe a -> m Source #

foldr :: (a -> b -> b) -> b -> Maybe a -> b Source #

foldr' :: (a -> b -> b) -> b -> Maybe a -> b Source #

foldl :: (b -> a -> b) -> b -> Maybe a -> b Source #

foldl' :: (b -> a -> b) -> b -> Maybe a -> b Source #

foldr1 :: (a -> a -> a) -> Maybe a -> a Source #

foldl1 :: (a -> a -> a) -> Maybe a -> a Source #

toList :: Maybe a -> [a] Source #

null :: Maybe a -> Bool Source #

length :: Maybe a -> Int Source #

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

maximum :: Ord a => Maybe a -> a Source #

minimum :: Ord a => Maybe a -> a Source #

sum :: Num a => Maybe a -> a Source #

product :: Num a => Maybe a -> a Source #

Foldable Solo | Since: base-4.15

Instance details

Defined in Data.Foldable

Methods

fold :: Monoid m => Solo m -> m Source #

foldMap :: Monoid m => (a -> m) -> Solo a -> m Source #

foldMap' :: Monoid m => (a -> m) -> Solo a -> m Source #

foldr :: (a -> b -> b) -> b -> Solo a -> b Source #

foldr' :: (a -> b -> b) -> b -> Solo a -> b Source #

foldl :: (b -> a -> b) -> b -> Solo a -> b Source #

foldl' :: (b -> a -> b) -> b -> Solo a -> b Source #

foldr1 :: (a -> a -> a) -> Solo a -> a Source #

foldl1 :: (a -> a -> a) -> Solo a -> a Source #

toList :: Solo a -> [a] Source #

null :: Solo a -> Bool Source #

length :: Solo a -> Int Source #

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

maximum :: Ord a => Solo a -> a Source #

minimum :: Ord a => Solo a -> a Source #

sum :: Num a => Solo a -> a Source #

product :: Num a => Solo a -> a Source #

Foldable [] | Since: base-2.1

Instance details

Defined in Data.Foldable

Methods

fold :: Monoid m => [m] -> m Source #

foldMap :: Monoid m => (a -> m) -> [a] -> m Source #

foldMap' :: Monoid m => (a -> m) -> [a] -> m Source #

foldr :: (a -> b -> b) -> b -> [a] -> b Source #

foldr' :: (a -> b -> b) -> b -> [a] -> b Source #

foldl :: (b -> a -> b) -> b -> [a] -> b Source #

foldl' :: (b -> a -> b) -> b -> [a] -> b Source #

foldr1 :: (a -> a -> a) -> [a] -> a Source #

foldl1 :: (a -> a -> a) -> [a] -> a Source #

toList :: [a] -> [a] Source #

null :: [a] -> Bool Source #

length :: [a] -> Int Source #

elem :: Eq a => a -> [a] -> Bool Source #

maximum :: Ord a => [a] -> a Source #

minimum :: Ord a => [a] -> a Source #

sum :: Num a => [a] -> a Source #

product :: Num a => [a] -> a Source #

Foldable (Either a) | Since: base-4.7.0.0

Instance details

Defined in Data.Foldable

Methods

fold :: Monoid m => Either a m -> m Source #

foldMap :: Monoid m => (a0 -> m) -> Either a a0 -> m Source #

foldMap' :: Monoid m => (a0 -> m) -> Either a a0 -> m Source #

foldr :: (a0 -> b -> b) -> b -> Either a a0 -> b Source #

foldr' :: (a0 -> b -> b) -> b -> Either a a0 -> b Source #

foldl :: (b -> a0 -> b) -> b -> Either a a0 -> b Source #

foldl' :: (b -> a0 -> b) -> b -> Either a a0 -> b Source #

foldr1 :: (a0 -> a0 -> a0) -> Either a a0 -> a0 Source #

foldl1 :: (a0 -> a0 -> a0) -> Either a a0 -> a0 Source #

toList :: Either a a0 -> [a0] Source #

null :: Either a a0 -> Bool Source #

length :: Either a a0 -> Int Source #

elem :: Eq a0 => a0 -> Either a a0 -> Bool Source #

maximum :: Ord a0 => Either a a0 -> a0 Source #

minimum :: Ord a0 => Either a a0 -> a0 Source #

sum :: Num a0 => Either a a0 -> a0 Source #

product :: Num a0 => Either a a0 -> a0 Source #

Foldable (Proxy :: Type -> Type) | Since: base-4.7.0.0

Instance details

Defined in Data.Foldable

Methods

fold :: Monoid m => Proxy m -> m Source #

foldMap :: Monoid m => (a -> m) -> Proxy a -> m Source #

foldMap' :: Monoid m => (a -> m) -> Proxy a -> m Source #

foldr :: (a -> b -> b) -> b -> Proxy a -> b Source #

foldr' :: (a -> b -> b) -> b -> Proxy a -> b Source #

foldl :: (b -> a -> b) -> b -> Proxy a -> b Source #

foldl' :: (b -> a -> b) -> b -> Proxy a -> b Source #

foldr1 :: (a -> a -> a) -> Proxy a -> a Source #

foldl1 :: (a -> a -> a) -> Proxy a -> a Source #

toList :: Proxy a -> [a] Source #

null :: Proxy a -> Bool Source #

length :: Proxy a -> Int Source #

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

maximum :: Ord a => Proxy a -> a Source #

minimum :: Ord a => Proxy a -> a Source #

sum :: Num a => Proxy a -> a Source #

product :: Num a => Proxy a -> a Source #

Foldable (Arg a) | Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

fold :: Monoid m => Arg a m -> m Source #

foldMap :: Monoid m => (a0 -> m) -> Arg a a0 -> m Source #

foldMap' :: Monoid m => (a0 -> m) -> Arg a a0 -> m Source #

foldr :: (a0 -> b -> b) -> b -> Arg a a0 -> b Source #

foldr' :: (a0 -> b -> b) -> b -> Arg a a0 -> b Source #

foldl :: (b -> a0 -> b) -> b -> Arg a a0 -> b Source #

foldl' :: (b -> a0 -> b) -> b -> Arg a a0 -> b Source #

foldr1 :: (a0 -> a0 -> a0) -> Arg a a0 -> a0 Source #

foldl1 :: (a0 -> a0 -> a0) -> Arg a a0 -> a0 Source #

toList :: Arg a a0 -> [a0] Source #

null :: Arg a a0 -> Bool Source #

length :: Arg a a0 -> Int Source #

elem :: Eq a0 => a0 -> Arg a a0 -> Bool Source #

maximum :: Ord a0 => Arg a a0 -> a0 Source #

minimum :: Ord a0 => Arg a a0 -> a0 Source #

sum :: Num a0 => Arg a a0 -> a0 Source #

product :: Num a0 => Arg a a0 -> a0 Source #

Foldable (Array i) | Since: base-4.8.0.0

Instance details

Defined in Data.Foldable

Methods

fold :: Monoid m => Array i m -> m Source #

foldMap :: Monoid m => (a -> m) -> Array i a -> m Source #

foldMap' :: Monoid m => (a -> m) -> Array i a -> m Source #

foldr :: (a -> b -> b) -> b -> Array i a -> b Source #

foldr' :: (a -> b -> b) -> b -> Array i a -> b Source #

foldl :: (b -> a -> b) -> b -> Array i a -> b Source #

foldl' :: (b -> a -> b) -> b -> Array i a -> b Source #

foldr1 :: (a -> a -> a) -> Array i a -> a Source #

foldl1 :: (a -> a -> a) -> Array i a -> a Source #

toList :: Array i a -> [a] Source #

null :: Array i a -> Bool Source #

length :: Array i a -> Int Source #

elem :: Eq a => a -> Array i a -> Bool Source #

maximum :: Ord a => Array i a -> a Source #

minimum :: Ord a => Array i a -> a Source #

sum :: Num a => Array i a -> a Source #

product :: Num a => Array i a -> a Source #

Foldable (U1 :: Type -> Type) | Since: base-4.9.0.0

Instance details

Defined in Data.Foldable

Methods

fold :: Monoid m => U1 m -> m Source #

foldMap :: Monoid m => (a -> m) -> U1 a -> m Source #

foldMap' :: Monoid m => (a -> m) -> U1 a -> m Source #

foldr :: (a -> b -> b) -> b -> U1 a -> b Source #

foldr' :: (a -> b -> b) -> b -> U1 a -> b Source #

foldl :: (b -> a -> b) -> b -> U1 a -> b Source #

foldl' :: (b -> a -> b) -> b -> U1 a -> b Source #

foldr1 :: (a -> a -> a) -> U1 a -> a Source #

foldl1 :: (a -> a -> a) -> U1 a -> a Source #

toList :: U1 a -> [a] Source #

null :: U1 a -> Bool Source #

length :: U1 a -> Int Source #

elem :: Eq a => a -> U1 a -> Bool Source #

maximum :: Ord a => U1 a -> a Source #

minimum :: Ord a => U1 a -> a Source #

sum :: Num a => U1 a -> a Source #

product :: Num a => U1 a -> a Source #

Foldable (UAddr :: Type -> Type) | Since: base-4.9.0.0

Instance details

Defined in Data.Foldable

Methods

fold :: Monoid m => UAddr m -> m Source #

foldMap :: Monoid m => (a -> m) -> UAddr a -> m Source #

foldMap' :: Monoid m => (a -> m) -> UAddr a -> m Source #

foldr :: (a -> b -> b) -> b -> UAddr a -> b Source #

foldr' :: (a -> b -> b) -> b -> UAddr a -> b Source #

foldl :: (b -> a -> b) -> b -> UAddr a -> b Source #

foldl' :: (b -> a -> b) -> b -> UAddr a -> b Source #

foldr1 :: (a -> a -> a) -> UAddr a -> a Source #

foldl1 :: (a -> a -> a) -> UAddr a -> a Source #

toList :: UAddr a -> [a] Source #

null :: UAddr a -> Bool Source #

length :: UAddr a -> Int Source #

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

maximum :: Ord a => UAddr a -> a Source #

minimum :: Ord a => UAddr a -> a Source #

sum :: Num a => UAddr a -> a Source #

product :: Num a => UAddr a -> a Source #

Foldable (UChar :: Type -> Type) | Since: base-4.9.0.0

Instance details

Defined in Data.Foldable

Methods

fold :: Monoid m => UChar m -> m Source #

foldMap :: Monoid m => (a -> m) -> UChar a -> m Source #

foldMap' :: Monoid m => (a -> m) -> UChar a -> m Source #

foldr :: (a -> b -> b) -> b -> UChar a -> b Source #

foldr' :: (a -> b -> b) -> b -> UChar a -> b Source #

foldl :: (b -> a -> b) -> b -> UChar a -> b Source #

foldl' :: (b -> a -> b) -> b -> UChar a -> b Source #

foldr1 :: (a -> a -> a) -> UChar a -> a Source #

foldl1 :: (a -> a -> a) -> UChar a -> a Source #

toList :: UChar a -> [a] Source #

null :: UChar a -> Bool Source #

length :: UChar a -> Int Source #

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

maximum :: Ord a => UChar a -> a Source #

minimum :: Ord a => UChar a -> a Source #

sum :: Num a => UChar a -> a Source #

product :: Num a => UChar a -> a Source #

Foldable (UDouble :: Type -> Type) | Since: base-4.9.0.0

Instance details

Defined in Data.Foldable

Methods

fold :: Monoid m => UDouble m -> m Source #

foldMap :: Monoid m => (a -> m) -> UDouble a -> m Source #

foldMap' :: Monoid m => (a -> m) -> UDouble a -> m Source #

foldr :: (a -> b -> b) -> b -> UDouble a -> b Source #

foldr' :: (a -> b -> b) -> b -> UDouble a -> b Source #

foldl :: (b -> a -> b) -> b -> UDouble a -> b Source #

foldl' :: (b -> a -> b) -> b -> UDouble a -> b Source #

foldr1 :: (a -> a -> a) -> UDouble a -> a Source #

foldl1 :: (a -> a -> a) -> UDouble a -> a Source #

toList :: UDouble a -> [a] Source #

null :: UDouble a -> Bool Source #

length :: UDouble a -> Int Source #

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

maximum :: Ord a => UDouble a -> a Source #

minimum :: Ord a => UDouble a -> a Source #

sum :: Num a => UDouble a -> a Source #

product :: Num a => UDouble a -> a Source #

Foldable (UFloat :: Type -> Type) | Since: base-4.9.0.0

Instance details

Defined in Data.Foldable

Methods

fold :: Monoid m => UFloat m -> m Source #

foldMap :: Monoid m => (a -> m) -> UFloat a -> m Source #

foldMap' :: Monoid m => (a -> m) -> UFloat a -> m Source #

foldr :: (a -> b -> b) -> b -> UFloat a -> b Source #

foldr' :: (a -> b -> b) -> b -> UFloat a -> b Source #

foldl :: (b -> a -> b) -> b -> UFloat a -> b Source #

foldl' :: (b -> a -> b) -> b -> UFloat a -> b Source #

foldr1 :: (a -> a -> a) -> UFloat a -> a Source #

foldl1 :: (a -> a -> a) -> UFloat a -> a Source #

toList :: UFloat a -> [a] Source #

null :: UFloat a -> Bool Source #

length :: UFloat a -> Int Source #

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

maximum :: Ord a => UFloat a -> a Source #

minimum :: Ord a => UFloat a -> a Source #

sum :: Num a => UFloat a -> a Source #

product :: Num a => UFloat a -> a Source #

Foldable (UInt :: Type -> Type) | Since: base-4.9.0.0

Instance details

Defined in Data.Foldable

Methods

fold :: Monoid m => UInt m -> m Source #

foldMap :: Monoid m => (a -> m) -> UInt a -> m Source #

foldMap' :: Monoid m => (a -> m) -> UInt a -> m Source #

foldr :: (a -> b -> b) -> b -> UInt a -> b Source #

foldr' :: (a -> b -> b) -> b -> UInt a -> b Source #

foldl :: (b -> a -> b) -> b -> UInt a -> b Source #

foldl' :: (b -> a -> b) -> b -> UInt a -> b Source #

foldr1 :: (a -> a -> a) -> UInt a -> a Source #

foldl1 :: (a -> a -> a) -> UInt a -> a Source #

toList :: UInt a -> [a] Source #

null :: UInt a -> Bool Source #

length :: UInt a -> Int Source #

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

maximum :: Ord a => UInt a -> a Source #

minimum :: Ord a => UInt a -> a Source #

sum :: Num a => UInt a -> a Source #

product :: Num a => UInt a -> a Source #

Foldable (UWord :: Type -> Type) | Since: base-4.9.0.0

Instance details

Defined in Data.Foldable

Methods

fold :: Monoid m => UWord m -> m Source #

foldMap :: Monoid m => (a -> m) -> UWord a -> m Source #

foldMap' :: Monoid m => (a -> m) -> UWord a -> m Source #

foldr :: (a -> b -> b) -> b -> UWord a -> b Source #

foldr' :: (a -> b -> b) -> b -> UWord a -> b Source #

foldl :: (b -> a -> b) -> b -> UWord a -> b Source #

foldl' :: (b -> a -> b) -> b -> UWord a -> b Source #

foldr1 :: (a -> a -> a) -> UWord a -> a Source #

foldl1 :: (a -> a -> a) -> UWord a -> a Source #

toList :: UWord a -> [a] Source #

null :: UWord a -> Bool Source #

length :: UWord a -> Int Source #

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

maximum :: Ord a => UWord a -> a Source #

minimum :: Ord a => UWord a -> a Source #

sum :: Num a => UWord a -> a Source #

product :: Num a => UWord a -> a Source #

Foldable (V1 :: Type -> Type) | Since: base-4.9.0.0

Instance details

Defined in Data.Foldable

Methods

fold :: Monoid m => V1 m -> m Source #

foldMap :: Monoid m => (a -> m) -> V1 a -> m Source #

foldMap' :: Monoid m => (a -> m) -> V1 a -> m Source #

foldr :: (a -> b -> b) -> b -> V1 a -> b Source #

foldr' :: (a -> b -> b) -> b -> V1 a -> b Source #

foldl :: (b -> a -> b) -> b -> V1 a -> b Source #

foldl' :: (b -> a -> b) -> b -> V1 a -> b Source #

foldr1 :: (a -> a -> a) -> V1 a -> a Source #

foldl1 :: (a -> a -> a) -> V1 a -> a Source #

toList :: V1 a -> [a] Source #

null :: V1 a -> Bool Source #

length :: V1 a -> Int Source #

elem :: Eq a => a -> V1 a -> Bool Source #

maximum :: Ord a => V1 a -> a Source #

minimum :: Ord a => V1 a -> a Source #

sum :: Num a => V1 a -> a Source #

product :: Num a => V1 a -> a Source #

Foldable (Map k) | Folds in order of increasing key.

Instance details

Defined in Data.Map.Internal

Methods

fold :: Monoid m => Map k m -> m Source #

foldMap :: Monoid m => (a -> m) -> Map k a -> m Source #

foldMap' :: Monoid m => (a -> m) -> Map k a -> m Source #

foldr :: (a -> b -> b) -> b -> Map k a -> b Source #

foldr' :: (a -> b -> b) -> b -> Map k a -> b Source #

foldl :: (b -> a -> b) -> b -> Map k a -> b Source #

foldl' :: (b -> a -> b) -> b -> Map k a -> b Source #

foldr1 :: (a -> a -> a) -> Map k a -> a Source #

foldl1 :: (a -> a -> a) -> Map k a -> a Source #

toList :: Map k a -> [a] Source #

null :: Map k a -> Bool Source #

length :: Map k a -> Int Source #

elem :: Eq a => a -> Map k a -> Bool Source #

maximum :: Ord a => Map k a -> a Source #

minimum :: Ord a => Map k a -> a Source #

sum :: Num a => Map k a -> a Source #

product :: Num a => Map k a -> a Source #

Foldable (HashMap k) |

Instance details

Defined in Data.HashMap.Internal

Methods

fold :: Monoid m => HashMap k m -> m Source #

foldMap :: Monoid m => (a -> m) -> HashMap k a -> m Source #

foldMap' :: Monoid m => (a -> m) -> HashMap k a -> m Source #

foldr :: (a -> b -> b) -> b -> HashMap k a -> b Source #

foldr' :: (a -> b -> b) -> b -> HashMap k a -> b Source #

foldl :: (b -> a -> b) -> b -> HashMap k a -> b Source #

foldl' :: (b -> a -> b) -> b -> HashMap k a -> b Source #

foldr1 :: (a -> a -> a) -> HashMap k a -> a Source #

foldl1 :: (a -> a -> a) -> HashMap k a -> a Source #

toList :: HashMap k a -> [a] Source #

null :: HashMap k a -> Bool Source #

length :: HashMap k a -> Int Source #

elem :: Eq a => a -> HashMap k a -> Bool Source #

maximum :: Ord a => HashMap k a -> a Source #

minimum :: Ord a => HashMap k a -> a Source #

sum :: Num a => HashMap k a -> a Source #

product :: Num a => HashMap k a -> a Source #

Foldable ((,) a) | Since: base-4.7.0.0

Instance details

Defined in Data.Foldable

Methods

fold :: Monoid m => (a, m) -> m Source #

foldMap :: Monoid m => (a0 -> m) -> (a, a0) -> m Source #

foldMap' :: Monoid m => (a0 -> m) -> (a, a0) -> m Source #

foldr :: (a0 -> b -> b) -> b -> (a, a0) -> b Source #

foldr' :: (a0 -> b -> b) -> b -> (a, a0) -> b Source #

foldl :: (b -> a0 -> b) -> b -> (a, a0) -> b Source #

foldl' :: (b -> a0 -> b) -> b -> (a, a0) -> b Source #

foldr1 :: (a0 -> a0 -> a0) -> (a, a0) -> a0 Source #

foldl1 :: (a0 -> a0 -> a0) -> (a, a0) -> a0 Source #

toList :: (a, a0) -> [a0] Source #

null :: (a, a0) -> Bool Source #

length :: (a, a0) -> Int Source #

elem :: Eq a0 => a0 -> (a, a0) -> Bool Source #

maximum :: Ord a0 => (a, a0) -> a0 Source #

minimum :: Ord a0 => (a, a0) -> a0 Source #

sum :: Num a0 => (a, a0) -> a0 Source #

product :: Num a0 => (a, a0) -> a0 Source #

Foldable (Const m :: Type -> Type) | Since: base-4.7.0.0

Instance details

Defined in Data.Functor.Const

Methods

fold :: Monoid m0 => Const m m0 -> m0 Source #

foldMap :: Monoid m0 => (a -> m0) -> Const m a -> m0 Source #

foldMap' :: Monoid m0 => (a -> m0) -> Const m a -> m0 Source #

foldr :: (a -> b -> b) -> b -> Const m a -> b Source #

foldr' :: (a -> b -> b) -> b -> Const m a -> b Source #

foldl :: (b -> a -> b) -> b -> Const m a -> b Source #

foldl' :: (b -> a -> b) -> b -> Const m a -> b Source #

foldr1 :: (a -> a -> a) -> Const m a -> a Source #

foldl1 :: (a -> a -> a) -> Const m a -> a Source #

toList :: Const m a -> [a] Source #

null :: Const m a -> Bool Source #

length :: Const m a -> Int Source #

elem :: Eq a => a -> Const m a -> Bool Source #

maximum :: Ord a => Const m a -> a Source #

minimum :: Ord a => Const m a -> a Source #

sum :: Num a => Const m a -> a Source #

product :: Num a => Const m a -> a Source #

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 Source #

foldMap :: Monoid m => (a -> m) -> Ap f a -> m Source #

foldMap' :: Monoid m => (a -> m) -> Ap f a -> m Source #

foldr :: (a -> b -> b) -> b -> Ap f a -> b Source #

foldr' :: (a -> b -> b) -> b -> Ap f a -> b Source #

foldl :: (b -> a -> b) -> b -> Ap f a -> b Source #

foldl' :: (b -> a -> b) -> b -> Ap f a -> b Source #

foldr1 :: (a -> a -> a) -> Ap f a -> a Source #

foldl1 :: (a -> a -> a) -> Ap f a -> a Source #

toList :: Ap f a -> [a] Source #

null :: Ap f a -> Bool Source #

length :: Ap f a -> Int Source #

elem :: Eq a => a -> Ap f a -> Bool Source #

maximum :: Ord a => Ap f a -> a Source #

minimum :: Ord a => Ap f a -> a Source #

sum :: Num a => Ap f a -> a Source #

product :: Num a => Ap f a -> a Source #

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 Source #

foldMap :: Monoid m => (a -> m) -> Alt f a -> m Source #

foldMap' :: Monoid m => (a -> m) -> Alt f a -> m Source #

foldr :: (a -> b -> b) -> b -> Alt f a -> b Source #

foldr' :: (a -> b -> b) -> b -> Alt f a -> b Source #

foldl :: (b -> a -> b) -> b -> Alt f a -> b Source #

foldl' :: (b -> a -> b) -> b -> Alt f a -> b Source #

foldr1 :: (a -> a -> a) -> Alt f a -> a Source #

foldl1 :: (a -> a -> a) -> Alt f a -> a Source #

toList :: Alt f a -> [a] Source #

null :: Alt f a -> Bool Source #

length :: Alt f a -> Int Source #

elem :: Eq a => a -> Alt f a -> Bool Source #

maximum :: Ord a => Alt f a -> a Source #

minimum :: Ord a => Alt f a -> a Source #

sum :: Num a => Alt f a -> a Source #

product :: Num a => Alt f a -> a Source #

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 Source #

foldMap :: Monoid m => (a -> m) -> Rec1 f a -> m Source #

foldMap' :: Monoid m => (a -> m) -> Rec1 f a -> m Source #

foldr :: (a -> b -> b) -> b -> Rec1 f a -> b Source #

foldr' :: (a -> b -> b) -> b -> Rec1 f a -> b Source #

foldl :: (b -> a -> b) -> b -> Rec1 f a -> b Source #

foldl' :: (b -> a -> b) -> b -> Rec1 f a -> b Source #

foldr1 :: (a -> a -> a) -> Rec1 f a -> a Source #

foldl1 :: (a -> a -> a) -> Rec1 f a -> a Source #

toList :: Rec1 f a -> [a] Source #

null :: Rec1 f a -> Bool Source #

length :: Rec1 f a -> Int Source #

elem :: Eq a => a -> Rec1 f a -> Bool Source #

maximum :: Ord a => Rec1 f a -> a Source #

minimum :: Ord a => Rec1 f a -> a Source #

sum :: Num a => Rec1 f a -> a Source #

product :: Num a => Rec1 f a -> a Source #

Bifoldable p => Foldable (Join p) |

Instance details

Defined in Data.Bifunctor.Join

Methods

fold :: Monoid m => Join p m -> m Source #

foldMap :: Monoid m => (a -> m) -> Join p a -> m Source #

foldMap' :: Monoid m => (a -> m) -> Join p a -> m Source #

foldr :: (a -> b -> b) -> b -> Join p a -> b Source #

foldr' :: (a -> b -> b) -> b -> Join p a -> b Source #

foldl :: (b -> a -> b) -> b -> Join p a -> b Source #

foldl' :: (b -> a -> b) -> b -> Join p a -> b Source #

foldr1 :: (a -> a -> a) -> Join p a -> a Source #

foldl1 :: (a -> a -> a) -> Join p a -> a Source #

toList :: Join p a -> [a] Source #

null :: Join p a -> Bool Source #

length :: Join p a -> Int Source #

elem :: Eq a => a -> Join p a -> Bool Source #

maximum :: Ord a => Join p a -> a Source #

minimum :: Ord a => Join p a -> a Source #

sum :: Num a => Join p a -> a Source #

product :: Num a => Join p a -> a Source #

Foldable (Tagged s) |

Instance details

Defined in Data.Tagged

Methods

fold :: Monoid m => Tagged s m -> m Source #

foldMap :: Monoid m => (a -> m) -> Tagged s a -> m Source #

foldMap' :: Monoid m => (a -> m) -> Tagged s a -> m Source #

foldr :: (a -> b -> b) -> b -> Tagged s a -> b Source #

foldr' :: (a -> b -> b) -> b -> Tagged s a -> b Source #

foldl :: (b -> a -> b) -> b -> Tagged s a -> b Source #

foldl' :: (b -> a -> b) -> b -> Tagged s a -> b Source #

foldr1 :: (a -> a -> a) -> Tagged s a -> a Source #

foldl1 :: (a -> a -> a) -> Tagged s a -> a Source #

toList :: Tagged s a -> [a] Source #

null :: Tagged s a -> Bool Source #

length :: Tagged s a -> Int Source #

elem :: Eq a => a -> Tagged s a -> Bool Source #

maximum :: Ord a => Tagged s a -> a Source #

minimum :: Ord a => Tagged s a -> a Source #

sum :: Num a => Tagged s a -> a Source #

product :: Num a => Tagged s a -> a Source #

Foldable f => Foldable (ErrorT e f) |

Instance details

Defined in Control.Monad.Trans.Error

Methods

fold :: Monoid m => ErrorT e f m -> m Source #

foldMap :: Monoid m => (a -> m) -> ErrorT e f a -> m Source #

foldMap' :: Monoid m => (a -> m) -> ErrorT e f a -> m Source #

foldr :: (a -> b -> b) -> b -> ErrorT e f a -> b Source #

foldr' :: (a -> b -> b) -> b -> ErrorT e f a -> b Source #

foldl :: (b -> a -> b) -> b -> ErrorT e f a -> b Source #

foldl' :: (b -> a -> b) -> b -> ErrorT e f a -> b Source #

foldr1 :: (a -> a -> a) -> ErrorT e f a -> a Source #

foldl1 :: (a -> a -> a) -> ErrorT e f a -> a Source #

toList :: ErrorT e f a -> [a] Source #

null :: ErrorT e f a -> Bool Source #

length :: ErrorT e f a -> Int Source #

elem :: Eq a => a -> ErrorT e f a -> Bool Source #

maximum :: Ord a => ErrorT e f a -> a Source #

minimum :: Ord a => ErrorT e f a -> a Source #

sum :: Num a => ErrorT e f a -> a Source #

product :: Num a => ErrorT e f a -> a Source #

(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 Source #

foldMap :: Monoid m => (a -> m) -> (f :*: g) a -> m Source #

foldMap' :: Monoid m => (a -> m) -> (f :*: g) a -> m Source #

foldr :: (a -> b -> b) -> b -> (f :*: g) a -> b Source #

foldr' :: (a -> b -> b) -> b -> (f :*: g) a -> b Source #

foldl :: (b -> a -> b) -> b -> (f :*: g) a -> b Source #

foldl' :: (b -> a -> b) -> b -> (f :*: g) a -> b Source #

foldr1 :: (a -> a -> a) -> (f :*: g) a -> a Source #

foldl1 :: (a -> a -> a) -> (f :*: g) a -> a Source #

toList :: (f :*: g) a -> [a] Source #

null :: (f :*: g) a -> Bool Source #

length :: (f :*: g) a -> Int Source #

elem :: Eq a => a -> (f :*: g) a -> Bool Source #

maximum :: Ord a => (f :*: g) a -> a Source #

minimum :: Ord a => (f :*: g) a -> a Source #

sum :: Num a => (f :*: g) a -> a Source #

product :: Num a => (f :*: g) a -> a Source #

(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 Source #

foldMap :: Monoid m => (a -> m) -> (f :+: g) a -> m Source #

foldMap' :: Monoid m => (a -> m) -> (f :+: g) a -> m Source #

foldr :: (a -> b -> b) -> b -> (f :+: g) a -> b Source #

foldr' :: (a -> b -> b) -> b -> (f :+: g) a -> b Source #

foldl :: (b -> a -> b) -> b -> (f :+: g) a -> b Source #

foldl' :: (b -> a -> b) -> b -> (f :+: g) a -> b Source #

foldr1 :: (a -> a -> a) -> (f :+: g) a -> a Source #

foldl1 :: (a -> a -> a) -> (f :+: g) a -> a Source #

toList :: (f :+: g) a -> [a] Source #

null :: (f :+: g) a -> Bool Source #

length :: (f :+: g) a -> Int Source #

elem :: Eq a => a -> (f :+: g) a -> Bool Source #

maximum :: Ord a => (f :+: g) a -> a Source #

minimum :: Ord a => (f :+: g) a -> a Source #

sum :: Num a => (f :+: g) a -> a Source #

product :: Num a => (f :+: g) a -> a Source #

Foldable (K1 i c :: Type -> Type) | Since: base-4.9.0.0

Instance details

Defined in Data.Foldable

Methods

fold :: Monoid m => K1 i c m -> m Source #

foldMap :: Monoid m => (a -> m) -> K1 i c a -> m Source #

foldMap' :: Monoid m => (a -> m) -> K1 i c a -> m Source #

foldr :: (a -> b -> b) -> b -> K1 i c a -> b Source #

foldr' :: (a -> b -> b) -> b -> K1 i c a -> b Source #

foldl :: (b -> a -> b) -> b -> K1 i c a -> b Source #

foldl' :: (b -> a -> b) -> b -> K1 i c a -> b Source #

foldr1 :: (a -> a -> a) -> K1 i c a -> a Source #

foldl1 :: (a -> a -> a) -> K1 i c a -> a Source #

toList :: K1 i c a -> [a] Source #

null :: K1 i c a -> Bool Source #

length :: K1 i c a -> Int Source #

elem :: Eq a => a -> K1 i c a -> Bool Source #

maximum :: Ord a => K1 i c a -> a Source #

minimum :: Ord a => K1 i c a -> a Source #

sum :: Num a => K1 i c a -> a Source #

product :: Num a => K1 i c a -> a Source #

Foldable (Forget r a :: Type -> Type) |

Instance details

Defined in Data.Profunctor.Types

Methods

fold :: Monoid m => Forget r a m -> m Source #

foldMap :: Monoid m => (a0 -> m) -> Forget r a a0 -> m Source #

foldMap' :: Monoid m => (a0 -> m) -> Forget r a a0 -> m Source #

foldr :: (a0 -> b -> b) -> b -> Forget r a a0 -> b Source #

foldr' :: (a0 -> b -> b) -> b -> Forget r a a0 -> b Source #

foldl :: (b -> a0 -> b) -> b -> Forget r a a0 -> b Source #

foldl' :: (b -> a0 -> b) -> b -> Forget r a a0 -> b Source #

foldr1 :: (a0 -> a0 -> a0) -> Forget r a a0 -> a0 Source #

foldl1 :: (a0 -> a0 -> a0) -> Forget r a a0 -> a0 Source #

toList :: Forget r a a0 -> [a0] Source #

null :: Forget r a a0 -> Bool Source #

length :: Forget r a a0 -> Int Source #

elem :: Eq a0 => a0 -> Forget r a a0 -> Bool Source #

maximum :: Ord a0 => Forget r a a0 -> a0 Source #

minimum :: Ord a0 => Forget r a a0 -> a0 Source #

sum :: Num a0 => Forget r a a0 -> a0 Source #

product :: Num a0 => Forget r a a0 -> a0 Source #

(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 Source #

foldMap :: Monoid m => (a -> m) -> Compose f g a -> m Source #

foldMap' :: Monoid m => (a -> m) -> Compose f g a -> m Source #

foldr :: (a -> b -> b) -> b -> Compose f g a -> b Source #

foldr' :: (a -> b -> b) -> b -> Compose f g a -> b Source #

foldl :: (b -> a -> b) -> b -> Compose f g a -> b Source #

foldl' :: (b -> a -> b) -> b -> Compose f g a -> b Source #

foldr1 :: (a -> a -> a) -> Compose f g a -> a Source #

foldl1 :: (a -> a -> a) -> Compose f g a -> a Source #

toList :: Compose f g a -> [a] Source #

null :: Compose f g a -> Bool Source #

length :: Compose f g a -> Int Source #

elem :: Eq a => a -> Compose f g a -> Bool Source #

maximum :: Ord a => Compose f g a -> a Source #

minimum :: Ord a => Compose f g a -> a Source #

sum :: Num a => Compose f g a -> a Source #

product :: Num a => Compose f g a -> a Source #

(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 Source #

foldMap :: Monoid m => (a -> m) -> (f :.: g) a -> m Source #

foldMap' :: Monoid m => (a -> m) -> (f :.: g) a -> m Source #

foldr :: (a -> b -> b) -> b -> (f :.: g) a -> b Source #

foldr' :: (a -> b -> b) -> b -> (f :.: g) a -> b Source #

foldl :: (b -> a -> b) -> b -> (f :.: g) a -> b Source #

foldl' :: (b -> a -> b) -> b -> (f :.: g) a -> b Source #

foldr1 :: (a -> a -> a) -> (f :.: g) a -> a Source #

foldl1 :: (a -> a -> a) -> (f :.: g) a -> a Source #

toList :: (f :.: g) a -> [a] Source #

null :: (f :.: g) a -> Bool Source #

length :: (f :.: g) a -> Int Source #

elem :: Eq a => a -> (f :.: g) a -> Bool Source #

maximum :: Ord a => (f :.: g) a -> a Source #

minimum :: Ord a => (f :.: g) a -> a Source #

sum :: Num a => (f :.: g) a -> a Source #

product :: Num a => (f :.: g) a -> a Source #

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 Source #

foldMap :: Monoid m => (a -> m) -> M1 i c f a -> m Source #

foldMap' :: Monoid m => (a -> m) -> M1 i c f a -> m Source #

foldr :: (a -> b -> b) -> b -> M1 i c f a -> b Source #

foldr' :: (a -> b -> b) -> b -> M1 i c f a -> b Source #

foldl :: (b -> a -> b) -> b -> M1 i c f a -> b Source #

foldl' :: (b -> a -> b) -> b -> M1 i c f a -> b Source #

foldr1 :: (a -> a -> a) -> M1 i c f a -> a Source #

foldl1 :: (a -> a -> a) -> M1 i c f a -> a Source #

toList :: M1 i c f a -> [a] Source #

null :: M1 i c f a -> Bool Source #

length :: M1 i c f a -> Int Source #

elem :: Eq a => a -> M1 i c f a -> Bool Source #

maximum :: Ord a => M1 i c f a -> a Source #

minimum :: Ord a => M1 i c f a -> a Source #

sum :: Num a => M1 i c f a -> a Source #

product :: Num a => M1 i c f a -> a Source #

Foldable (Clown f a :: Type -> Type) |

Instance details

Defined in Data.Bifunctor.Clown

Methods

fold :: Monoid m => Clown f a m -> m Source #

foldMap :: Monoid m => (a0 -> m) -> Clown f a a0 -> m Source #

foldMap' :: Monoid m => (a0 -> m) -> Clown f a a0 -> m Source #

foldr :: (a0 -> b -> b) -> b -> Clown f a a0 -> b Source #

foldr' :: (a0 -> b -> b) -> b -> Clown f a a0 -> b Source #

foldl :: (b -> a0 -> b) -> b -> Clown f a a0 -> b Source #

foldl' :: (b -> a0 -> b) -> b -> Clown f a a0 -> b Source #

foldr1 :: (a0 -> a0 -> a0) -> Clown f a a0 -> a0 Source #

foldl1 :: (a0 -> a0 -> a0) -> Clown f a a0 -> a0 Source #

toList :: Clown f a a0 -> [a0] Source #

null :: Clown f a a0 -> Bool Source #

length :: Clown f a a0 -> Int Source #

elem :: Eq a0 => a0 -> Clown f a a0 -> Bool Source #

maximum :: Ord a0 => Clown f a a0 -> a0 Source #

minimum :: Ord a0 => Clown f a a0 -> a0 Source #

sum :: Num a0 => Clown f a a0 -> a0 Source #

product :: Num a0 => Clown f a a0 -> a0 Source #

Bifoldable p => Foldable (Flip p a) |

Instance details

Defined in Data.Bifunctor.Flip

Methods

fold :: Monoid m => Flip p a m -> m Source #

foldMap :: Monoid m => (a0 -> m) -> Flip p a a0 -> m Source #

foldMap' :: Monoid m => (a0 -> m) -> Flip p a a0 -> m Source #

foldr :: (a0 -> b -> b) -> b -> Flip p a a0 -> b Source #

foldr' :: (a0 -> b -> b) -> b -> Flip p a a0 -> b Source #

foldl :: (b -> a0 -> b) -> b -> Flip p a a0 -> b Source #

foldl' :: (b -> a0 -> b) -> b -> Flip p a a0 -> b Source #

foldr1 :: (a0 -> a0 -> a0) -> Flip p a a0 -> a0 Source #

foldl1 :: (a0 -> a0 -> a0) -> Flip p a a0 -> a0 Source #

toList :: Flip p a a0 -> [a0] Source #

null :: Flip p a a0 -> Bool Source #

length :: Flip p a a0 -> Int Source #

elem :: Eq a0 => a0 -> Flip p a a0 -> Bool Source #

maximum :: Ord a0 => Flip p a a0 -> a0 Source #

minimum :: Ord a0 => Flip p a a0 -> a0 Source #

sum :: Num a0 => Flip p a a0 -> a0 Source #

product :: Num a0 => Flip p a a0 -> a0 Source #

Foldable g => Foldable (Joker g a) |

Instance details

Defined in Data.Bifunctor.Joker

Methods

fold :: Monoid m => Joker g a m -> m Source #

foldMap :: Monoid m => (a0 -> m) -> Joker g a a0 -> m Source #

foldMap' :: Monoid m => (a0 -> m) -> Joker g a a0 -> m Source #

foldr :: (a0 -> b -> b) -> b -> Joker g a a0 -> b Source #

foldr' :: (a0 -> b -> b) -> b -> Joker g a a0 -> b Source #

foldl :: (b -> a0 -> b) -> b -> Joker g a a0 -> b Source #

foldl' :: (b -> a0 -> b) -> b -> Joker g a a0 -> b Source #

foldr1 :: (a0 -> a0 -> a0) -> Joker g a a0 -> a0 Source #

foldl1 :: (a0 -> a0 -> a0) -> Joker g a a0 -> a0 Source #

toList :: Joker g a a0 -> [a0] Source #

null :: Joker g a a0 -> Bool Source #

length :: Joker g a a0 -> Int Source #

elem :: Eq a0 => a0 -> Joker g a a0 -> Bool Source #

maximum :: Ord a0 => Joker g a a0 -> a0 Source #

minimum :: Ord a0 => Joker g a a0 -> a0 Source #

sum :: Num a0 => Joker g a a0 -> a0 Source #

product :: Num a0 => Joker g a a0 -> a0 Source #

Bifoldable p => Foldable (WrappedBifunctor p a) |

Instance details

Defined in Data.Bifunctor.Wrapped

Methods

fold :: Monoid m => WrappedBifunctor p a m -> m Source #

foldMap :: Monoid m => (a0 -> m) -> WrappedBifunctor p a a0 -> m Source #

foldMap' :: Monoid m => (a0 -> m) -> WrappedBifunctor p a a0 -> m Source #

foldr :: (a0 -> b -> b) -> b -> WrappedBifunctor p a a0 -> b Source #

foldr' :: (a0 -> b -> b) -> b -> WrappedBifunctor p a a0 -> b Source #

foldl :: (b -> a0 -> b) -> b -> WrappedBifunctor p a a0 -> b Source #

foldl' :: (b -> a0 -> b) -> b -> WrappedBifunctor p a a0 -> b Source #

foldr1 :: (a0 -> a0 -> a0) -> WrappedBifunctor p a a0 -> a0 Source #

foldl1 :: (a0 -> a0 -> a0) -> WrappedBifunctor p a a0 -> a0 Source #

toList :: WrappedBifunctor p a a0 -> [a0] Source #

null :: WrappedBifunctor p a a0 -> Bool Source #

length :: WrappedBifunctor p a a0 -> Int Source #

elem :: Eq a0 => a0 -> WrappedBifunctor p a a0 -> Bool Source #

maximum :: Ord a0 => WrappedBifunctor p a a0 -> a0 Source #

minimum :: Ord a0 => WrappedBifunctor p a a0 -> a0 Source #

sum :: Num a0 => WrappedBifunctor p a a0 -> a0 Source #

product :: Num a0 => WrappedBifunctor p a a0 -> a0 Source #

(Foldable (f a), Foldable (g a)) => Foldable (Product f g a) |

Instance details

Defined in Data.Bifunctor.Product

Methods

fold :: Monoid m => Product f g a m -> m Source #

foldMap :: Monoid m => (a0 -> m) -> Product f g a a0 -> m Source #

foldMap' :: Monoid m => (a0 -> m) -> Product f g a a0 -> m Source #

foldr :: (a0 -> b -> b) -> b -> Product f g a a0 -> b Source #

foldr' :: (a0 -> b -> b) -> b -> Product f g a a0 -> b Source #

foldl :: (b -> a0 -> b) -> b -> Product f g a a0 -> b Source #

foldl' :: (b -> a0 -> b) -> b -> Product f g a a0 -> b Source #

foldr1 :: (a0 -> a0 -> a0) -> Product f g a a0 -> a0 Source #

foldl1 :: (a0 -> a0 -> a0) -> Product f g a a0 -> a0 Source #

toList :: Product f g a a0 -> [a0] Source #

null :: Product f g a a0 -> Bool Source #

length :: Product f g a a0 -> Int Source #

elem :: Eq a0 => a0 -> Product f g a a0 -> Bool Source #

maximum :: Ord a0 => Product f g a a0 -> a0 Source #

minimum :: Ord a0 => Product f g a a0 -> a0 Source #

sum :: Num a0 => Product f g a a0 -> a0 Source #

product :: Num a0 => Product f g a a0 -> a0 Source #

(Foldable (f a), Foldable (g a)) => Foldable (Sum f g a) |

Instance details

Defined in Data.Bifunctor.Sum

Methods

fold :: Monoid m => Sum f g a m -> m Source #

foldMap :: Monoid m => (a0 -> m) -> Sum f g a a0 -> m Source #

foldMap' :: Monoid m => (a0 -> m) -> Sum f g a a0 -> m Source #

foldr :: (a0 -> b -> b) -> b -> Sum f g a a0 -> b Source #

foldr' :: (a0 -> b -> b) -> b -> Sum f g a a0 -> b Source #

foldl :: (b -> a0 -> b) -> b -> Sum f g a a0 -> b Source #

foldl' :: (b -> a0 -> b) -> b -> Sum f g a a0 -> b Source #

foldr1 :: (a0 -> a0 -> a0) -> Sum f g a a0 -> a0 Source #

foldl1 :: (a0 -> a0 -> a0) -> Sum f g a a0 -> a0 Source #

toList :: Sum f g a a0 -> [a0] Source #

null :: Sum f g a a0 -> Bool Source #

length :: Sum f g a a0 -> Int Source #

elem :: Eq a0 => a0 -> Sum f g a a0 -> Bool Source #

maximum :: Ord a0 => Sum f g a a0 -> a0 Source #

minimum :: Ord a0 => Sum f g a a0 -> a0 Source #

sum :: Num a0 => Sum f g a a0 -> a0 Source #

product :: Num a0 => Sum f g a a0 -> a0 Source #

(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 Source #

foldMap :: Monoid m => (a0 -> m) -> Tannen f p a a0 -> m Source #

foldMap' :: Monoid m => (a0 -> m) -> Tannen f p a a0 -> m Source #

foldr :: (a0 -> b -> b) -> b -> Tannen f p a a0 -> b Source #

foldr' :: (a0 -> b -> b) -> b -> Tannen f p a a0 -> b Source #

foldl :: (b -> a0 -> b) -> b -> Tannen f p a a0 -> b Source #

foldl' :: (b -> a0 -> b) -> b -> Tannen f p a a0 -> b Source #

foldr1 :: (a0 -> a0 -> a0) -> Tannen f p a a0 -> a0 Source #

foldl1 :: (a0 -> a0 -> a0) -> Tannen f p a a0 -> a0 Source #

toList :: Tannen f p a a0 -> [a0] Source #

null :: Tannen f p a a0 -> Bool Source #

length :: Tannen f p a a0 -> Int Source #

elem :: Eq a0 => a0 -> Tannen f p a a0 -> Bool Source #

maximum :: Ord a0 => Tannen f p a a0 -> a0 Source #

minimum :: Ord a0 => Tannen f p a a0 -> a0 Source #

sum :: Num a0 => Tannen f p a a0 -> a0 Source #

product :: Num a0 => Tannen f p a a0 -> a0 Source #

(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 Source #

foldMap :: Monoid m => (a0 -> m) -> Biff p f g a a0 -> m Source #

foldMap' :: Monoid m => (a0 -> m) -> Biff p f g a a0 -> m Source #

foldr :: (a0 -> b -> b) -> b -> Biff p f g a a0 -> b Source #

foldr' :: (a0 -> b -> b) -> b -> Biff p f g a a0 -> b Source #

foldl :: (b -> a0 -> b) -> b -> Biff p f g a a0 -> b Source #

foldl' :: (b -> a0 -> b) -> b -> Biff p f g a a0 -> b Source #

foldr1 :: (a0 -> a0 -> a0) -> Biff p f g a a0 -> a0 Source #

foldl1 :: (a0 -> a0 -> a0) -> Biff p f g a a0 -> a0 Source #

toList :: Biff p f g a a0 -> [a0] Source #

null :: Biff p f g a a0 -> Bool Source #

length :: Biff p f g a a0 -> Int Source #

elem :: Eq a0 => a0 -> Biff p f g a a0 -> Bool Source #

maximum :: Ord a0 => Biff p f g a a0 -> a0 Source #

minimum :: Ord a0 => Biff p f g a a0 -> a0 Source #

sum :: Num a0 => Biff p f g a a0 -> a0 Source #

product :: Num a0 => Biff p f g a a0 -> a0 Source #

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

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:

- `basicUnsafeFreeze`
- `basicUnsafeThaw`
- `basicLength`
- `basicUnsafeSlice`
- `basicUnsafeIndexM`

Minimal complete definition

basicUnsafeFreeze, basicUnsafeThaw, basicLength, basicUnsafeSlice, basicUnsafeIndexM

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

`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.