Control.Foldl

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 L

Use fold to apply a Fold to a list:

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

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

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

Taking the sum, the sum of squares, ..., upto the sum of x^5

>>> import Data.Traversable
>>> let powerSums = sequenceA [L.premap (^n) L.sum | n <- [1..5]]
>>> L.fold powerSums [1..10]
[55,385,3025,25333,220825]

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

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

Fold Types

data Fold a b

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

Choice Fold

Defined in Control.Foldl

Methods

left' :: Fold a b -> Fold (Either a c) (Either b c)

right' :: Fold a b -> Fold (Either c a) (Either c b)

Profunctor Fold

Defined in Control.Foldl

Methods

dimap :: (a -> b) -> (c -> d) -> Fold b c -> Fold a d

lmap :: (a -> b) -> Fold b c -> Fold a c

rmap :: (b -> c) -> Fold a b -> Fold a c

(#.) :: forall a b c q. Coercible c b => q b c -> Fold a b -> Fold a c

(.#) :: forall a b c q. Coercible b a => Fold b c -> q a b -> Fold a c

Functor (Fold a)

Defined in Control.Foldl

Methods

fmap :: (a0 -> b) -> Fold a a0 -> Fold a b

(<$) :: a0 -> Fold a b -> Fold a a0

Applicative (Fold a)

Defined in Control.Foldl

Methods

pure :: a0 -> Fold a a0

(<*>) :: Fold a (a0 -> b) -> Fold a a0 -> Fold a b

liftA2 :: (a0 -> b -> c) -> Fold a a0 -> Fold a b -> Fold a c

(*>) :: Fold a a0 -> Fold a b -> Fold a b

(<*) :: Fold a a0 -> Fold a b -> Fold a a0

Comonad (Fold a)

Defined in Control.Foldl

Methods

extract :: Fold a a0 -> a0

duplicate :: Fold a a0 -> Fold a (Fold a a0)

extend :: (Fold a a0 -> b) -> Fold a a0 -> Fold a b

Semigroupoid Fold

Defined in Control.Foldl

Methods

o :: forall (j :: k) (k1 :: k) (i :: k). Fold j k1 -> Fold i j -> Fold i k1

Floating b => Floating (Fold a b)

Defined in Control.Foldl

Methods

pi :: Fold a b

exp :: Fold a b -> Fold a b

log :: Fold a b -> Fold a b

sqrt :: Fold a b -> Fold a b

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

logBase :: Fold a b -> Fold a b -> Fold a b

sin :: Fold a b -> Fold a b

cos :: Fold a b -> Fold a b

tan :: Fold a b -> Fold a b

asin :: Fold a b -> Fold a b

acos :: Fold a b -> Fold a b

atan :: Fold a b -> Fold a b

sinh :: Fold a b -> Fold a b

cosh :: Fold a b -> Fold a b

tanh :: Fold a b -> Fold a b

asinh :: Fold a b -> Fold a b

acosh :: Fold a b -> Fold a b

atanh :: Fold a b -> Fold a b

log1p :: Fold a b -> Fold a b

expm1 :: Fold a b -> Fold a b

log1pexp :: Fold a b -> Fold a b

log1mexp :: Fold a b -> Fold a b

Fractional b => Fractional (Fold a b)

Defined in Control.Foldl

Methods

(/) :: Fold a b -> Fold a b -> Fold a b

recip :: Fold a b -> Fold a b

fromRational :: Rational -> Fold a b

Num b => Num (Fold a b)

Defined in Control.Foldl

Methods

(+) :: Fold a b -> Fold a b -> Fold a b

(-) :: Fold a b -> Fold a b -> Fold a b

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

negate :: Fold a b -> Fold a b

abs :: Fold a b -> Fold a b

signum :: Fold a b -> Fold a b

fromInteger :: Integer -> Fold a b

Semigroup b => Semigroup (Fold a b)

Defined in Control.Foldl

Methods

(<>) :: Fold a b -> Fold a b -> Fold a b

sconcat :: NonEmpty (Fold a b) -> Fold a b

stimes :: Integral b0 => b0 -> Fold a b -> Fold a b

Monoid b => Monoid (Fold a b)

Defined in Control.Foldl

Methods

mempty :: Fold a b

mappend :: Fold a b -> Fold a b -> Fold a b

mconcat :: [Fold a b] -> Fold a b

data FoldM m a b

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

Functor m => Profunctor (FoldM m)

Defined in Control.Foldl

Methods

dimap :: (a -> b) -> (c -> d) -> FoldM m b c -> FoldM m a d

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

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

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

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

Functor m => Functor (FoldM m a)

Defined in Control.Foldl

Methods

fmap :: (a0 -> b) -> FoldM m a a0 -> FoldM m a b

(<$) :: a0 -> FoldM m a b -> FoldM m a a0

Applicative m => Applicative (FoldM m a)

Defined in Control.Foldl

Methods

pure :: a0 -> FoldM m a a0

(<*>) :: FoldM m a (a0 -> b) -> FoldM m a a0 -> FoldM m a b

liftA2 :: (a0 -> b -> c) -> FoldM m a a0 -> FoldM m a b -> FoldM m a c

(*>) :: FoldM m a a0 -> FoldM m a b -> FoldM m a b

(<*) :: FoldM m a a0 -> FoldM m a b -> FoldM m a a0

(Monad m, Floating b) => Floating (FoldM m a b)

Defined in Control.Foldl

Methods

pi :: FoldM m a b

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

(Monad m, Fractional b) => Fractional (FoldM m a b)

Defined in Control.Foldl

Methods

(/) :: FoldM m a b -> FoldM m a b -> FoldM m a b

recip :: FoldM m a b -> FoldM m a b

fromRational :: Rational -> FoldM m a b

(Monad m, Num b) => Num (FoldM m a b)

Defined in Control.Foldl

Methods

(+) :: FoldM m a b -> FoldM m a b -> FoldM m a b

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

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

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

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

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

fromInteger :: Integer -> FoldM m a b

(Semigroup b, Monad m) => Semigroup (FoldM m a b)

Defined in Control.Foldl

Methods

(<>) :: FoldM m a b -> FoldM m a b -> FoldM m a b

sconcat :: NonEmpty (FoldM m a b) -> FoldM m a b

stimes :: Integral b0 => b0 -> FoldM m a b -> FoldM m a b

(Monoid b, Monad m) => Monoid (FoldM m a b)

Defined in Control.Foldl

Methods

mempty :: FoldM m a b

mappend :: FoldM m a b -> FoldM m a b -> FoldM m a b

mconcat :: [FoldM m a b] -> FoldM m a b

Folding

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

Apply a strict left Fold to a Foldable container

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

Like fold, but monadic

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

Convert a strict left Fold into a scan

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

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

Convert a Fold into a prescan for any Traversable type

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

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

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

Convert a Fold into a postscan for any Traversable type

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

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

Folds

mconcat :: Monoid a => Fold a a

Fold all values within a container using mappend and mempty

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

Convert a "foldMap" to a Fold

head :: Fold a (Maybe a)

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

last :: Fold a (Maybe a)

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

lastDef :: a -> Fold a a

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

lastN :: Int -> Fold a [a]

Return the last N elements

null :: Fold a Bool

Returns True if the container is empty, False otherwise

length :: Fold a Int

Return the length of the container

and :: Fold Bool Bool

Returns True if all elements are True, False otherwise

or :: Fold Bool Bool

Returns True if any element is True, False otherwise

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

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

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

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

sum :: Num a => Fold a a

Computes the sum of all elements

product :: Num a => Fold a a

Computes the product of all elements

mean :: Fractional a => Fold a a

Compute a numerically stable arithmetic mean of all elements

variance :: Fractional a => Fold a a

Compute a numerically stable (population) variance over all elements

std :: Floating a => Fold a a

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

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

Computes the maximum element

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

Computes the maximum element with respect to the given comparison function

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

Computes the minimum element

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

Computes the minimum element with respect to the given comparison function

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

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

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

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

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

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

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

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

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

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

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

(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)

(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)

Pick a random element, using reservoir sampling

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

Pick several random elements, using reservoir sampling

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

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

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

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

Like length, except with a more general Num return value

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

Like index, except with a more general Integral argument

Container folds

list :: Fold a [a]

Fold all values into a list

revList :: Fold a [a]

Fold all values into a list, in reverse order

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

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

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

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

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

Fold values into a set

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

Fold values into a hash-set

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

Fold pairs into a map.

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

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)

Fold pairs into a hash-map.

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

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)

Fold all values into a vector

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

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

Upgrade a fold to accept the Fold type

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

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

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

Upgrade a more traditional monadic fold to accept the FoldM type

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

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

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

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)

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

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

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

_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

(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 L.mconcat) [1..10]
Sum {getSum = 55}

>>> fold L.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

(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

(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

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

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

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

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

(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)

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

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

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

(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)

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

>>> L.foldM (L.dropM 10 (L.generalize L.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

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

(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 L.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

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

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

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

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

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

L.foldOver folded == L.fold

newtype EndoM m a

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

Monad m => Semigroup (EndoM m a)

Defined in Control.Foldl

Methods

(<>) :: EndoM m a -> EndoM m a -> EndoM m a

sconcat :: NonEmpty (EndoM m a) -> EndoM m a

stimes :: Integral b => b -> EndoM m a -> EndoM m a

Monad m => Monoid (EndoM m a)

Defined in Control.Foldl

Methods

mempty :: EndoM m a

mappend :: EndoM m a -> EndoM m a -> EndoM m a

mconcat :: [EndoM m a] -> EndoM m a

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

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

(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

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

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

L.foldOverM folded == L.foldM

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

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

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

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

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

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)

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)

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

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

Nest a fold in an applicative.

Re-exports

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

Data.Foldable re-exports the Foldable type class

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

data RealWorld

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

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

Class of monads which can perform primitive state-transformer actions

Minimal complete definition

primitive

Instances

PrimMonad IO

Defined in Control.Monad.Primitive

Associated Types

type PrimState IO

Methods

primitive :: (State# (PrimState IO) -> (# State# (PrimState IO), a #)) -> IO a

PrimMonad (ST s)

Defined in Control.Monad.Primitive

Associated Types

type PrimState (ST s)

Methods

primitive :: (State# (PrimState (ST s)) -> (# State# (PrimState (ST s)), a #)) -> ST s a

PrimMonad (ST s)

Defined in Control.Monad.Primitive

Associated Types

type PrimState (ST s)

Methods

primitive :: (State# (PrimState (ST s)) -> (# State# (PrimState (ST s)), a #)) -> ST s a

PrimMonad m => PrimMonad (ListT m)

Defined in Control.Monad.Primitive

Associated Types

type PrimState (ListT m)

Methods

primitive :: (State# (PrimState (ListT m)) -> (# State# (PrimState (ListT m)), a #)) -> ListT m a

PrimMonad m => PrimMonad (MaybeT m)

Defined in Control.Monad.Primitive

Associated Types

type PrimState (MaybeT m)

Methods

primitive :: (State# (PrimState (MaybeT m)) -> (# State# (PrimState (MaybeT m)), a #)) -> MaybeT m a

PrimMonad m => PrimMonad (IdentityT m)

Defined in Control.Monad.Primitive

Associated Types

type PrimState (IdentityT m)

Methods

primitive :: (State# (PrimState (IdentityT m)) -> (# State# (PrimState (IdentityT m)), a #)) -> IdentityT m a

(Error e, PrimMonad m) => PrimMonad (ErrorT e m)

Defined in Control.Monad.Primitive

Associated Types

type PrimState (ErrorT e m)

Methods

primitive :: (State# (PrimState (ErrorT e m)) -> (# State# (PrimState (ErrorT e m)), a #)) -> ErrorT e m a

PrimMonad m => PrimMonad (ExceptT e m)

Defined in Control.Monad.Primitive

Associated Types

type PrimState (ExceptT e m)

Methods

primitive :: (State# (PrimState (ExceptT e m)) -> (# State# (PrimState (ExceptT e m)), a #)) -> ExceptT e m a

PrimMonad m => PrimMonad (ReaderT r m)

Defined in Control.Monad.Primitive

Associated Types

type PrimState (ReaderT r m)

Methods

primitive :: (State# (PrimState (ReaderT r m)) -> (# State# (PrimState (ReaderT r m)), a #)) -> ReaderT r m a

PrimMonad m => PrimMonad (StateT s m)

Defined in Control.Monad.Primitive

Associated Types

type PrimState (StateT s m)

Methods

primitive :: (State# (PrimState (StateT s m)) -> (# State# (PrimState (StateT s m)), a #)) -> StateT s m a

PrimMonad m => PrimMonad (StateT s m)

Defined in Control.Monad.Primitive

Associated Types

type PrimState (StateT s m)

Methods

primitive :: (State# (PrimState (StateT s m)) -> (# State# (PrimState (StateT s m)), a #)) -> StateT s m a

(Monoid w, PrimMonad m) => PrimMonad (WriterT w m)

Defined in Control.Monad.Primitive

Associated Types

type PrimState (WriterT w m)

Methods

primitive :: (State# (PrimState (WriterT w m)) -> (# State# (PrimState (WriterT w m)), a #)) -> WriterT w m a

(Monoid w, PrimMonad m) => PrimMonad (WriterT w m)

Defined in Control.Monad.Primitive

Associated Types

type PrimState (WriterT w m)

Methods

primitive :: (State# (PrimState (WriterT w m)) -> (# State# (PrimState (WriterT w m)), a #)) -> WriterT w m a

(Monoid w, PrimMonad m) => PrimMonad (AccumT w m)

Since: primitive-0.6.3.0

Defined in Control.Monad.Primitive

Associated Types

type PrimState (AccumT w m)

Methods

primitive :: (State# (PrimState (AccumT w m)) -> (# State# (PrimState (AccumT w m)), a #)) -> AccumT w m a

(Monoid w, PrimMonad m) => PrimMonad (WriterT w m)

Defined in Control.Monad.Primitive

Associated Types

type PrimState (WriterT w m)

Methods

primitive :: (State# (PrimState (WriterT w m)) -> (# State# (PrimState (WriterT w m)), a #)) -> WriterT w m a

PrimMonad m => PrimMonad (SelectT r m)

Defined in Control.Monad.Primitive

Associated Types

type PrimState (SelectT r m)

Methods

primitive :: (State# (PrimState (SelectT r m)) -> (# State# (PrimState (SelectT r m)), a #)) -> SelectT r m a

PrimMonad m => PrimMonad (ContT r m)

Since: primitive-0.6.3.0

Defined in Control.Monad.Primitive

Associated Types

type PrimState (ContT r m)

Methods

primitive :: (State# (PrimState (ContT r m)) -> (# State# (PrimState (ContT r m)), a #)) -> ContT r m a

(Monoid w, PrimMonad m) => PrimMonad (RWST r w s m)

Defined in Control.Monad.Primitive

Associated Types

type PrimState (RWST r w s m)

Methods

primitive :: (State# (PrimState (RWST r w s m)) -> (# State# (PrimState (RWST r w s m)), a #)) -> RWST r w s m a

(Monoid w, PrimMonad m) => PrimMonad (RWST r w s m)

Defined in Control.Monad.Primitive

Associated Types

type PrimState (RWST r w s m)

Methods

primitive :: (State# (PrimState (RWST r w s m)) -> (# State# (PrimState (RWST r w s m)), a #)) -> RWST r w s m a

(Monoid w, PrimMonad m) => PrimMonad (RWST r w s m)

Defined in Control.Monad.Primitive

Associated Types

type PrimState (RWST r w s m)

Methods

primitive :: (State# (PrimState (RWST r w s m)) -> (# State# (PrimState (RWST r w s m)), a #)) -> RWST r w s m a

class Foldable (t :: Type -> Type)

Data structures that can be folded.

For example, given a data type

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

a suitable instance would be

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

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

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

Foldable instances are expected to satisfy the following laws:

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

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

fold = foldMap id

length = getSum . foldMap (Sum . const  1)

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

sum = getSum . foldMap Sum

but may be less defined.

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

foldMap f = fold . fmap f

which implies that

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

Minimal complete definition

foldMap | foldr

Instances

Foldable []

Since: base-2.1

Defined in Data.Foldable

Methods

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

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

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

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

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

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

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

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

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

toList :: [a] -> [a]

null :: [a] -> Bool

length :: [a] -> Int

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

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

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

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

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

Foldable Maybe

Since: base-2.1

Defined in Data.Foldable

Methods

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

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

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

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

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

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

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

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

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

toList :: Maybe a -> [a]

null :: Maybe a -> Bool

length :: Maybe a -> Int

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

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

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

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

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

Foldable Par1

Since: base-4.9.0.0

Defined in Data.Foldable

Methods

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

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

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

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

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

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

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

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

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

toList :: Par1 a -> [a]

null :: Par1 a -> Bool

length :: Par1 a -> Int

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

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

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

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

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

Foldable Complex

Since: base-4.9.0.0

Defined in Data.Complex

Methods

fold :: Monoid m => Complex m -> m

foldMap :: Monoid m => (a -> m) -> Complex a -> m

foldMap' :: Monoid m => (a -> m) -> Complex a -> m

foldr :: (a -> b -> b) -> b -> Complex a -> b

foldr' :: (a -> b -> b) -> b -> Complex a -> b

foldl :: (b -> a -> b) -> b -> Complex a -> b

foldl' :: (b -> a -> b) -> b -> Complex a -> b

foldr1 :: (a -> a -> a) -> Complex a -> a

foldl1 :: (a -> a -> a) -> Complex a -> a

toList :: Complex a -> [a]

null :: Complex a -> Bool

length :: Complex a -> Int

elem :: Eq a => a -> Complex a -> Bool

maximum :: Ord a => Complex a -> a

minimum :: Ord a => Complex a -> a

sum :: Num a => Complex a -> a

product :: Num a => Complex a -> a

Foldable Min

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

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

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

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

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

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

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

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

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

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

toList :: Min a -> [a]

null :: Min a -> Bool

length :: Min a -> Int

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

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

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

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

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

Foldable Max

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

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

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

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

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

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

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

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

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

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

toList :: Max a -> [a]

null :: Max a -> Bool

length :: Max a -> Int

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

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

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

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

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

Foldable First

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

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

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

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

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

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

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

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

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

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

toList :: First a -> [a]

null :: First a -> Bool

length :: First a -> Int

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

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

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

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

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

Foldable Last

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

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

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

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

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

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

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

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

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

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

toList :: Last a -> [a]

null :: Last a -> Bool

length :: Last a -> Int

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

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

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

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

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

Foldable Option

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

fold :: Monoid m => Option m -> m

foldMap :: Monoid m => (a -> m) -> Option a -> m

foldMap' :: Monoid m => (a -> m) -> Option a -> m

foldr :: (a -> b -> b) -> b -> Option a -> b

foldr' :: (a -> b -> b) -> b -> Option a -> b

foldl :: (b -> a -> b) -> b -> Option a -> b

foldl' :: (b -> a -> b) -> b -> Option a -> b

foldr1 :: (a -> a -> a) -> Option a -> a

foldl1 :: (a -> a -> a) -> Option a -> a

toList :: Option a -> [a]

null :: Option a -> Bool

length :: Option a -> Int

elem :: Eq a => a -> Option a -> Bool

maximum :: Ord a => Option a -> a

minimum :: Ord a => Option a -> a

sum :: Num a => Option a -> a

product :: Num a => Option a -> a

Foldable ZipList

Since: base-4.9.0.0

Defined in Control.Applicative

Methods

fold :: Monoid m => ZipList m -> m

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

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

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

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

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

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

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

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

toList :: ZipList a -> [a]

null :: ZipList a -> Bool

length :: ZipList a -> Int

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

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

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

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

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

Foldable Identity

Since: base-4.8.0.0

Defined in Data.Functor.Identity

Methods

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

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

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

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

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

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

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

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

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

toList :: Identity a -> [a]

null :: Identity a -> Bool

length :: Identity a -> Int

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

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

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

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

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

Foldable First

Since: base-4.8.0.0

Defined in Data.Foldable

Methods

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

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

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

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

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

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

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

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

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

toList :: First a -> [a]

null :: First a -> Bool

length :: First a -> Int

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

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

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

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

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

Foldable Last

Since: base-4.8.0.0

Defined in Data.Foldable

Methods

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

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

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

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

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

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

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

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

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

toList :: Last a -> [a]

null :: Last a -> Bool

length :: Last a -> Int

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

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

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

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

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

Foldable Dual

Since: base-4.8.0.0

Defined in Data.Foldable

Methods

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

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

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

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

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

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

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

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

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

toList :: Dual a -> [a]

null :: Dual a -> Bool

length :: Dual a -> Int

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

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

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

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

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

Foldable Sum

Since: base-4.8.0.0

Defined in Data.Foldable

Methods

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

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

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

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

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

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

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

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

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

toList :: Sum a -> [a]

null :: Sum a -> Bool

length :: Sum a -> Int

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

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

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

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

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

Foldable Product

Since: base-4.8.0.0

Defined in Data.Foldable

Methods

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

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

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

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

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

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

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

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

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

toList :: Product a -> [a]

null :: Product a -> Bool

length :: Product a -> Int

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

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

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

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

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

Foldable Down

Since: base-4.12.0.0

Defined in Data.Foldable

Methods

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

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

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

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

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

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

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

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

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

toList :: Down a -> [a]

null :: Down a -> Bool

length :: Down a -> Int

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

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

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

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

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

Foldable NonEmpty

Since: base-4.9.0.0

Defined in Data.Foldable

Methods

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

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

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

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

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

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

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

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

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

toList :: NonEmpty a -> [a]

null :: NonEmpty a -> Bool

length :: NonEmpty a -> Int

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

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

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

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

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

Foldable IntMap

Folds in order of increasing key.

Defined in Data.IntMap.Internal

Methods

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

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

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

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

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

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

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

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

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

toList :: IntMap a -> [a]

null :: IntMap a -> Bool

length :: IntMap a -> Int

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

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

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

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

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

Foldable Tree

Defined in Data.Tree

Methods

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

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

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

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

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

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

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

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

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

toList :: Tree a -> [a]

null :: Tree a -> Bool

length :: Tree a -> Int

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

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

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

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

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

Foldable Seq

Defined in Data.Sequence.Internal

Methods

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

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

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

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

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

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

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

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

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

toList :: Seq a -> [a]

null :: Seq a -> Bool

length :: Seq a -> Int

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

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

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

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

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

Foldable FingerTree

Defined in Data.Sequence.Internal

Methods

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

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

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

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

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

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

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

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

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

toList :: FingerTree a -> [a]

null :: FingerTree a -> Bool

length :: FingerTree a -> Int

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

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

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

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

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

Foldable Digit

Defined in Data.Sequence.Internal

Methods

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

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

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

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

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

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

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

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

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

toList :: Digit a -> [a]

null :: Digit a -> Bool

length :: Digit a -> Int

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

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

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

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

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

Foldable Node

Defined in Data.Sequence.Internal

Methods

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

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

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

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

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

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

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

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

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

toList :: Node a -> [a]

null :: Node a -> Bool

length :: Node a -> Int

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

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

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

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

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

Foldable Elem

Defined in Data.Sequence.Internal

Methods

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

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

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

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

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

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

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

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

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

toList :: Elem a -> [a]

null :: Elem a -> Bool

length :: Elem a -> Int

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

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

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

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

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

Foldable ViewL

Defined in Data.Sequence.Internal

Methods

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

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

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

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

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

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

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

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

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

toList :: ViewL a -> [a]

null :: ViewL a -> Bool

length :: ViewL a -> Int

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

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

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

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

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

Foldable ViewR

Defined in Data.Sequence.Internal

Methods

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

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

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

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

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

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

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

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

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

toList :: ViewR a -> [a]

null :: ViewR a -> Bool

length :: ViewR a -> Int

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

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

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

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

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

Foldable Set

Folds in order of increasing key.

Defined in Data.Set.Internal

Methods

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

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

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

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

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

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

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

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

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

toList :: Set a -> [a]

null :: Set a -> Bool

length :: Set a -> Int

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

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

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

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

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

Foldable Hashed

Defined in Data.Hashable.Class

Methods

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

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

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

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

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

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

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

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

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

toList :: Hashed a -> [a]

null :: Hashed a -> Bool

length :: Hashed a -> Int

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

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

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

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

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

Foldable SmallArray

Defined in Data.Primitive.SmallArray

Methods

fold :: Monoid m => SmallArray m -> m

foldMap :: Monoid m => (a -> m) -> SmallArray a -> m

foldMap' :: Monoid m => (a -> m) -> SmallArray a -> m

foldr :: (a -> b -> b) -> b -> SmallArray a -> b

foldr' :: (a -> b -> b) -> b -> SmallArray a -> b

foldl :: (b -> a -> b) -> b -> SmallArray a -> b

foldl' :: (b -> a -> b) -> b -> SmallArray a -> b

foldr1 :: (a -> a -> a) -> SmallArray a -> a

foldl1 :: (a -> a -> a) -> SmallArray a -> a

toList :: SmallArray a -> [a]

null :: SmallArray a -> Bool

length :: SmallArray a -> Int

elem :: Eq a => a -> SmallArray a -> Bool

maximum :: Ord a => SmallArray a -> a

minimum :: Ord a => SmallArray a -> a

sum :: Num a => SmallArray a -> a

product :: Num a => SmallArray a -> a

Foldable Array

Defined in Data.Primitive.Array

Methods

fold :: Monoid m => Array m -> m

foldMap :: Monoid m => (a -> m) -> Array a -> m

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

foldr :: (a -> b -> b) -> b -> Array a -> b

foldr' :: (a -> b -> b) -> b -> Array a -> b

foldl :: (b -> a -> b) -> b -> Array a -> b

foldl' :: (b -> a -> b) -> b -> Array a -> b

foldr1 :: (a -> a -> a) -> Array a -> a

foldl1 :: (a -> a -> a) -> Array a -> a

toList :: Array a -> [a]

null :: Array a -> Bool

length :: Array a -> Int

elem :: Eq a => a -> Array a -> Bool

maximum :: Ord a => Array a -> a

minimum :: Ord a => Array a -> a

sum :: Num a => Array a -> a

product :: Num a => Array a -> a

Foldable HashSet

Defined in Data.HashSet.Internal

Methods

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

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

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

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

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

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

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

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

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

toList :: HashSet a -> [a]

null :: HashSet a -> Bool

length :: HashSet a -> Int

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

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

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

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

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

Foldable (Either a)

Since: base-4.7.0.0

Defined in Data.Foldable

Methods

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

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

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

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

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

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

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

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

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

toList :: Either a a0 -> [a0]

null :: Either a a0 -> Bool

length :: Either a a0 -> Int

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

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

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

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

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

Foldable (V1 :: Type -> Type)

Since: base-4.9.0.0

Defined in Data.Foldable

Methods

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

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

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

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

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

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

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

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

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

toList :: V1 a -> [a]

null :: V1 a -> Bool

length :: V1 a -> Int

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

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

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

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

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

Foldable (U1 :: Type -> Type)

Since: base-4.9.0.0

Defined in Data.Foldable

Methods

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

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

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

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

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

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

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

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

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

toList :: U1 a -> [a]

null :: U1 a -> Bool

length :: U1 a -> Int

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

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

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

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

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

Foldable (UAddr :: Type -> Type)

Since: base-4.9.0.0

Defined in Data.Foldable

Methods

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

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

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

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

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

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

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

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

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

toList :: UAddr a -> [a]

null :: UAddr a -> Bool

length :: UAddr a -> Int

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

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

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

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

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

Foldable (UChar :: Type -> Type)

Since: base-4.9.0.0

Defined in Data.Foldable

Methods

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

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

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

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

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

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

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

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

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

toList :: UChar a -> [a]

null :: UChar a -> Bool

length :: UChar a -> Int

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

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

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

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

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

Foldable (UDouble :: Type -> Type)

Since: base-4.9.0.0

Defined in Data.Foldable

Methods

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

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

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

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

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

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

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

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

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

toList :: UDouble a -> [a]

null :: UDouble a -> Bool

length :: UDouble a -> Int

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

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

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

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

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

Foldable (UFloat :: Type -> Type)

Since: base-4.9.0.0

Defined in Data.Foldable

Methods

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

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

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

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

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

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

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

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

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

toList :: UFloat a -> [a]

null :: UFloat a -> Bool

length :: UFloat a -> Int

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

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

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

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

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

Foldable (UInt :: Type -> Type)

Since: base-4.9.0.0

Defined in Data.Foldable

Methods

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

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

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

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

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

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

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

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

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

toList :: UInt a -> [a]

null :: UInt a -> Bool

length :: UInt a -> Int

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

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

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

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

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

Foldable (UWord :: Type -> Type)

Since: base-4.9.0.0

Defined in Data.Foldable

Methods

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

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

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

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

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

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

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

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

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

toList :: UWord a -> [a]

null :: UWord a -> Bool

length :: UWord a -> Int

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

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

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

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

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

Foldable ((,) a)

Since: base-4.7.0.0

Defined in Data.Foldable

Methods

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

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

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

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

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

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

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

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

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

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

null :: (a, a0) -> Bool

length :: (a, a0) -> Int

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

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

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

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

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

Foldable (Array i)

Since: base-4.8.0.0

Defined in Data.Foldable

Methods

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

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

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

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

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

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

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

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

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

toList :: Array i a -> [a]

null :: Array i a -> Bool

length :: Array i a -> Int

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

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

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

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

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

Foldable (Arg a)

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

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

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

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

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

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

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

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

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

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

toList :: Arg a a0 -> [a0]

null :: Arg a a0 -> Bool

length :: Arg a a0 -> Int

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

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

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

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

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

Foldable (Proxy :: Type -> Type)

Since: base-4.7.0.0

Defined in Data.Foldable

Methods

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

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

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

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

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

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

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

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

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

toList :: Proxy a -> [a]

null :: Proxy a -> Bool

length :: Proxy a -> Int

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

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

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

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

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

Foldable (Map k)

Folds in order of increasing key.

Defined in Data.Map.Internal

Methods

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

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

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

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

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

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

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

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

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

toList :: Map k a -> [a]

null :: Map k a -> Bool

length :: Map k a -> Int

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

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

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

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

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

Foldable f => Foldable (ListT f)

Defined in Control.Monad.Trans.List

Methods

fold :: Monoid m => ListT f m -> m

foldMap :: Monoid m => (a -> m) -> ListT f a -> m

foldMap' :: Monoid m => (a -> m) -> ListT f a -> m

foldr :: (a -> b -> b) -> b -> ListT f a -> b

foldr' :: (a -> b -> b) -> b -> ListT f a -> b

foldl :: (b -> a -> b) -> b -> ListT f a -> b

foldl' :: (b -> a -> b) -> b -> ListT f a -> b

foldr1 :: (a -> a -> a) -> ListT f a -> a

foldl1 :: (a -> a -> a) -> ListT f a -> a

toList :: ListT f a -> [a]

null :: ListT f a -> Bool

length :: ListT f a -> Int

elem :: Eq a => a -> ListT f a -> Bool

maximum :: Ord a => ListT f a -> a

minimum :: Ord a => ListT f a -> a

sum :: Num a => ListT f a -> a

product :: Num a => ListT f a -> a

Foldable f => Foldable (MaybeT f)

Defined in Control.Monad.Trans.Maybe

Methods

fold :: Monoid m => MaybeT f m -> m

foldMap :: Monoid m => (a -> m) -> MaybeT f a -> m

foldMap' :: Monoid m => (a -> m) -> MaybeT f a -> m

foldr :: (a -> b -> b) -> b -> MaybeT f a -> b

foldr' :: (a -> b -> b) -> b -> MaybeT f a -> b

foldl :: (b -> a -> b) -> b -> MaybeT f a -> b

foldl' :: (b -> a -> b) -> b -> MaybeT f a -> b

foldr1 :: (a -> a -> a) -> MaybeT f a -> a

foldl1 :: (a -> a -> a) -> MaybeT f a -> a

toList :: MaybeT f a -> [a]

null :: MaybeT f a -> Bool

length :: MaybeT f a -> Int

elem :: Eq a => a -> MaybeT f a -> Bool

maximum :: Ord a => MaybeT f a -> a

minimum :: Ord a => MaybeT f a -> a

sum :: Num a => MaybeT f a -> a

product :: Num a => MaybeT f a -> a

Foldable (HashMap k)

Defined in Data.HashMap.Internal

Methods

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

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

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

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

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

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

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

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

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

toList :: HashMap k a -> [a]

null :: HashMap k a -> Bool

length :: HashMap k a -> Int

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

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

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

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

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

Foldable f => Foldable (Rec1 f)

Since: base-4.9.0.0

Defined in Data.Foldable

Methods

fold :: Monoid m => Rec1 f m -> m

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

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

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

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

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

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

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

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

toList :: Rec1 f a -> [a]

null :: Rec1 f a -> Bool

length :: Rec1 f a -> Int

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

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

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

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

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

Foldable (Const m :: Type -> Type)

Since: base-4.7.0.0

Defined in Data.Functor.Const

Methods

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

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

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

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

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

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

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

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

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

toList :: Const m a -> [a]

null :: Const m a -> Bool

length :: Const m a -> Int

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

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

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

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

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

Foldable f => Foldable (Ap f)

Since: base-4.12.0.0

Defined in Data.Foldable

Methods

fold :: Monoid m => Ap f m -> m

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

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

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

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

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

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

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

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

toList :: Ap f a -> [a]

null :: Ap f a -> Bool

length :: Ap f a -> Int

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

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

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

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

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

Foldable f => Foldable (Alt f)

Since: base-4.12.0.0

Defined in Data.Foldable

Methods

fold :: Monoid m => Alt f m -> m

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

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

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

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

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

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

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

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

toList :: Alt f a -> [a]

null :: Alt f a -> Bool

length :: Alt f a -> Int

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

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

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

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

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

Bifoldable p => Foldable (Join p)

Defined in Data.Bifunctor.Join

Methods

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

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

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

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

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

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

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

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

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

toList :: Join p a -> [a]

null :: Join p a -> Bool

length :: Join p a -> Int

elem :: Eq a => a -> Join p a -> Bool

maximum :: Ord a => Join p a -> a

minimum :: Ord a => Join p a -> a

sum :: Num a => Join p a -> a

product :: Num a => Join p a -> a

Foldable f => Foldable (IdentityT f)

Defined in Control.Monad.Trans.Identity

Methods

fold :: Monoid m => IdentityT f m -> m

foldMap :: Monoid m => (a -> m) -> IdentityT f a -> m

foldMap' :: Monoid m => (a -> m) -> IdentityT f a -> m

foldr :: (a -> b -> b) -> b -> IdentityT f a -> b

foldr' :: (a -> b -> b) -> b -> IdentityT f a -> b

foldl :: (b -> a -> b) -> b -> IdentityT f a -> b

foldl' :: (b -> a -> b) -> b -> IdentityT f a -> b

foldr1 :: (a -> a -> a) -> IdentityT f a -> a

foldl1 :: (a -> a -> a) -> IdentityT f a -> a

toList :: IdentityT f a -> [a]

null :: IdentityT f a -> Bool

length :: IdentityT f a -> Int

elem :: Eq a => a -> IdentityT f a -> Bool

maximum :: Ord a => IdentityT f a -> a

minimum :: Ord a => IdentityT f a -> a

sum :: Num a => IdentityT f a -> a

product :: Num a => IdentityT f a -> a

Foldable f => Foldable (ErrorT e f)

Defined in Control.Monad.Trans.Error

Methods

fold :: Monoid m => ErrorT e f m -> m

foldMap :: Monoid m => (a -> m) -> ErrorT e f a -> m

foldMap' :: Monoid m => (a -> m) -> ErrorT e f a -> m

foldr :: (a -> b -> b) -> b -> ErrorT e f a -> b

foldr' :: (a -> b -> b) -> b -> ErrorT e f a -> b

foldl :: (b -> a -> b) -> b -> ErrorT e f a -> b

foldl' :: (b -> a -> b) -> b -> ErrorT e f a -> b

foldr1 :: (a -> a -> a) -> ErrorT e f a -> a

foldl1 :: (a -> a -> a) -> ErrorT e f a -> a

toList :: ErrorT e f a -> [a]

null :: ErrorT e f a -> Bool

length :: ErrorT e f a -> Int

elem :: Eq a => a -> ErrorT e f a -> Bool

maximum :: Ord a => ErrorT e f a -> a

minimum :: Ord a => ErrorT e f a -> a

sum :: Num a => ErrorT e f a -> a

product :: Num a => ErrorT e f a -> a

Foldable f => Foldable (ExceptT e f)

Defined in Control.Monad.Trans.Except

Methods

fold :: Monoid m => ExceptT e f m -> m

foldMap :: Monoid m => (a -> m) -> ExceptT e f a -> m

foldMap' :: Monoid m => (a -> m) -> ExceptT e f a -> m

foldr :: (a -> b -> b) -> b -> ExceptT e f a -> b

foldr' :: (a -> b -> b) -> b -> ExceptT e f a -> b

foldl :: (b -> a -> b) -> b -> ExceptT e f a -> b

foldl' :: (b -> a -> b) -> b -> ExceptT e f a -> b

foldr1 :: (a -> a -> a) -> ExceptT e f a -> a

foldl1 :: (a -> a -> a) -> ExceptT e f a -> a

toList :: ExceptT e f a -> [a]

null :: ExceptT e f a -> Bool

length :: ExceptT e f a -> Int

elem :: Eq a => a -> ExceptT e f a -> Bool

maximum :: Ord a => ExceptT e f a -> a

minimum :: Ord a => ExceptT e f a -> a

sum :: Num a => ExceptT e f a -> a

product :: Num a => ExceptT e f a -> a

Foldable f => Foldable (WriterT w f)

Defined in Control.Monad.Trans.Writer.Lazy

Methods

fold :: Monoid m => WriterT w f m -> m

foldMap :: Monoid m => (a -> m) -> WriterT w f a -> m

foldMap' :: Monoid m => (a -> m) -> WriterT w f a -> m

foldr :: (a -> b -> b) -> b -> WriterT w f a -> b

foldr' :: (a -> b -> b) -> b -> WriterT w f a -> b

foldl :: (b -> a -> b) -> b -> WriterT w f a -> b

foldl' :: (b -> a -> b) -> b -> WriterT w f a -> b

foldr1 :: (a -> a -> a) -> WriterT w f a -> a

foldl1 :: (a -> a -> a) -> WriterT w f a -> a

toList :: WriterT w f a -> [a]

null :: WriterT w f a -> Bool

length :: WriterT w f a -> Int

elem :: Eq a => a -> WriterT w f a -> Bool

maximum :: Ord a => WriterT w f a -> a

minimum :: Ord a => WriterT w f a -> a

sum :: Num a => WriterT w f a -> a

product :: Num a => WriterT w f a -> a

Foldable f => Foldable (WriterT w f)

Defined in Control.Monad.Trans.Writer.Strict

Methods

fold :: Monoid m => WriterT w f m -> m

foldMap :: Monoid m => (a -> m) -> WriterT w f a -> m

foldMap' :: Monoid m => (a -> m) -> WriterT w f a -> m

foldr :: (a -> b -> b) -> b -> WriterT w f a -> b

foldr' :: (a -> b -> b) -> b -> WriterT w f a -> b

foldl :: (b -> a -> b) -> b -> WriterT w f a -> b

foldl' :: (b -> a -> b) -> b -> WriterT w f a -> b

foldr1 :: (a -> a -> a) -> WriterT w f a -> a

foldl1 :: (a -> a -> a) -> WriterT w f a -> a

toList :: WriterT w f a -> [a]

null :: WriterT w f a -> Bool

length :: WriterT w f a -> Int

elem :: Eq a => a -> WriterT w f a -> Bool

maximum :: Ord a => WriterT w f a -> a

minimum :: Ord a => WriterT w f a -> a

sum :: Num a => WriterT w f a -> a

product :: Num a => WriterT w f a -> a

Foldable (Tagged s)

Defined in Data.Tagged

Methods

fold :: Monoid m => Tagged s m -> m

foldMap :: Monoid m => (a -> m) -> Tagged s a -> m

foldMap' :: Monoid m => (a -> m) -> Tagged s a -> m

foldr :: (a -> b -> b) -> b -> Tagged s a -> b

foldr' :: (a -> b -> b) -> b -> Tagged s a -> b

foldl :: (b -> a -> b) -> b -> Tagged s a -> b

foldl' :: (b -> a -> b) -> b -> Tagged s a -> b

foldr1 :: (a -> a -> a) -> Tagged s a -> a

foldl1 :: (a -> a -> a) -> Tagged s a -> a

toList :: Tagged s a -> [a]

null :: Tagged s a -> Bool

length :: Tagged s a -> Int

elem :: Eq a => a -> Tagged s a -> Bool

maximum :: Ord a => Tagged s a -> a

minimum :: Ord a => Tagged s a -> a

sum :: Num a => Tagged s a -> a

product :: Num a => Tagged s a -> a

Foldable (K1 i c :: Type -> Type)

Since: base-4.9.0.0

Defined in Data.Foldable

Methods

fold :: Monoid m => K1 i c m -> m

foldMap :: Monoid m => (a -> m) -> K1 i c a -> m

foldMap' :: Monoid m => (a -> m) -> K1 i c a -> m

foldr :: (a -> b -> b) -> b -> K1 i c a -> b

foldr' :: (a -> b -> b) -> b -> K1 i c a -> b

foldl :: (b -> a -> b) -> b -> K1 i c a -> b

foldl' :: (b -> a -> b) -> b -> K1 i c a -> b

foldr1 :: (a -> a -> a) -> K1 i c a -> a

foldl1 :: (a -> a -> a) -> K1 i c a -> a

toList :: K1 i c a -> [a]

null :: K1 i c a -> Bool

length :: K1 i c a -> Int

elem :: Eq a => a -> K1 i c a -> Bool

maximum :: Ord a => K1 i c a -> a

minimum :: Ord a => K1 i c a -> a

sum :: Num a => K1 i c a -> a

product :: Num a => K1 i c a -> a

(Foldable f, Foldable g) => Foldable (f :+: g)

Since: base-4.9.0.0

Defined in Data.Foldable

Methods

fold :: Monoid m => (f :+: g) m -> m

foldMap :: Monoid m => (a -> m) -> (f :+: g) a -> m

foldMap' :: Monoid m => (a -> m) -> (f :+: g) a -> m

foldr :: (a -> b -> b) -> b -> (f :+: g) a -> b

foldr' :: (a -> b -> b) -> b -> (f :+: g) a -> b

foldl :: (b -> a -> b) -> b -> (f :+: g) a -> b

foldl' :: (b -> a -> b) -> b -> (f :+: g) a -> b

foldr1 :: (a -> a -> a) -> (f :+: g) a -> a

foldl1 :: (a -> a -> a) -> (f :+: g) a -> a

toList :: (f :+: g) a -> [a]

null :: (f :+: g) a -> Bool

length :: (f :+: g) a -> Int

elem :: Eq a => a -> (f :+: g) a -> Bool

maximum :: Ord a => (f :+: g) a -> a

minimum :: Ord a => (f :+: g) a -> a

sum :: Num a => (f :+: g) a -> a

product :: Num a => (f :+: g) a -> a

(Foldable f, Foldable g) => Foldable (f :*: g)

Since: base-4.9.0.0

Defined in Data.Foldable

Methods

fold :: Monoid m => (f :*: g) m -> m

foldMap :: Monoid m => (a -> m) -> (f :*: g) a -> m

foldMap' :: Monoid m => (a -> m) -> (f :*: g) a -> m

foldr :: (a -> b -> b) -> b -> (f :*: g) a -> b

foldr' :: (a -> b -> b) -> b -> (f :*: g) a -> b

foldl :: (b -> a -> b) -> b -> (f :*: g) a -> b

foldl' :: (b -> a -> b) -> b -> (f :*: g) a -> b

foldr1 :: (a -> a -> a) -> (f :*: g) a -> a

foldl1 :: (a -> a -> a) -> (f :*: g) a -> a

toList :: (f :*: g) a -> [a]

null :: (f :*: g) a -> Bool

length :: (f :*: g) a -> Int

elem :: Eq a => a -> (f :*: g) a -> Bool

maximum :: Ord a => (f :*: g) a -> a

minimum :: Ord a => (f :*: g) a -> a

sum :: Num a => (f :*: g) a -> a

product :: Num a => (f :*: g) a -> a

(Foldable f, Foldable g) => Foldable (Product f g)

Since: base-4.9.0.0

Defined in Data.Functor.Product

Methods

fold :: Monoid m => Product f g m -> m

foldMap :: Monoid m => (a -> m) -> Product f g a -> m

foldMap' :: Monoid m => (a -> m) -> Product f g a -> m

foldr :: (a -> b -> b) -> b -> Product f g a -> b

foldr' :: (a -> b -> b) -> b -> Product f g a -> b

foldl :: (b -> a -> b) -> b -> Product f g a -> b

foldl' :: (b -> a -> b) -> b -> Product f g a -> b

foldr1 :: (a -> a -> a) -> Product f g a -> a

foldl1 :: (a -> a -> a) -> Product f g a -> a

toList :: Product f g a -> [a]

null :: Product f g a -> Bool

length :: Product f g a -> Int

elem :: Eq a => a -> Product f g a -> Bool

maximum :: Ord a => Product f g a -> a

minimum :: Ord a => Product f g a -> a

sum :: Num a => Product f g a -> a

product :: Num a => Product f g a -> a

(Foldable f, Foldable g) => Foldable (Sum f g)

Since: base-4.9.0.0

Defined in Data.Functor.Sum

Methods

fold :: Monoid m => Sum f g m -> m

foldMap :: Monoid m => (a -> m) -> Sum f g a -> m

foldMap' :: Monoid m => (a -> m) -> Sum f g a -> m

foldr :: (a -> b -> b) -> b -> Sum f g a -> b

foldr' :: (a -> b -> b) -> b -> Sum f g a -> b

foldl :: (b -> a -> b) -> b -> Sum f g a -> b

foldl' :: (b -> a -> b) -> b -> Sum f g a -> b

foldr1 :: (a -> a -> a) -> Sum f g a -> a

foldl1 :: (a -> a -> a) -> Sum f g a -> a

toList :: Sum f g a -> [a]

null :: Sum f g a -> Bool

length :: Sum f g a -> Int

elem :: Eq a => a -> Sum f g a -> Bool

maximum :: Ord a => Sum f g a -> a

minimum :: Ord a => Sum f g a -> a

sum :: Num a => Sum f g a -> a

product :: Num a => Sum f g a -> a

Foldable (Forget r a :: Type -> Type)

Defined in Data.Profunctor.Types

Methods

fold :: Monoid m => Forget r a m -> m

foldMap :: Monoid m => (a0 -> m) -> Forget r a a0 -> m

foldMap' :: Monoid m => (a0 -> m) -> Forget r a a0 -> m

foldr :: (a0 -> b -> b) -> b -> Forget r a a0 -> b

foldr' :: (a0 -> b -> b) -> b -> Forget r a a0 -> b

foldl :: (b -> a0 -> b) -> b -> Forget r a a0 -> b

foldl' :: (b -> a0 -> b) -> b -> Forget r a a0 -> b

foldr1 :: (a0 -> a0 -> a0) -> Forget r a a0 -> a0

foldl1 :: (a0 -> a0 -> a0) -> Forget r a a0 -> a0

toList :: Forget r a a0 -> [a0]

null :: Forget r a a0 -> Bool

length :: Forget r a a0 -> Int

elem :: Eq a0 => a0 -> Forget r a a0 -> Bool

maximum :: Ord a0 => Forget r a a0 -> a0

minimum :: Ord a0 => Forget r a a0 -> a0

sum :: Num a0 => Forget r a a0 -> a0

product :: Num a0 => Forget r a a0 -> a0

Foldable f => Foldable (M1 i c f)

Since: base-4.9.0.0

Defined in Data.Foldable

Methods

fold :: Monoid m => M1 i c f m -> m

foldMap :: Monoid m => (a -> m) -> M1 i c f a -> m

foldMap' :: Monoid m => (a -> m) -> M1 i c f a -> m

foldr :: (a -> b -> b) -> b -> M1 i c f a -> b

foldr' :: (a -> b -> b) -> b -> M1 i c f a -> b

foldl :: (b -> a -> b) -> b -> M1 i c f a -> b

foldl' :: (b -> a -> b) -> b -> M1 i c f a -> b

foldr1 :: (a -> a -> a) -> M1 i c f a -> a

foldl1 :: (a -> a -> a) -> M1 i c f a -> a

toList :: M1 i c f a -> [a]

null :: M1 i c f a -> Bool

length :: M1 i c f a -> Int

elem :: Eq a => a -> M1 i c f a -> Bool

maximum :: Ord a => M1 i c f a -> a

minimum :: Ord a => M1 i c f a -> a

sum :: Num a => M1 i c f a -> a

product :: Num a => M1 i c f a -> a

(Foldable f, Foldable g) => Foldable (f :.: g)

Since: base-4.9.0.0

Defined in Data.Foldable

Methods

fold :: Monoid m => (f :.: g) m -> m

foldMap :: Monoid m => (a -> m) -> (f :.: g) a -> m

foldMap' :: Monoid m => (a -> m) -> (f :.: g) a -> m

foldr :: (a -> b -> b) -> b -> (f :.: g) a -> b

foldr' :: (a -> b -> b) -> b -> (f :.: g) a -> b

foldl :: (b -> a -> b) -> b -> (f :.: g) a -> b

foldl' :: (b -> a -> b) -> b -> (f :.: g) a -> b

foldr1 :: (a -> a -> a) -> (f :.: g) a -> a

foldl1 :: (a -> a -> a) -> (f :.: g) a -> a

toList :: (f :.: g) a -> [a]

null :: (f :.: g) a -> Bool

length :: (f :.: g) a -> Int

elem :: Eq a => a -> (f :.: g) a -> Bool

maximum :: Ord a => (f :.: g) a -> a

minimum :: Ord a => (f :.: g) a -> a

sum :: Num a => (f :.: g) a -> a

product :: Num a => (f :.: g) a -> a

(Foldable f, Foldable g) => Foldable (Compose f g)

Since: base-4.9.0.0

Defined in Data.Functor.Compose

Methods

fold :: Monoid m => Compose f g m -> m

foldMap :: Monoid m => (a -> m) -> Compose f g a -> m

foldMap' :: Monoid m => (a -> m) -> Compose f g a -> m

foldr :: (a -> b -> b) -> b -> Compose f g a -> b

foldr' :: (a -> b -> b) -> b -> Compose f g a -> b

foldl :: (b -> a -> b) -> b -> Compose f g a -> b

foldl' :: (b -> a -> b) -> b -> Compose f g a -> b

foldr1 :: (a -> a -> a) -> Compose f g a -> a

foldl1 :: (a -> a -> a) -> Compose f g a -> a

toList :: Compose f g a -> [a]

null :: Compose f g a -> Bool

length :: Compose f g a -> Int

elem :: Eq a => a -> Compose f g a -> Bool

maximum :: Ord a => Compose f g a -> a

minimum :: Ord a => Compose f g a -> a

sum :: Num a => Compose f g a -> a

product :: Num a => Compose f g a -> a

Bifoldable p => Foldable (WrappedBifunctor p a)

Defined in Data.Bifunctor.Wrapped

Methods

fold :: Monoid m => WrappedBifunctor p a m -> m

foldMap :: Monoid m => (a0 -> m) -> WrappedBifunctor p a a0 -> m

foldMap' :: Monoid m => (a0 -> m) -> WrappedBifunctor p a a0 -> m

foldr :: (a0 -> b -> b) -> b -> WrappedBifunctor p a a0 -> b

foldr' :: (a0 -> b -> b) -> b -> WrappedBifunctor p a a0 -> b

foldl :: (b -> a0 -> b) -> b -> WrappedBifunctor p a a0 -> b

foldl' :: (b -> a0 -> b) -> b -> WrappedBifunctor p a a0 -> b

foldr1 :: (a0 -> a0 -> a0) -> WrappedBifunctor p a a0 -> a0

foldl1 :: (a0 -> a0 -> a0) -> WrappedBifunctor p a a0 -> a0

toList :: WrappedBifunctor p a a0 -> [a0]

null :: WrappedBifunctor p a a0 -> Bool

length :: WrappedBifunctor p a a0 -> Int

elem :: Eq a0 => a0 -> WrappedBifunctor p a a0 -> Bool

maximum :: Ord a0 => WrappedBifunctor p a a0 -> a0

minimum :: Ord a0 => WrappedBifunctor p a a0 -> a0

sum :: Num a0 => WrappedBifunctor p a a0 -> a0

product :: Num a0 => WrappedBifunctor p a a0 -> a0

Foldable g => Foldable (Joker g a)

Defined in Data.Bifunctor.Joker

Methods

fold :: Monoid m => Joker g a m -> m

foldMap :: Monoid m => (a0 -> m) -> Joker g a a0 -> m

foldMap' :: Monoid m => (a0 -> m) -> Joker g a a0 -> m

foldr :: (a0 -> b -> b) -> b -> Joker g a a0 -> b

foldr' :: (a0 -> b -> b) -> b -> Joker g a a0 -> b

foldl :: (b -> a0 -> b) -> b -> Joker g a a0 -> b

foldl' :: (b -> a0 -> b) -> b -> Joker g a a0 -> b

foldr1 :: (a0 -> a0 -> a0) -> Joker g a a0 -> a0

foldl1 :: (a0 -> a0 -> a0) -> Joker g a a0 -> a0

toList :: Joker g a a0 -> [a0]

null :: Joker g a a0 -> Bool

length :: Joker g a a0 -> Int

elem :: Eq a0 => a0 -> Joker g a a0 -> Bool

maximum :: Ord a0 => Joker g a a0 -> a0

minimum :: Ord a0 => Joker g a a0 -> a0

sum :: Num a0 => Joker g a a0 -> a0

product :: Num a0 => Joker g a a0 -> a0

Bifoldable p => Foldable (Flip p a)

Defined in Data.Bifunctor.Flip

Methods

fold :: Monoid m => Flip p a m -> m

foldMap :: Monoid m => (a0 -> m) -> Flip p a a0 -> m

foldMap' :: Monoid m => (a0 -> m) -> Flip p a a0 -> m

foldr :: (a0 -> b -> b) -> b -> Flip p a a0 -> b

foldr' :: (a0 -> b -> b) -> b -> Flip p a a0 -> b

foldl :: (b -> a0 -> b) -> b -> Flip p a a0 -> b

foldl' :: (b -> a0 -> b) -> b -> Flip p a a0 -> b

foldr1 :: (a0 -> a0 -> a0) -> Flip p a a0 -> a0

foldl1 :: (a0 -> a0 -> a0) -> Flip p a a0 -> a0

toList :: Flip p a a0 -> [a0]

null :: Flip p a a0 -> Bool

length :: Flip p a a0 -> Int

elem :: Eq a0 => a0 -> Flip p a a0 -> Bool

maximum :: Ord a0 => Flip p a a0 -> a0

minimum :: Ord a0 => Flip p a a0 -> a0

sum :: Num a0 => Flip p a a0 -> a0

product :: Num a0 => Flip p a a0 -> a0

Foldable (Clown f a :: Type -> Type)

Defined in Data.Bifunctor.Clown

Methods

fold :: Monoid m => Clown f a m -> m

foldMap :: Monoid m => (a0 -> m) -> Clown f a a0 -> m

foldMap' :: Monoid m => (a0 -> m) -> Clown f a a0 -> m

foldr :: (a0 -> b -> b) -> b -> Clown f a a0 -> b

foldr' :: (a0 -> b -> b) -> b -> Clown f a a0 -> b

foldl :: (b -> a0 -> b) -> b -> Clown f a a0 -> b

foldl' :: (b -> a0 -> b) -> b -> Clown f a a0 -> b

foldr1 :: (a0 -> a0 -> a0) -> Clown f a a0 -> a0

foldl1 :: (a0 -> a0 -> a0) -> Clown f a a0 -> a0

toList :: Clown f a a0 -> [a0]

null :: Clown f a a0 -> Bool

length :: Clown f a a0 -> Int

elem :: Eq a0 => a0 -> Clown f a a0 -> Bool

maximum :: Ord a0 => Clown f a a0 -> a0

minimum :: Ord a0 => Clown f a a0 -> a0

sum :: Num a0 => Clown f a a0 -> a0

product :: Num a0 => Clown f a a0 -> a0

(Foldable f, Bifoldable p) => Foldable (Tannen f p a)

Defined in Data.Bifunctor.Tannen

Methods

fold :: Monoid m => Tannen f p a m -> m

foldMap :: Monoid m => (a0 -> m) -> Tannen f p a a0 -> m

foldMap' :: Monoid m => (a0 -> m) -> Tannen f p a a0 -> m

foldr :: (a0 -> b -> b) -> b -> Tannen f p a a0 -> b

foldr' :: (a0 -> b -> b) -> b -> Tannen f p a a0 -> b

foldl :: (b -> a0 -> b) -> b -> Tannen f p a a0 -> b

foldl' :: (b -> a0 -> b) -> b -> Tannen f p a a0 -> b

foldr1 :: (a0 -> a0 -> a0) -> Tannen f p a a0 -> a0

foldl1 :: (a0 -> a0 -> a0) -> Tannen f p a a0 -> a0

toList :: Tannen f p a a0 -> [a0]

null :: Tannen f p a a0 -> Bool

length :: Tannen f p a a0 -> Int

elem :: Eq a0 => a0 -> Tannen f p a a0 -> Bool

maximum :: Ord a0 => Tannen f p a a0 -> a0

minimum :: Ord a0 => Tannen f p a a0 -> a0

sum :: Num a0 => Tannen f p a a0 -> a0

product :: Num a0 => Tannen f p a a0 -> a0

(Bifoldable p, Foldable g) => Foldable (Biff p f g a)

Defined in Data.Bifunctor.Biff

Methods

fold :: Monoid m => Biff p f g a m -> m

foldMap :: Monoid m => (a0 -> m) -> Biff p f g a a0 -> m

foldMap' :: Monoid m => (a0 -> m) -> Biff p f g a a0 -> m

foldr :: (a0 -> b -> b) -> b -> Biff p f g a a0 -> b

foldr' :: (a0 -> b -> b) -> b -> Biff p f g a a0 -> b

foldl :: (b -> a0 -> b) -> b -> Biff p f g a a0 -> b

foldl' :: (b -> a0 -> b) -> b -> Biff p f g a a0 -> b

foldr1 :: (a0 -> a0 -> a0) -> Biff p f g a a0 -> a0

foldl1 :: (a0 -> a0 -> a0) -> Biff p f g a a0 -> a0

toList :: Biff p f g a a0 -> [a0]

null :: Biff p f g a a0 -> Bool

length :: Biff p f g a a0 -> Int

elem :: Eq a0 => a0 -> Biff p f g a a0 -> Bool

maximum :: Ord a0 => Biff p f g a a0 -> a0

minimum :: Ord a0 => Biff p f g a a0 -> a0

sum :: Num a0 => Biff p f g a a0 -> a0

product :: Num a0 => Biff p f g a a0 -> a0

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

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

Instances

type Mutable Vector

Defined in Data.Vector.Unboxed.Base

type Mutable Vector = MVector

type Mutable Vector

Defined in Data.Vector.Primitive

type Mutable Vector = MVector

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

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

Minimum complete implementation:

• basicUnsafeFreeze
• basicUnsafeThaw
• basicLength
• basicUnsafeSlice
• basicUnsafeIndexM

Minimal complete definition

basicUnsafeFreeze, basicUnsafeThaw, basicLength, basicUnsafeSlice, basicUnsafeIndexM

Instances

Vector Vector Bool

Defined in Data.Vector.Unboxed.Base

Methods

basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) Bool -> m (Vector Bool)

basicUnsafeThaw :: PrimMonad m => Vector Bool -> m (Mutable Vector (PrimState m) Bool)

basicLength :: Vector Bool -> Int

basicUnsafeSlice :: Int -> Int -> Vector Bool -> Vector Bool

basicUnsafeIndexM :: Monad m => Vector Bool -> Int -> m Bool

basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) Bool -> Vector Bool -> m ()

elemseq :: Vector Bool -> Bool -> b -> b

Vector Vector Char

Defined in Data.Vector.Unboxed.Base

Methods

basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) Char -> m (Vector Char)

basicUnsafeThaw :: PrimMonad m => Vector Char -> m (Mutable Vector (PrimState m) Char)

basicLength :: Vector Char -> Int

basicUnsafeSlice :: Int -> Int -> Vector Char -> Vector Char

basicUnsafeIndexM :: Monad m => Vector Char -> Int -> m Char

basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) Char -> Vector Char -> m ()

elemseq :: Vector Char -> Char -> b -> b

Vector Vector Double

Defined in Data.Vector.Unboxed.Base

Methods

basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) Double -> m (Vector Double)

basicUnsafeThaw :: PrimMonad m => Vector Double -> m (Mutable Vector (PrimState m) Double)

basicLength :: Vector Double -> Int

basicUnsafeSlice :: Int -> Int -> Vector Double -> Vector Double

basicUnsafeIndexM :: Monad m => Vector Double -> Int -> m Double

basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) Double -> Vector Double -> m ()

elemseq :: Vector Double -> Double -> b -> b

Vector Vector Float

Defined in Data.Vector.Unboxed.Base

Methods

basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) Float -> m (Vector Float)

basicUnsafeThaw :: PrimMonad m => Vector Float -> m (Mutable Vector (PrimState m) Float)

basicLength :: Vector Float -> Int

basicUnsafeSlice :: Int -> Int -> Vector Float -> Vector Float

basicUnsafeIndexM :: Monad m => Vector Float -> Int -> m Float

basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) Float -> Vector Float -> m ()

elemseq :: Vector Float -> Float -> b -> b

Vector Vector Int

Defined in Data.Vector.Unboxed.Base

Methods

basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) Int -> m (Vector Int)

basicUnsafeThaw :: PrimMonad m => Vector Int -> m (Mutable Vector (PrimState m) Int)

basicLength :: Vector Int -> Int

basicUnsafeSlice :: Int -> Int -> Vector Int -> Vector Int

basicUnsafeIndexM :: Monad m => Vector Int -> Int -> m Int

basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) Int -> Vector Int -> m ()

elemseq :: Vector Int -> Int -> b -> b

Vector Vector Int8

Defined in Data.Vector.Unboxed.Base

Methods

basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) Int8 -> m (Vector Int8)

basicUnsafeThaw :: PrimMonad m => Vector Int8 -> m (Mutable Vector (PrimState m) Int8)

basicLength :: Vector Int8 -> Int

basicUnsafeSlice :: Int -> Int -> Vector Int8 -> Vector Int8

basicUnsafeIndexM :: Monad m => Vector Int8 -> Int -> m Int8

basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) Int8 -> Vector Int8 -> m ()

elemseq :: Vector Int8 -> Int8 -> b -> b

Vector Vector Int16

Defined in Data.Vector.Unboxed.Base

Methods

basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) Int16 -> m (Vector Int16)

basicUnsafeThaw :: PrimMonad m => Vector Int16 -> m (Mutable Vector (PrimState m) Int16)

basicLength :: Vector Int16 -> Int

basicUnsafeSlice :: Int -> Int -> Vector Int16 -> Vector Int16

basicUnsafeIndexM :: Monad m => Vector Int16 -> Int -> m Int16

basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) Int16 -> Vector Int16 -> m ()

elemseq :: Vector Int16 -> Int16 -> b -> b

Vector Vector Int32

Defined in Data.Vector.Unboxed.Base

Methods

basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) Int32 -> m (Vector Int32)

basicUnsafeThaw :: PrimMonad m => Vector Int32 -> m (Mutable Vector (PrimState m) Int32)

basicLength :: Vector Int32 -> Int

basicUnsafeSlice :: Int -> Int -> Vector Int32 -> Vector Int32

basicUnsafeIndexM :: Monad m => Vector Int32 -> Int -> m Int32

basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) Int32 -> Vector Int32 -> m ()

elemseq :: Vector Int32 -> Int32 -> b -> b

Vector Vector Int64

Defined in Data.Vector.Unboxed.Base

Methods

basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) Int64 -> m (Vector Int64)

basicUnsafeThaw :: PrimMonad m => Vector Int64 -> m (Mutable Vector (PrimState m) Int64)

basicLength :: Vector Int64 -> Int

basicUnsafeSlice :: Int -> Int -> Vector Int64 -> Vector Int64

basicUnsafeIndexM :: Monad m => Vector Int64 -> Int -> m Int64

basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) Int64 -> Vector Int64 -> m ()

elemseq :: Vector Int64 -> Int64 -> b -> b

Vector Vector Word

Defined in Data.Vector.Unboxed.Base

Methods

basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) Word -> m (Vector Word)

basicUnsafeThaw :: PrimMonad m => Vector Word -> m (Mutable Vector (PrimState m) Word)

basicLength :: Vector Word -> Int

basicUnsafeSlice :: Int -> Int -> Vector Word -> Vector Word

basicUnsafeIndexM :: Monad m => Vector Word -> Int -> m Word

basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) Word -> Vector Word -> m ()

elemseq :: Vector Word -> Word -> b -> b

Vector Vector Word8

Defined in Data.Vector.Unboxed.Base

Methods

basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) Word8 -> m (Vector Word8)

basicUnsafeThaw :: PrimMonad m => Vector Word8 -> m (Mutable Vector (PrimState m) Word8)

basicLength :: Vector Word8 -> Int

basicUnsafeSlice :: Int -> Int -> Vector Word8 -> Vector Word8

basicUnsafeIndexM :: Monad m => Vector Word8 -> Int -> m Word8

basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) Word8 -> Vector Word8 -> m ()

elemseq :: Vector Word8 -> Word8 -> b -> b

Vector Vector Word16

Defined in Data.Vector.Unboxed.Base

Methods

basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) Word16 -> m (Vector Word16)

basicUnsafeThaw :: PrimMonad m => Vector Word16 -> m (Mutable Vector (PrimState m) Word16)

basicLength :: Vector Word16 -> Int

basicUnsafeSlice :: Int -> Int -> Vector Word16 -> Vector Word16

basicUnsafeIndexM :: Monad m => Vector Word16 -> Int -> m Word16

basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) Word16 -> Vector Word16 -> m ()

elemseq :: Vector Word16 -> Word16 -> b -> b

Vector Vector Word32

Defined in Data.Vector.Unboxed.Base

Methods

basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) Word32 -> m (Vector Word32)

basicUnsafeThaw :: PrimMonad m => Vector Word32 -> m (Mutable Vector (PrimState m) Word32)

basicLength :: Vector Word32 -> Int

basicUnsafeSlice :: Int -> Int -> Vector Word32 -> Vector Word32

basicUnsafeIndexM :: Monad m => Vector Word32 -> Int -> m Word32

basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) Word32 -> Vector Word32 -> m ()

elemseq :: Vector Word32 -> Word32 -> b -> b

Vector Vector Word64

Defined in Data.Vector.Unboxed.Base

Methods

basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) Word64 -> m (Vector Word64)

basicUnsafeThaw :: PrimMonad m => Vector Word64 -> m (Mutable Vector (PrimState m) Word64)

basicLength :: Vector Word64 -> Int

basicUnsafeSlice :: Int -> Int -> Vector Word64 -> Vector Word64

basicUnsafeIndexM :: Monad m => Vector Word64 -> Int -> m Word64

basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) Word64 -> Vector Word64 -> m ()

elemseq :: Vector Word64 -> Word64 -> b -> b

Vector Vector ()

Defined in Data.Vector.Unboxed.Base

Methods

basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) () -> m (Vector ())

basicUnsafeThaw :: PrimMonad m => Vector () -> m (Mutable Vector (PrimState m) ())

basicLength :: Vector () -> Int

basicUnsafeSlice :: Int -> Int -> Vector () -> Vector ()

basicUnsafeIndexM :: Monad m => Vector () -> Int -> m ()

basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) () -> Vector () -> m ()

elemseq :: Vector () -> () -> b -> b

Vector Vector All

Defined in Data.Vector.Unboxed.Base

Methods

basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) All -> m (Vector All)

basicUnsafeThaw :: PrimMonad m => Vector All -> m (Mutable Vector (PrimState m) All)

basicLength :: Vector All -> Int

basicUnsafeSlice :: Int -> Int -> Vector All -> Vector All

basicUnsafeIndexM :: Monad m => Vector All -> Int -> m All

basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) All -> Vector All -> m ()

elemseq :: Vector All -> All -> b -> b

Vector Vector Any

Defined in Data.Vector.Unboxed.Base

Methods

basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) Any -> m (Vector Any)

basicUnsafeThaw :: PrimMonad m => Vector Any -> m (Mutable Vector (PrimState m) Any)

basicLength :: Vector Any -> Int

basicUnsafeSlice :: Int -> Int -> Vector Any -> Vector Any

basicUnsafeIndexM :: Monad m => Vector Any -> Int -> m Any

basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) Any -> Vector Any -> m ()

elemseq :: Vector Any -> Any -> b -> b

Prim a => Vector Vector a

Defined in Data.Vector.Primitive

Methods

basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) a -> m (Vector a)

basicUnsafeThaw :: PrimMonad m => Vector a -> m (Mutable Vector (PrimState m) a)

basicLength :: Vector a -> Int

basicUnsafeSlice :: Int -> Int -> Vector a -> Vector a

basicUnsafeIndexM :: Monad m => Vector a -> Int -> m a

basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) a -> Vector a -> m ()

elemseq :: Vector a -> a -> b -> b

Unbox a => Vector Vector (Complex a)

Defined in Data.Vector.Unboxed.Base

Methods

basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) (Complex a) -> m (Vector (Complex a))

basicUnsafeThaw :: PrimMonad m => Vector (Complex a) -> m (Mutable Vector (PrimState m) (Complex a))

basicLength :: Vector (Complex a) -> Int

basicUnsafeSlice :: Int -> Int -> Vector (Complex a) -> Vector (Complex a)

basicUnsafeIndexM :: Monad m => Vector (Complex a) -> Int -> m (Complex a)

basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) (Complex a) -> Vector (Complex a) -> m ()

elemseq :: Vector (Complex a) -> Complex a -> b -> b

Unbox a => Vector Vector (Min a)

Defined in Data.Vector.Unboxed.Base

Methods

basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) (Min a) -> m (Vector (Min a))

basicUnsafeThaw :: PrimMonad m => Vector (Min a) -> m (Mutable Vector (PrimState m) (Min a))

basicLength :: Vector (Min a) -> Int

basicUnsafeSlice :: Int -> Int -> Vector (Min a) -> Vector (Min a)

basicUnsafeIndexM :: Monad m => Vector (Min a) -> Int -> m (Min a)

basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) (Min a) -> Vector (Min a) -> m ()

elemseq :: Vector (Min a) -> Min a -> b -> b

Unbox a => Vector Vector (Max a)

Defined in Data.Vector.Unboxed.Base

Methods

basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) (Max a) -> m (Vector (Max a))

basicUnsafeThaw :: PrimMonad m => Vector (Max a) -> m (Mutable Vector (PrimState m) (Max a))

basicLength :: Vector (Max a) -> Int

basicUnsafeSlice :: Int -> Int -> Vector (Max a) -> Vector (Max a)

basicUnsafeIndexM :: Monad m => Vector (Max a) -> Int -> m (Max a)

basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) (Max a) -> Vector (Max a) -> m ()

elemseq :: Vector (Max a) -> Max a -> b -> b

Unbox a => Vector Vector (First a)

Defined in Data.Vector.Unboxed.Base

Methods

basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) (First a) -> m (Vector (First a))

basicUnsafeThaw :: PrimMonad m => Vector (First a) -> m (Mutable Vector (PrimState m) (First a))

basicLength :: Vector (First a) -> Int

basicUnsafeSlice :: Int -> Int -> Vector (First a) -> Vector (First a)

basicUnsafeIndexM :: Monad m => Vector (First a) -> Int -> m (First a)

basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) (First a) -> Vector (First a) -> m ()

elemseq :: Vector (First a) -> First a -> b -> b

Unbox a => Vector Vector (Last a)

Defined in Data.Vector.Unboxed.Base

Methods

basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) (Last a) -> m (Vector (Last a))

basicUnsafeThaw :: PrimMonad m => Vector (Last a) -> m (Mutable Vector (PrimState m) (Last a))

basicLength :: Vector (Last a) -> Int

basicUnsafeSlice :: Int -> Int -> Vector (Last a) -> Vector (Last a)

basicUnsafeIndexM :: Monad m => Vector (Last a) -> Int -> m (Last a)

basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) (Last a) -> Vector (Last a) -> m ()

elemseq :: Vector (Last a) -> Last a -> b -> b

Unbox a => Vector Vector (WrappedMonoid a)

Defined in Data.Vector.Unboxed.Base

Methods

basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) (WrappedMonoid a) -> m (Vector (WrappedMonoid a))

basicUnsafeThaw :: PrimMonad m => Vector (WrappedMonoid a) -> m (Mutable Vector (PrimState m) (WrappedMonoid a))

basicLength :: Vector (WrappedMonoid a) -> Int

basicUnsafeSlice :: Int -> Int -> Vector (WrappedMonoid a) -> Vector (WrappedMonoid a)

basicUnsafeIndexM :: Monad m => Vector (WrappedMonoid a) -> Int -> m (WrappedMonoid a)

basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) (WrappedMonoid a) -> Vector (WrappedMonoid a) -> m ()

elemseq :: Vector (WrappedMonoid a) -> WrappedMonoid a -> b -> b

Unbox a => Vector Vector (Identity a)

Defined in Data.Vector.Unboxed.Base

Methods

basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) (Identity a) -> m (Vector (Identity a))

basicUnsafeThaw :: PrimMonad m => Vector (Identity a) -> m (Mutable Vector (PrimState m) (Identity a))

basicLength :: Vector (Identity a) -> Int

basicUnsafeSlice :: Int -> Int -> Vector (Identity a) -> Vector (Identity a)

basicUnsafeIndexM :: Monad m => Vector (Identity a) -> Int -> m (Identity a)

basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) (Identity a) -> Vector (Identity a) -> m ()

elemseq :: Vector (Identity a) -> Identity a -> b -> b

Unbox a => Vector Vector (Dual a)

Defined in Data.Vector.Unboxed.Base

Methods

basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) (Dual a) -> m (Vector (Dual a))

basicUnsafeThaw :: PrimMonad m => Vector (Dual a) -> m (Mutable Vector (PrimState m) (Dual a))

basicLength :: Vector (Dual a) -> Int

basicUnsafeSlice :: Int -> Int -> Vector (Dual a) -> Vector (Dual a)

basicUnsafeIndexM :: Monad m => Vector (Dual a) -> Int -> m (Dual a)

basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) (Dual a) -> Vector (Dual a) -> m ()

elemseq :: Vector (Dual a) -> Dual a -> b -> b

Unbox a => Vector Vector (Sum a)

Defined in Data.Vector.Unboxed.Base

Methods

basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) (Sum a) -> m (Vector (Sum a))

basicUnsafeThaw :: PrimMonad m => Vector (Sum a) -> m (Mutable Vector (PrimState m) (Sum a))

basicLength :: Vector (Sum a) -> Int

basicUnsafeSlice :: Int -> Int -> Vector (Sum a) -> Vector (Sum a)

basicUnsafeIndexM :: Monad m => Vector (Sum a) -> Int -> m (Sum a)

basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) (Sum a) -> Vector (Sum a) -> m ()

elemseq :: Vector (Sum a) -> Sum a -> b -> b

Unbox a => Vector Vector (Product a)

Defined in Data.Vector.Unboxed.Base

Methods

basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) (Product a) -> m (Vector (Product a))

basicUnsafeThaw :: PrimMonad m => Vector (Product a) -> m (Mutable Vector (PrimState m) (Product a))

basicLength :: Vector (Product a) -> Int

basicUnsafeSlice :: Int -> Int -> Vector (Product a) -> Vector (Product a)

basicUnsafeIndexM :: Monad m => Vector (Product a) -> Int -> m (Product a)

basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) (Product a) -> Vector (Product a) -> m ()

elemseq :: Vector (Product a) -> Product a -> b -> b

Unbox a => Vector Vector (Down a)

Defined in Data.Vector.Unboxed.Base

Methods

basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) (Down a) -> m (Vector (Down a))

basicUnsafeThaw :: PrimMonad m => Vector (Down a) -> m (Mutable Vector (PrimState m) (Down a))

basicLength :: Vector (Down a) -> Int

basicUnsafeSlice :: Int -> Int -> Vector (Down a) -> Vector (Down a)

basicUnsafeIndexM :: Monad m => Vector (Down a) -> Int -> m (Down a)

basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) (Down a) -> Vector (Down a) -> m ()

elemseq :: Vector (Down a) -> Down a -> b -> b

(Unbox a, Unbox b) => Vector Vector (a, b)

Defined in Data.Vector.Unboxed.Base

Methods

basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) (a, b) -> m (Vector (a, b))

basicUnsafeThaw :: PrimMonad m => Vector (a, b) -> m (Mutable Vector (PrimState m) (a, b))

basicLength :: Vector (a, b) -> Int

basicUnsafeSlice :: Int -> Int -> Vector (a, b) -> Vector (a, b)

basicUnsafeIndexM :: Monad m => Vector (a, b) -> Int -> m (a, b)

basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) (a, b) -> Vector (a, b) -> m ()

elemseq :: Vector (a, b) -> (a, b) -> b0 -> b0

(Unbox a, Unbox b) => Vector Vector (Arg a b)

Defined in Data.Vector.Unboxed.Base

Methods

basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) (Arg a b) -> m (Vector (Arg a b))

basicUnsafeThaw :: PrimMonad m => Vector (Arg a b) -> m (Mutable Vector (PrimState m) (Arg a b))

basicLength :: Vector (Arg a b) -> Int

basicUnsafeSlice :: Int -> Int -> Vector (Arg a b) -> Vector (Arg a b)

basicUnsafeIndexM :: Monad m => Vector (Arg a b) -> Int -> m (Arg a b)

basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) (Arg a b) -> Vector (Arg a b) -> m ()

elemseq :: Vector (Arg a b) -> Arg a b -> b0 -> b0

(Unbox a, Unbox b, Unbox c) => Vector Vector (a, b, c)

Defined in Data.Vector.Unboxed.Base

Methods

basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) (a, b, c) -> m (Vector (a, b, c))

basicUnsafeThaw :: PrimMonad m => Vector (a, b, c) -> m (Mutable Vector (PrimState m) (a, b, c))

basicLength :: Vector (a, b, c) -> Int

basicUnsafeSlice :: Int -> Int -> Vector (a, b, c) -> Vector (a, b, c)

basicUnsafeIndexM :: Monad m => Vector (a, b, c) -> Int -> m (a, b, c)

basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) (a, b, c) -> Vector (a, b, c) -> m ()

elemseq :: Vector (a, b, c) -> (a, b, c) -> b0 -> b0

Unbox a => Vector Vector (Const a b)

Defined in Data.Vector.Unboxed.Base

Methods

basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) (Const a b) -> m (Vector (Const a b))

basicUnsafeThaw :: PrimMonad m => Vector (Const a b) -> m (Mutable Vector (PrimState m) (Const a b))

basicLength :: Vector (Const a b) -> Int

basicUnsafeSlice :: Int -> Int -> Vector (Const a b) -> Vector (Const a b)

basicUnsafeIndexM :: Monad m => Vector (Const a b) -> Int -> m (Const a b)

basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) (Const a b) -> Vector (Const a b) -> m ()

elemseq :: Vector (Const a b) -> Const a b -> b0 -> b0

Unbox (f a) => Vector Vector (Alt f a)

Defined in Data.Vector.Unboxed.Base

Methods

basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) (Alt f a) -> m (Vector (Alt f a))

basicUnsafeThaw :: PrimMonad m => Vector (Alt f a) -> m (Mutable Vector (PrimState m) (Alt f a))

basicLength :: Vector (Alt f a) -> Int

basicUnsafeSlice :: Int -> Int -> Vector (Alt f a) -> Vector (Alt f a)

basicUnsafeIndexM :: Monad m => Vector (Alt f a) -> Int -> m (Alt f a)

basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) (Alt f a) -> Vector (Alt f a) -> m ()

elemseq :: Vector (Alt f a) -> Alt f a -> b -> b

(Unbox a, Unbox b, Unbox c, Unbox d) => Vector Vector (a, b, c, d)

Defined in Data.Vector.Unboxed.Base

Methods

basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) (a, b, c, d) -> m (Vector (a, b, c, d))

basicUnsafeThaw :: PrimMonad m => Vector (a, b, c, d) -> m (Mutable Vector (PrimState m) (a, b, c, d))

basicLength :: Vector (a, b, c, d) -> Int

basicUnsafeSlice :: Int -> Int -> Vector (a, b, c, d) -> Vector (a, b, c, d)

basicUnsafeIndexM :: Monad m => Vector (a, b, c, d) -> Int -> m (a, b, c, d)

basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) (a, b, c, d) -> Vector (a, b, c, d) -> m ()

elemseq :: Vector (a, b, c, d) -> (a, b, c, d) -> b0 -> b0

(Unbox a, Unbox b, Unbox c, Unbox d, Unbox e) => Vector Vector (a, b, c, d, e)

Defined in Data.Vector.Unboxed.Base

Methods

basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) (a, b, c, d, e) -> m (Vector (a, b, c, d, e))

basicUnsafeThaw :: PrimMonad m => Vector (a, b, c, d, e) -> m (Mutable Vector (PrimState m) (a, b, c, d, e))

basicLength :: Vector (a, b, c, d, e) -> Int

basicUnsafeSlice :: Int -> Int -> Vector (a, b, c, d, e) -> Vector (a, b, c, d, e)

basicUnsafeIndexM :: Monad m => Vector (a, b, c, d, e) -> Int -> m (a, b, c, d, e)

basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) (a, b, c, d, e) -> Vector (a, b, c, d, e) -> m ()

elemseq :: Vector (a, b, c, d, e) -> (a, b, c, d, e) -> b0 -> b0

Unbox (f (g a)) => Vector Vector (Compose f g a)

Defined in Data.Vector.Unboxed.Base

Methods

basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) (Compose f g a) -> m (Vector (Compose f g a))

basicUnsafeThaw :: PrimMonad m => Vector (Compose f g a) -> m (Mutable Vector (PrimState m) (Compose f g a))

basicLength :: Vector (Compose f g a) -> Int

basicUnsafeSlice :: Int -> Int -> Vector (Compose f g a) -> Vector (Compose f g a)

basicUnsafeIndexM :: Monad m => Vector (Compose f g a) -> Int -> m (Compose f g a)

basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) (Compose f g a) -> Vector (Compose f g a) -> m ()

elemseq :: Vector (Compose f g a) -> Compose f g a -> b -> b

(Unbox a, Unbox b, Unbox c, Unbox d, Unbox e, Unbox f) => Vector Vector (a, b, c, d, e, f)

Defined in Data.Vector.Unboxed.Base

Methods

basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) (a, b, c, d, e, f) -> m (Vector (a, b, c, d, e, f))

basicUnsafeThaw :: PrimMonad m => Vector (a, b, c, d, e, f) -> m (Mutable Vector (PrimState m) (a, b, c, d, e, f))

basicLength :: Vector (a, b, c, d, e, f) -> Int

basicUnsafeSlice :: Int -> Int -> Vector (a, b, c, d, e, f) -> Vector (a, b, c, d, e, f)

basicUnsafeIndexM :: Monad m => Vector (a, b, c, d, e, f) -> Int -> m (a, b, c, d, e, f)

basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) (a, b, c, d, e, f) -> Vector (a, b, c, d, e, f) -> m ()

elemseq :: Vector (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> b0 -> b0