Pipes

This module is the recommended entry point to the pipes library.

Read Pipes.Tutorial if you want a tutorial explaining how to use this library.

The Proxy Monad Transformer

data Proxy a' a b' b m r

A Proxy is a monad transformer that receives and sends information on both an upstream and downstream interface.

The type variables signify:

• a' and a - The upstream interface, where (a')s go out and (a)s come in
• b' and b - The downstream interface, where (b)s go out and (b')s come in
• m - The base monad
• r - The return value

Instances

MonadError e m => MonadError e (Proxy a' a b' b m)

Methods

throwError :: e -> Proxy a' a b' b m a

catchError :: Proxy a' a b' b m a -> (e -> Proxy a' a b' b m a) -> Proxy a' a b' b m a

MonadReader r m => MonadReader r (Proxy a' a b' b m)

Methods

ask :: Proxy a' a b' b m r

local :: (r -> r) -> Proxy a' a b' b m a -> Proxy a' a b' b m a

reader :: (r -> a) -> Proxy a' a b' b m a

MonadState s m => MonadState s (Proxy a' a b' b m)

Methods

get :: Proxy a' a b' b m s

put :: s -> Proxy a' a b' b m ()

state :: (s -> (a, s)) -> Proxy a' a b' b m a

MonadWriter w m => MonadWriter w (Proxy a' a b' b m)

Methods

writer :: (a, w) -> Proxy a' a b' b m a

tell :: w -> Proxy a' a b' b m ()

listen :: Proxy a' a b' b m a -> Proxy a' a b' b m (a, w)

pass :: Proxy a' a b' b m (a, w -> w) -> Proxy a' a b' b m a

MFunctor * (Proxy a' a b' b)

Methods

hoist :: Monad m => (forall c. m c -> n c) -> t m b -> t n b

MMonad (Proxy a' a b' b)

Methods

embed :: Monad n => (forall c. m c -> Proxy a' a b' b n c) -> Proxy a' a b' b m b -> Proxy a' a b' b n b

MonadTrans (Proxy a' a b' b)

Methods

lift :: Monad m => m a -> Proxy a' a b' b m a

Monad m => Monad (Proxy a' a b' b m)

Methods

(>>=) :: Proxy a' a b' b m a -> (a -> Proxy a' a b' b m b) -> Proxy a' a b' b m b

(>>) :: Proxy a' a b' b m a -> Proxy a' a b' b m b -> Proxy a' a b' b m b

return :: a -> Proxy a' a b' b m a

fail :: String -> Proxy a' a b' b m a

Monad m => Functor (Proxy a' a b' b m)

Methods

fmap :: (a -> b) -> Proxy a' a b' b m a -> Proxy a' a b' b m b

(<$) :: a -> Proxy a' a b' b m b -> Proxy a' a b' b m a

Monad m => Applicative (Proxy a' a b' b m)

Methods

pure :: a -> Proxy a' a b' b m a

(<*>) :: Proxy a' a b' b m (a -> b) -> Proxy a' a b' b m a -> Proxy a' a b' b m b

(*>) :: Proxy a' a b' b m a -> Proxy a' a b' b m b -> Proxy a' a b' b m b

(<*) :: Proxy a' a b' b m a -> Proxy a' a b' b m b -> Proxy a' a b' b m a

MonadIO m => MonadIO (Proxy a' a b' b m)

Methods

liftIO :: IO a -> Proxy a' a b' b m a

MonadThrow m => MonadThrow (Proxy a' a b' b m)

Methods

throwM :: Exception e => e -> Proxy a' a b' b m a

MonadCatch m => MonadCatch (Proxy a' a b' b m)

Methods

catch :: Exception e => Proxy a' a b' b m a -> (e -> Proxy a' a b' b m a) -> Proxy a' a b' b m a

(Monad m, Semigroup r) => Semigroup (Proxy a' a b' b m r)

Methods

(<>) :: Proxy a' a b' b m r -> Proxy a' a b' b m r -> Proxy a' a b' b m r

sconcat :: NonEmpty (Proxy a' a b' b m r) -> Proxy a' a b' b m r

stimes :: Integral b => b -> Proxy a' a b' b m r -> Proxy a' a b' b m r

(Monad m, Monoid r, Semigroup r) => Monoid (Proxy a' a b' b m r)

Methods

mempty :: Proxy a' a b' b m r

mappend :: Proxy a' a b' b m r -> Proxy a' a b' b m r -> Proxy a' a b' b m r

mconcat :: [Proxy a' a b' b m r] -> Proxy a' a b' b m r

type X = Void

The empty type, used to close output ends

type Effect = Proxy X () () X

An effect in the base monad

Effects neither await nor yield

type Effect' m r = forall x' x y' y. Proxy x' x y' y m r

Like Effect, but with a polymorphic type

runEffect :: Monad m => Effect m r -> m r

Run a self-contained Effect, converting it back to the base monad

Producers

Use yield to produce output and (~>) / for to substitute yields.

yield and (~>) obey the Category laws:

-- Substituting 'yield' with 'f' gives 'f'
yield ~> f = f

-- Substituting every 'yield' with another 'yield' does nothing
f ~> yield = f

-- 'yield' substitution is associative
(f ~> g) ~> h = f ~> (g ~> h)

These are equivalent to the following "for loop laws":

-- Looping over a single yield simplifies to function application
for (yield x) f = f x

-- Re-yielding every element of a stream returns the original stream
for s yield = s

-- Nested for loops can become a sequential for loops if the inner loop
-- body ignores the outer loop variable
for s (\a -> for (f a) g) = for (for s f) g = for s (f ~> g)

type Producer b = Proxy X () () b

Producers can only yield

type Producer' b m r = forall x' x. Proxy x' x () b m r

Like Producer, but with a polymorphic type

yield :: Monad m => a -> Producer' a m ()

Produce a value

yield :: Monad m => a -> Pipe x a m ()

for

Arguments

:: Monad m

=> Proxy x' x b' b m a'

-> (b -> Proxy x' x c' c m b')

-> Proxy x' x c' c m a'

(for p body) loops over p replacing each yield with body.

for :: Monad m => Producer b m r -> (b -> Effect       m ()) -> Effect       m r
for :: Monad m => Producer b m r -> (b -> Producer   c m ()) -> Producer   c m r
for :: Monad m => Pipe   x b m r -> (b -> Consumer x   m ()) -> Consumer x   m r
for :: Monad m => Pipe   x b m r -> (b -> Pipe     x c m ()) -> Pipe     x c m r

The following diagrams show the flow of information:

                              .--->   b
                             /        |
   +-----------+            /   +-----|-----+                 +---------------+
   |           |           /    |     v     |                 |               |
   |           |          /     |           |                 |               |
x ==>    p    ==> b   ---'   x ==>   body  ==> c     =     x ==> for p body  ==> c
   |           |                |           |                 |               |
   |     |     |                |     |     |                 |       |       |
   +-----|-----+                +-----|-----+                 +-------|-------+
         v                            v                               v
         r                            ()                              r

For a more complete diagram including bidirectional flow, see Pipes.Core.

(~>) infixr 4

Arguments

:: Monad m

=> (a -> Proxy x' x b' b m a')

-> (b -> Proxy x' x c' c m b')

-> a -> Proxy x' x c' c m a'

Compose loop bodies

(~>) :: Monad m => (a -> Producer b m r) -> (b -> Effect       m ()) -> (a -> Effect       m r)
(~>) :: Monad m => (a -> Producer b m r) -> (b -> Producer   c m ()) -> (a -> Producer   c m r)
(~>) :: Monad m => (a -> Pipe   x b m r) -> (b -> Consumer x   m ()) -> (a -> Consumer x   m r)
(~>) :: Monad m => (a -> Pipe   x b m r) -> (b -> Pipe     x c m ()) -> (a -> Pipe     x c m r)

The following diagrams show the flow of information:

         a                    .--->   b                              a
         |                   /        |                              |
   +-----|-----+            /   +-----|-----+                 +------|------+
   |     v     |           /    |     v     |                 |      v      |
   |           |          /     |           |                 |             |
x ==>    f    ==> b   ---'   x ==>    g    ==> c     =     x ==>   f ~> g  ==> c
   |           |                |           |                 |             |
   |     |     |                |     |     |                 |      |      |
   +-----|-----+                +-----|-----+                 +------|------+
         v                            v                              v
         r                            ()                             r

For a more complete diagram including bidirectional flow, see Pipes.Core.

(<~) infixl 4

Arguments

:: Monad m

=> (b -> Proxy x' x c' c m b')

-> (a -> Proxy x' x b' b m a')

-> a -> Proxy x' x c' c m a'

(~>) with the arguments flipped

Consumers

Use await to request input and (>~) to substitute awaits.

await and (>~) obey the Category laws:

-- Substituting every 'await' with another 'await' does nothing
await >~ f = f

-- Substituting 'await' with 'f' gives 'f'
f >~ await = f

-- 'await' substitution is associative
(f >~ g) >~ h = f >~ (g >~ h)

type Consumer a = Proxy () a () X

Consumers can only await

type Consumer' a m r = forall y' y. Proxy () a y' y m r

Like Consumer, but with a polymorphic type

await :: Monad m => Consumer' a m a

Consume a value

await :: Monad m => Pipe a y m a

(>~) infixr 5

Arguments

:: Monad m

=> Proxy a' a y' y m b

-> Proxy () b y' y m c

-> Proxy a' a y' y m c

(draw >~ p) loops over p replacing each await with draw

(>~) :: Monad m => Effect       m b -> Consumer b   m c -> Effect       m c
(>~) :: Monad m => Consumer a   m b -> Consumer b   m c -> Consumer a   m c
(>~) :: Monad m => Producer   y m b -> Pipe     b y m c -> Producer   y m c
(>~) :: Monad m => Pipe     a y m b -> Pipe     b y m c -> Pipe     a y m c

The following diagrams show the flow of information:

   +-----------+                 +-----------+                 +-------------+
   |           |                 |           |                 |             |
   |           |                 |           |                 |             |
a ==>    f    ==> y   .--->   b ==>    g    ==> y     =     a ==>   f >~ g  ==> y
   |           |     /           |           |                 |             |
   |     |     |    /            |     |     |                 |      |      |
   +-----|-----+   /             +-----|-----+                 +------|------+
         v        /                    v                              v
         b   ----'                     c                              c

For a more complete diagram including bidirectional flow, see Pipes.Core.

(~<) infixl 5

Arguments

:: Monad m

=> Proxy () b y' y m c

-> Proxy a' a y' y m b

-> Proxy a' a y' y m c

(>~) with the arguments flipped

Pipes

Use await and yield to build Pipes and (>->) to connect Pipes.

cat and (>->) obey the Category laws:

-- Useless use of cat
cat >-> f = f

-- Redirecting output to cat does nothing
f >-> cat = f

-- The pipe operator is associative
(f >-> g) >-> h = f >-> (g >-> h)

type Pipe a b = Proxy () a () b

Pipes can both await and yield

cat :: Monad m => Pipe a a m r

The identity Pipe, analogous to the Unix cat program

(>->) infixl 7

Arguments

:: Monad m

=> Proxy a' a () b m r

-> Proxy () b c' c m r

-> Proxy a' a c' c m r

Pipe composition, analogous to the Unix pipe operator

(>->) :: Monad m => Producer b m r -> Consumer b   m r -> Effect       m r
(>->) :: Monad m => Producer b m r -> Pipe     b c m r -> Producer   c m r
(>->) :: Monad m => Pipe   a b m r -> Consumer b   m r -> Consumer a   m r
(>->) :: Monad m => Pipe   a b m r -> Pipe     b c m r -> Pipe     a c m r

The following diagrams show the flow of information:

   +-----------+     +-----------+                 +-------------+
   |           |     |           |                 |             |
   |           |     |           |                 |             |
a ==>    f    ==> b ==>    g    ==> c     =     a ==>  f >-> g  ==> c
   |           |     |           |                 |             |
   |     |     |     |     |     |                 |      |      |
   +-----|-----+     +-----|-----+                 +------|------+
         v                 v                              v
         r                 r                              r

For a more complete diagram including bidirectional flow, see Pipes.Core.

(<-<) infixr 7

Arguments

:: Monad m

=> Proxy () b c' c m r

-> Proxy a' a () b m r

-> Proxy a' a c' c m r

(>->) with the arguments flipped

ListT

newtype ListT m a

The list monad transformer, which extends a monad with non-determinism

return corresponds to yield, yielding a single value

(>>=) corresponds to for, calling the second computation once for each time the first computation yields.

Constructors

Select

Fields

• enumerate :: Producer a m ()

Instances

MMonad ListT

Methods

embed :: Monad n => (forall a. m a -> ListT n a) -> ListT m b -> ListT n b

MonadTrans ListT

Methods

lift :: Monad m => m a -> ListT m a

Enumerable ListT

Methods

toListT :: Monad m => ListT m a -> ListT m a

MonadError e m => MonadError e (ListT m)

Methods

throwError :: e -> ListT m a

catchError :: ListT m a -> (e -> ListT m a) -> ListT m a

MonadReader i m => MonadReader i (ListT m)

Methods

ask :: ListT m i

local :: (i -> i) -> ListT m a -> ListT m a

reader :: (i -> a) -> ListT m a

MonadState s m => MonadState s (ListT m)

Methods

get :: ListT m s

put :: s -> ListT m ()

state :: (s -> (a, s)) -> ListT m a

MonadWriter w m => MonadWriter w (ListT m)

Methods

writer :: (a, w) -> ListT m a

tell :: w -> ListT m ()

listen :: ListT m a -> ListT m (a, w)

pass :: ListT m (a, w -> w) -> ListT m a

Monad m => Monad (ListT m)

Methods

(>>=) :: ListT m a -> (a -> ListT m b) -> ListT m b

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

return :: a -> ListT m a

fail :: String -> ListT m a

Monad m => Functor (ListT m)

Methods

fmap :: (a -> b) -> ListT m a -> ListT m b

(<$) :: a -> ListT m b -> ListT m a

Monad m => Applicative (ListT m)

Methods

pure :: a -> ListT m a

(<*>) :: ListT m (a -> b) -> ListT m a -> ListT m b

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

(<*) :: ListT m a -> ListT m b -> ListT m a

Foldable m => Foldable (ListT m)

Methods

fold :: Monoid m => ListT m m -> m

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

foldr :: (a -> b -> b) -> b -> ListT m a -> b

foldr' :: (a -> b -> b) -> b -> ListT m a -> b

foldl :: (b -> a -> b) -> b -> ListT m a -> b

foldl' :: (b -> a -> b) -> b -> ListT m a -> b

foldr1 :: (a -> a -> a) -> ListT m a -> a

foldl1 :: (a -> a -> a) -> ListT m a -> a

toList :: ListT m a -> [a]

null :: ListT m a -> Bool

length :: ListT m a -> Int

elem :: Eq a => a -> ListT m a -> Bool

maximum :: Ord a => ListT m a -> a

minimum :: Ord a => ListT m a -> a

sum :: Num a => ListT m a -> a

product :: Num a => ListT m a -> a

(Monad m, Traversable m) => Traversable (ListT m)

Methods

traverse :: Applicative f => (a -> f b) -> ListT m a -> f (ListT m b)

sequenceA :: Applicative f => ListT m (f a) -> f (ListT m a)

mapM :: Monad m => (a -> m b) -> ListT m a -> m (ListT m b)

sequence :: Monad m => ListT m (m a) -> m (ListT m a)

Monad m => MonadZip (ListT m)

Methods

mzip :: ListT m a -> ListT m b -> ListT m (a, b)

mzipWith :: (a -> b -> c) -> ListT m a -> ListT m b -> ListT m c

munzip :: ListT m (a, b) -> (ListT m a, ListT m b)

MonadIO m => MonadIO (ListT m)

Methods

liftIO :: IO a -> ListT m a

Monad m => Alternative (ListT m)

Methods

empty :: ListT m a

(<|>) :: ListT m a -> ListT m a -> ListT m a

some :: ListT m a -> ListT m [a]

many :: ListT m a -> ListT m [a]

Monad m => MonadPlus (ListT m)

Methods

mzero :: ListT m a

mplus :: ListT m a -> ListT m a -> ListT m a

MonadThrow m => MonadThrow (ListT m)

Methods

throwM :: Exception e => e -> ListT m a

MonadCatch m => MonadCatch (ListT m)

Methods

catch :: Exception e => ListT m a -> (e -> ListT m a) -> ListT m a

MFunctor * ListT

Methods

hoist :: Monad m => (forall a. m a -> n a) -> t m b -> t n b

Monad m => Semigroup (ListT m a)

Methods

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

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

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

Monad m => Monoid (ListT m a)

Methods

mempty :: ListT m a

mappend :: ListT m a -> ListT m a -> ListT m a

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

runListT :: Monad m => ListT m a -> m ()

Run a self-contained ListT computation

class Enumerable t where

Enumerable generalizes Foldable, converting effectful containers to ListTs.

Instances of Enumerable must satisfy these two laws:

toListT (return r) = return r

toListT $ do x <- m  =  do x <- toListT m
             f x           toListT (f x)

In other words, toListT is monad morphism.

Minimal complete definition

toListT

Methods

toListT :: Monad m => t m a -> ListT m a

Instances

Enumerable MaybeT

Methods

toListT :: Monad m => MaybeT m a -> ListT m a

Enumerable ListT

Methods

toListT :: Monad m => ListT m a -> ListT m a

Enumerable (ExceptT e)

Methods

toListT :: Monad m => ExceptT e m a -> ListT m a

Enumerable (IdentityT *)

Methods

toListT :: Monad m => IdentityT * m a -> ListT m a

Utilities

next :: Monad m => Producer a m r -> m (Either r (a, Producer a m r))

Consume the first value from a Producer

next either fails with a Left if the Producer terminates or succeeds with a Right providing the next value and the remainder of the Producer.

each :: (Monad m, Foldable f) => f a -> Producer' a m ()

Convert a Foldable to a Producer

every :: (Monad m, Enumerable t) => t m a -> Producer' a m ()

Convert an Enumerable to a Producer

discard :: Monad m => a -> m ()

Discards a value

Re-exports

Control.Monad re-exports void

Control.Monad.IO.Class re-exports MonadIO.

Control.Monad.Trans.Class re-exports MonadTrans.

Control.Monad.Morph re-exports MFunctor.

Data.Foldable re-exports Foldable (the class name only).

module Control.Monad

module Control.Monad.IO.Class

module Control.Monad.Trans.Class

module Control.Monad.Morph

class Foldable t

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

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 []

Methods

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

Methods

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

Methods

fold :: Monoid m => V1 m -> 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

Methods

fold :: Monoid m => U1 m -> 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 Par1

Methods

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

Methods

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

Methods

fold :: Monoid m => Min m -> 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

Methods

fold :: Monoid m => Max m -> 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

Methods

fold :: Monoid m => First m -> 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

Methods

fold :: Monoid m => Last m -> 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

Methods

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

Methods

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

Methods

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

Methods

fold :: Monoid m => Dual m -> 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

Methods

fold :: Monoid m => Sum m -> 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

Methods

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

Methods

fold :: Monoid m => First m -> 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

Methods

fold :: Monoid m => Last m -> 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 (Either a)

Methods

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

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

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

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

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

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

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

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

toList :: Either a a -> [a]

null :: Either a a -> Bool

length :: Either a a -> Int

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

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

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

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

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

Foldable f => Foldable (Rec1 f)

Methods

fold :: Monoid m => Rec1 f m -> 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 (URec Char)

Methods

fold :: Monoid m => URec Char m -> m

foldMap :: Monoid m => (a -> m) -> URec Char a -> m

foldr :: (a -> b -> b) -> b -> URec Char a -> b

foldr' :: (a -> b -> b) -> b -> URec Char a -> b

foldl :: (b -> a -> b) -> b -> URec Char a -> b

foldl' :: (b -> a -> b) -> b -> URec Char a -> b

foldr1 :: (a -> a -> a) -> URec Char a -> a

foldl1 :: (a -> a -> a) -> URec Char a -> a

toList :: URec Char a -> [a]

null :: URec Char a -> Bool

length :: URec Char a -> Int

elem :: Eq a => a -> URec Char a -> Bool

maximum :: Ord a => URec Char a -> a

minimum :: Ord a => URec Char a -> a

sum :: Num a => URec Char a -> a

product :: Num a => URec Char a -> a

Foldable (URec Double)

Methods

fold :: Monoid m => URec Double m -> m

foldMap :: Monoid m => (a -> m) -> URec Double a -> m

foldr :: (a -> b -> b) -> b -> URec Double a -> b

foldr' :: (a -> b -> b) -> b -> URec Double a -> b

foldl :: (b -> a -> b) -> b -> URec Double a -> b

foldl' :: (b -> a -> b) -> b -> URec Double a -> b

foldr1 :: (a -> a -> a) -> URec Double a -> a

foldl1 :: (a -> a -> a) -> URec Double a -> a

toList :: URec Double a -> [a]

null :: URec Double a -> Bool

length :: URec Double a -> Int

elem :: Eq a => a -> URec Double a -> Bool

maximum :: Ord a => URec Double a -> a

minimum :: Ord a => URec Double a -> a

sum :: Num a => URec Double a -> a

product :: Num a => URec Double a -> a

Foldable (URec Float)

Methods

fold :: Monoid m => URec Float m -> m

foldMap :: Monoid m => (a -> m) -> URec Float a -> m

foldr :: (a -> b -> b) -> b -> URec Float a -> b

foldr' :: (a -> b -> b) -> b -> URec Float a -> b

foldl :: (b -> a -> b) -> b -> URec Float a -> b

foldl' :: (b -> a -> b) -> b -> URec Float a -> b

foldr1 :: (a -> a -> a) -> URec Float a -> a

foldl1 :: (a -> a -> a) -> URec Float a -> a

toList :: URec Float a -> [a]

null :: URec Float a -> Bool

length :: URec Float a -> Int

elem :: Eq a => a -> URec Float a -> Bool

maximum :: Ord a => URec Float a -> a

minimum :: Ord a => URec Float a -> a

sum :: Num a => URec Float a -> a

product :: Num a => URec Float a -> a

Foldable (URec Int)

Methods

fold :: Monoid m => URec Int m -> m

foldMap :: Monoid m => (a -> m) -> URec Int a -> m

foldr :: (a -> b -> b) -> b -> URec Int a -> b

foldr' :: (a -> b -> b) -> b -> URec Int a -> b

foldl :: (b -> a -> b) -> b -> URec Int a -> b

foldl' :: (b -> a -> b) -> b -> URec Int a -> b

foldr1 :: (a -> a -> a) -> URec Int a -> a

foldl1 :: (a -> a -> a) -> URec Int a -> a

toList :: URec Int a -> [a]

null :: URec Int a -> Bool

length :: URec Int a -> Int

elem :: Eq a => a -> URec Int a -> Bool

maximum :: Ord a => URec Int a -> a

minimum :: Ord a => URec Int a -> a

sum :: Num a => URec Int a -> a

product :: Num a => URec Int a -> a

Foldable (URec Word)

Methods

fold :: Monoid m => URec Word m -> m

foldMap :: Monoid m => (a -> m) -> URec Word a -> m

foldr :: (a -> b -> b) -> b -> URec Word a -> b

foldr' :: (a -> b -> b) -> b -> URec Word a -> b

foldl :: (b -> a -> b) -> b -> URec Word a -> b

foldl' :: (b -> a -> b) -> b -> URec Word a -> b

foldr1 :: (a -> a -> a) -> URec Word a -> a

foldl1 :: (a -> a -> a) -> URec Word a -> a

toList :: URec Word a -> [a]

null :: URec Word a -> Bool

length :: URec Word a -> Int

elem :: Eq a => a -> URec Word a -> Bool

maximum :: Ord a => URec Word a -> a

minimum :: Ord a => URec Word a -> a

sum :: Num a => URec Word a -> a

product :: Num a => URec Word a -> a

Foldable (URec (Ptr ()))

Methods

fold :: Monoid m => URec (Ptr ()) m -> m

foldMap :: Monoid m => (a -> m) -> URec (Ptr ()) a -> m

foldr :: (a -> b -> b) -> b -> URec (Ptr ()) a -> b

foldr' :: (a -> b -> b) -> b -> URec (Ptr ()) a -> b

foldl :: (b -> a -> b) -> b -> URec (Ptr ()) a -> b

foldl' :: (b -> a -> b) -> b -> URec (Ptr ()) a -> b

foldr1 :: (a -> a -> a) -> URec (Ptr ()) a -> a

foldl1 :: (a -> a -> a) -> URec (Ptr ()) a -> a

toList :: URec (Ptr ()) a -> [a]

null :: URec (Ptr ()) a -> Bool

length :: URec (Ptr ()) a -> Int

elem :: Eq a => a -> URec (Ptr ()) a -> Bool

maximum :: Ord a => URec (Ptr ()) a -> a

minimum :: Ord a => URec (Ptr ()) a -> a

sum :: Num a => URec (Ptr ()) a -> a

product :: Num a => URec (Ptr ()) a -> a

Foldable ((,) a)

Methods

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

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

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

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

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

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

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

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

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

null :: (a, a) -> Bool

length :: (a, a) -> Int

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

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

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

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

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

Foldable (Array i)

Methods

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

Methods

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

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

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

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

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

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

foldr1 :: (a -> a -> a) -> Arg a a -> a

foldl1 :: (a -> a -> a) -> Arg a a -> a

toList :: Arg a a -> [a]

null :: Arg a a -> Bool

length :: Arg a a -> Int

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

maximum :: Ord a => Arg a a -> a

minimum :: Ord a => Arg a a -> a

sum :: Num a => Arg a a -> a

product :: Num a => Arg a a -> a

Foldable (Proxy *)

Methods

fold :: Monoid m => Proxy * m -> 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 f => Foldable (ListT f)

Methods

fold :: Monoid m => ListT f m -> 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)

Methods

fold :: Monoid m => MaybeT f m -> 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 m => Foldable (ListT m)

Methods

fold :: Monoid m => ListT m m -> m

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

foldr :: (a -> b -> b) -> b -> ListT m a -> b

foldr' :: (a -> b -> b) -> b -> ListT m a -> b

foldl :: (b -> a -> b) -> b -> ListT m a -> b

foldl' :: (b -> a -> b) -> b -> ListT m a -> b

foldr1 :: (a -> a -> a) -> ListT m a -> a

foldl1 :: (a -> a -> a) -> ListT m a -> a

toList :: ListT m a -> [a]

null :: ListT m a -> Bool

length :: ListT m a -> Int

elem :: Eq a => a -> ListT m a -> Bool

maximum :: Ord a => ListT m a -> a

minimum :: Ord a => ListT m a -> a

sum :: Num a => ListT m a -> a

product :: Num a => ListT m a -> a

Foldable (K1 i c)

Methods

fold :: Monoid m => K1 i c m -> 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)

Methods

fold :: Monoid m => (f :+: g) m -> 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)

Methods

fold :: Monoid m => (f :*: g) m -> 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)

Methods

fold :: Monoid m => (f :.: g) m -> 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 (Const * m)

Methods

fold :: Monoid m => Const * m m -> m

foldMap :: Monoid m => (a -> m) -> Const * m a -> m

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 (ErrorT e f)

Methods

fold :: Monoid m => ErrorT e f m -> 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)

Methods

fold :: Monoid m => ExceptT e f m -> 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)

Methods

fold :: Monoid m => WriterT w f m -> 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)

Methods

fold :: Monoid m => WriterT w f m -> 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 (IdentityT * f)

Methods

fold :: Monoid m => IdentityT * f m -> 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 (M1 i c f)

Methods

fold :: Monoid m => M1 i c f m -> 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 (Product * f g)

Methods

fold :: Monoid m => Product * f g m -> 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 (Compose * * f g)

Methods

fold :: Monoid m => Compose * * f g m -> 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