Streaming

An iterable streaming monad transformer

The Stream data type can be used to represent any effectful succession of steps arising in some monad. The form of the steps is specified by the first ("functor") parameter in Stream f m r. The monad of the underlying effects is expressed by the second parameter.

This module exports combinators that pertain to that general case. Some of these are quite abstract and pervade any use of the library, e.g.

  maps ::    (forall x . f x -> g x)     -> Stream f m r -> Stream g m r
  mapped ::  (forall x . f x -> m (g x)) -> Stream f m r -> Stream g m r
  hoist ::   (forall x . m x -> n x)     -> Stream f m r -> Stream f n r -- from the MFunctor instance
  concats :: Stream (Stream f m) m r -> Stream f m r   

(assuming here and thoughout that m or n satisfies a Monad constraint, and f or g a Functor constraint.)

Others are surprisingly determinate in content:

  chunksOf     :: Int -> Stream f m r -> Stream (Stream f m) m r
  splitsAt     :: Int -> Stream f m r -> Stream f m (Stream f m r)
  zipsWith     :: (forall x y. f x -> g y -> h (x, y))

• > Stream f m r -> Stream g m r -> Stream h m r > zipsWith' :: (forall x y p. (x -> y -> p) -> f x -> g y -> h p)
• > Stream f m r -> Stream g m r -> Stream h m r > intercalates :: Stream f m () -> Stream (Stream f m) m r -> Stream f m r > unzips :: Stream (Compose f g) m r -> Stream f (Stream g m) r > separate :: Stream (Sum f g) m r -> Stream f (Stream g) m r -- cp. partitionEithers > unseparate :: Stream f (Stream g) m r -> Stream (Sum f g) m r > groups :: Stream (Sum f g) m r -> Stream (Sum (Stream f m) (Stream g m)) m r

One way to see that any streaming library needs some such general type is that it is required to represent the segmentation of a stream, and to express the equivalents of Prelude/Data.List combinators that involve 'lists of lists' and the like. See for example this post on the correct expression of a streaming 'lines' function.

The module Streaming.Prelude exports combinators relating to

Stream (Of a) m r

where Of a r = !a :> r is a left-strict pair.

This expresses the concept of a Producer or Source or Generator and easily inter-operates with types with such names in e.g. conduit, iostreams and pipes.

data Stream f m r

Instances

(Functor f, MonadError e m) => MonadError e (Stream f m)

Methods

throwError :: e -> Stream f m a

catchError :: Stream f m a -> (e -> Stream f m a) -> Stream f m a

(Functor f, MonadReader r m) => MonadReader r (Stream f m)

Methods

ask :: Stream f m r

local :: (r -> r) -> Stream f m a -> Stream f m a

reader :: (r -> a) -> Stream f m a

(Functor f, MonadState s m) => MonadState s (Stream f m)

Methods

get :: Stream f m s

put :: s -> Stream f m ()

state :: (s -> (a, s)) -> Stream f m a

Functor f => MMonad (Stream f)

Methods

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

Functor f => MonadTrans (Stream f)

Methods

lift :: Monad m => m a -> Stream f m a

Functor f => MFunctor * (Stream f)

Methods

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

(Functor f, Monad m) => Monad (Stream f m)

Methods

(>>=) :: Stream f m a -> (a -> Stream f m b) -> Stream f m b

(>>) :: Stream f m a -> Stream f m b -> Stream f m b

return :: a -> Stream f m a

fail :: String -> Stream f m a

(Functor f, Monad m) => Functor (Stream f m)

Methods

fmap :: (a -> b) -> Stream f m a -> Stream f m b

(<$) :: a -> Stream f m b -> Stream f m a

(Functor f, Monad m) => Applicative (Stream f m)

Methods

pure :: a -> Stream f m a

(<*>) :: Stream f m (a -> b) -> Stream f m a -> Stream f m b

(*>) :: Stream f m a -> Stream f m b -> Stream f m b

(<*) :: Stream f m a -> Stream f m b -> Stream f m a

(Monad m, Functor f, Eq1 m, Eq1 f) => Eq1 (Stream f m)

Methods

liftEq :: (a -> b -> Bool) -> Stream f m a -> Stream f m b -> Bool

(Monad m, Functor f, Ord1 m, Ord1 f) => Ord1 (Stream f m)

Methods

liftCompare :: (a -> b -> Ordering) -> Stream f m a -> Stream f m b -> Ordering

(Monad m, Functor f, Show (m ShowSWrapper), Show (f ShowSWrapper)) => Show1 (Stream f m)

Methods

liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> Stream f m a -> ShowS

liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [Stream f m a] -> ShowS

(MonadIO m, Functor f) => MonadIO (Stream f m)

Methods

liftIO :: IO a -> Stream f m a

(Applicative f, Monad m) => Alternative (Stream f m)

The Alternative instance glues streams together stepwise.

empty = never
(<|>) = zipsWith (liftA2 (,))

See also never, untilJust and delays

Methods

empty :: Stream f m a

(<|>) :: Stream f m a -> Stream f m a -> Stream f m a

some :: Stream f m a -> Stream f m [a]

many :: Stream f m a -> Stream f m [a]

(Applicative f, Monad m) => MonadPlus (Stream f m)

Methods

mzero :: Stream f m a

mplus :: Stream f m a -> Stream f m a -> Stream f m a

(Monad m, Eq (m (Either r (f (Stream f m r))))) => Eq (Stream f m r)

Methods

(==) :: Stream f m r -> Stream f m r -> Bool

(/=) :: Stream f m r -> Stream f m r -> Bool

(Monad m, Ord (m (Either r (f (Stream f m r))))) => Ord (Stream f m r)

Methods

compare :: Stream f m r -> Stream f m r -> Ordering

(<) :: Stream f m r -> Stream f m r -> Bool

(<=) :: Stream f m r -> Stream f m r -> Bool

(>) :: Stream f m r -> Stream f m r -> Bool

(>=) :: Stream f m r -> Stream f m r -> Bool

max :: Stream f m r -> Stream f m r -> Stream f m r

min :: Stream f m r -> Stream f m r -> Stream f m r

(Monad m, Show r, Show (m ShowSWrapper), Show (f (Stream f m r))) => Show (Stream f m r)

Methods

showsPrec :: Int -> Stream f m r -> ShowS

show :: Stream f m r -> String

showList :: [Stream f m r] -> ShowS

(Functor f, Monad m, Monoid w) => Monoid (Stream f m w)

Methods

mempty :: Stream f m w

mappend :: Stream f m w -> Stream f m w -> Stream f m w

mconcat :: [Stream f m w] -> Stream f m w

Constructing a Stream on a given functor

yields :: (Monad m, Functor f) => f r -> Stream f m r

yields is like lift for items in the streamed functor. It makes a singleton or one-layer succession.

lift :: (Monad m, Functor f)    => m r -> Stream f m r
yields ::  (Monad m, Functor f) => f r -> Stream f m r

Viewed in another light, it is like a functor-general version of yield:

S.yield a = yields (a :> ())

effect :: (Monad m, Functor f) => m (Stream f m r) -> Stream f m r

Wrap an effect that returns a stream

effect = join . lift

wrap :: (Monad m, Functor f) => f (Stream f m r) -> Stream f m r

Wrap a new layer of a stream. So, e.g.

S.cons :: Monad m => a -> Stream (Of a) m r -> Stream (Of a) m r
S.cons a str = wrap (a :> str)

and, recursively:

S.each :: (Monad m, Foldable t) => t a -> Stream (Of a) m ()
S.each = foldr (\a b -> wrap (a :> b)) (return ())

The two operations

wrap :: (Monad m, Functor f )   => f (Stream f m r) -> Stream f m r
effect :: (Monad m, Functor f ) => m (Stream f m r) -> Stream f m r

are fundamental. We can define the parallel operations yields and lift in terms of them

yields :: (Monad m, Functor f )  => f r -> Stream f m r
yields = wrap . fmap return
lift ::  (Monad m, Functor f )   => m r -> Stream f m r
lift = effect . fmap return

replicates :: (Monad m, Functor f) => Int -> f () -> Stream f m ()

Repeat a functorial layer, command or instruction a fixed number of times.

replicates n = takes n . repeats

repeats :: (Monad m, Functor f) => f () -> Stream f m r

Repeat a functorial layer (a "command" or "instruction") forever.

repeatsM :: (Monad m, Functor f) => m (f ()) -> Stream f m r

Repeat an effect containing a functorial layer, command or instruction forever.

unfold :: (Monad m, Functor f) => (s -> m (Either r (f s))) -> s -> Stream f m r

Build a Stream by unfolding steps starting from a seed. See also the specialized unfoldr in the prelude.

unfold inspect = id -- modulo the quotient we work with
unfold Pipes.next :: Monad m => Producer a m r -> Stream ((,) a) m r
unfold (curry (:>) . Pipes.next) :: Monad m => Producer a m r -> Stream (Of a) m r

never :: (Monad m, Applicative f) => Stream f m r

never interleaves the pure applicative action with the return of the monad forever. It is the empty of the Alternative instance, thus

never <|> a = a
a <|> never = a

and so on. If w is a monoid then never :: Stream (Of w) m r is the infinite sequence of mempty, and str1 <|> str2 appends the elements monoidally until one of streams ends. Thus we have, e.g.

>>> S.stdoutLn $ S.take 2 $ S.stdinLn <|> S.repeat " " <|> S.stdinLn  <|> S.repeat " " <|> S.stdinLn
1<Enter>
2<Enter>
3<Enter>
1 2 3
4<Enter>
5<Enter>
6<Enter>
4 5 6

This is equivalent to

>>> S.stdoutLn $ S.take 2 $ foldr (<|>) never [S.stdinLn, S.repeat " ", S.stdinLn, S.repeat " ", S.stdinLn ]

Where f is a monad, (<|>) sequences the conjoined streams stepwise. See the definition of paste here, where the separate steps are bytestreams corresponding to the lines of a file.

Given, say,

data Branch r = Branch r r deriving Functor  -- add obvious applicative instance

then never :: Stream Branch Identity r is the pure infinite binary tree with (inaccessible) rs in its leaves. Given two binary trees, tree1 <|> tree2 intersects them, preserving the leaves that came first, so tree1 <|> never = tree1

Stream Identity m r is an action in m that is indefinitely delayed. Such an action can be constructed with e.g. untilJust.

untilJust :: (Monad m, Applicative f) => m (Maybe r) -> Stream f m r

Given two such items, <|> instance races them. It is thus the iterative monad transformer specially defined in Control.Monad.Trans.Iter

So, for example, we might write

>>> let justFour str = if length str == 4 then Just str else Nothing
>>> let four = untilJust (fmap justFour getLine)
>>> run four
one<Enter>
two<Enter>
three<Enter>
four<Enter>
"four"

The Alternative instance in Control.Monad.Trans.Free is avowedly wrong, though no explanation is given for this.

untilJust :: (Monad m, Applicative f) => m (Maybe r) -> Stream f m r

Repeat a

streamBuild :: (forall b. (r -> b) -> (m b -> b) -> (f b -> b) -> b) -> Stream f m r

Reflect a church-encoded stream; cp. GHC.Exts.build

streamFold return_ effect_ step_ (streamBuild psi)  = psi return_ effect_ step_

delays :: (MonadIO m, Applicative f) => Double -> Stream f m r

Transforming streams

maps :: (Monad m, Functor f) => (forall x. f x -> g x) -> Stream f m r -> Stream g m r

Map layers of one functor to another with a transformation. Compare hoist, which has a similar effect on the monadic parameter.

maps id = id
maps f . maps g = maps (f . g)

mapsPost :: forall m f g r. (Monad m, Functor g) => (forall x. f x -> g x) -> Stream f m r -> Stream g m r

Map layers of one functor to another with a transformation. Compare hoist, which has a similar effect on the monadic parameter.

mapsPost id = id
mapsPost f . mapsPost g = mapsPost (f . g)
mapsPost f = mapsPost f

mapsPost is essentially the same as maps, but it imposes a Functor constraint on its target functor rather than its source functor. It should be preferred if fmap is cheaper for the target functor than for the source functor.

mapsM :: (Monad m, Functor f) => (forall x. f x -> m (g x)) -> Stream f m r -> Stream g m r

Map layers of one functor to another with a transformation involving the base monad. maps is more fundamental than mapsM, which is best understood as a convenience for effecting this frequent composition:

mapsM phi = decompose . maps (Compose . phi)

The streaming prelude exports the same function under the better name mapped, which overlaps with the lens libraries.

mapsMPost :: forall m f g r. (Monad m, Functor g) => (forall x. f x -> m (g x)) -> Stream f m r -> Stream g m r

Map layers of one functor to another with a transformation involving the base monad. mapsMPost is essentially the same as mapsM, but it imposes a Functor constraint on its target functor rather than its source functor. It should be preferred if fmap is cheaper for the target functor than for the source functor.

mapsPost is more fundamental than mapsMPost, which is best understood as a convenience for effecting this frequent composition:

mapsMPost phi = decompose . mapsPost (Compose . phi)

The streaming prelude exports the same function under the better name mappedPost, which overlaps with the lens libraries.

mapped :: (Monad m, Functor f) => (forall x. f x -> m (g x)) -> Stream f m r -> Stream g m r

Map layers of one functor to another with a transformation involving the base monad. This could be trivial, e.g.

let noteBeginning text x = putStrLn text >> return text

this puts the is completely functor-general

maps and mapped obey these rules:

maps id              = id
mapped return        = id
maps f . maps g      = maps (f . g)
mapped f . mapped g  = mapped (f <=< g)
maps f . mapped g    = mapped (fmap f . g)
mapped f . maps g    = mapped (f <=< fmap g)

maps is more fundamental than mapped, which is best understood as a convenience for effecting this frequent composition:

mapped phi = decompose . maps (Compose . phi)

mappedPost :: (Monad m, Functor g) => (forall x. f x -> m (g x)) -> Stream f m r -> Stream g m r

A version of mapped that imposes a Functor constraint on the target functor rather than the source functor. This version should be preferred if fmap on the target functor is cheaper.

hoistUnexposed :: (Monad m, Functor f) => (forall a. m a -> n a) -> Stream f m r -> Stream f n r

A less-efficient version of hoist that works properly even when its argument is not a monad morphism.

hoistUnexposed = hoist . unexposed

distribute :: (Monad m, Functor f, MonadTrans t, MFunctor t, Monad (t (Stream f m))) => Stream f (t m) r -> t (Stream f m) r

Make it possible to 'run' the underlying transformed monad.

groups :: (Monad m, Functor f, Functor g) => Stream (Sum f g) m r -> Stream (Sum (Stream f m) (Stream g m)) m r

Group layers in an alternating stream into adjoining sub-streams of one type or another.

Inspecting a stream

inspect :: Monad m => Stream f m r -> m (Either r (f (Stream f m r)))

Inspect the first stage of a freely layered sequence. Compare Pipes.next and the replica Streaming.Prelude.next. This is the uncons for the general unfold.

unfold inspect = id
Streaming.Prelude.unfoldr StreamingPrelude.next = id

Splitting and joining Streams

splitsAt :: (Monad m, Functor f) => Int -> Stream f m r -> Stream f m (Stream f m r)

Split a succession of layers after some number, returning a streaming or effectful pair.

>>> rest <- S.print $ S.splitAt 1 $ each [1..3]
1
>>> S.print rest
2
3

splitAt 0 = return
splitAt n >=> splitAt m = splitAt (m+n)

Thus, e.g.

>>> rest <- S.print $ splitsAt 2 >=> splitsAt 2 $ each [1..5]
1
2
3
4
>>> S.print rest
5

takes :: (Monad m, Functor f) => Int -> Stream f m r -> Stream f m ()

chunksOf :: (Monad m, Functor f) => Int -> Stream f m r -> Stream (Stream f m) m r

Break a stream into substreams each with n functorial layers.

>>> S.print $ mapped S.sum $ chunksOf 2 $ each [1,1,1,1,1]
2
2
1

concats :: (Monad m, Functor f) => Stream (Stream f m) m r -> Stream f m r

Dissolves the segmentation into layers of Stream f m layers.

intercalates :: (Monad m, Monad (t m), MonadTrans t) => t m x -> Stream (t m) m r -> t m r

Interpolate a layer at each segment. This specializes to e.g.

intercalates :: (Monad m, Functor f) => Stream f m () -> Stream (Stream f m) m r -> Stream f m r

cutoff :: (Monad m, Functor f) => Int -> Stream f m r -> Stream f m (Maybe r)

Zipping, unzipping, separating and unseparating streams

zipsWith :: forall f g h m r. (Monad m, Functor h) => (forall x y. f x -> g y -> h (x, y)) -> Stream f m r -> Stream g m r -> Stream h m r

Zip two streams together. The zipsWith' function should generally be preferred for efficiency.

zipsWith' :: forall f g h m r. Monad m => (forall x y p. (x -> y -> p) -> f x -> g y -> h p) -> Stream f m r -> Stream g m r -> Stream h m r

Zip two streams together.

zips :: (Monad m, Functor f, Functor g) => Stream f m r -> Stream g m r -> Stream (Compose f g) m r

unzips :: (Monad m, Functor f, Functor g) => Stream (Compose f g) m r -> Stream f (Stream g m) r

interleaves :: (Monad m, Applicative h) => Stream h m r -> Stream h m r -> Stream h m r

Interleave functor layers, with the effects of the first preceding the effects of the second. When the first stream runs out, any remaining effects in the second are ignored.

interleaves = zipsWith (liftA2 (,))

>>> let paste = \a b -> interleaves (Q.lines a) (maps (Q.cons' '\t') (Q.lines b))
>>> Q.stdout $ Q.unlines $ paste "hello\nworld\n" "goodbye\nworld\n"
hello	goodbye
world	world

separate :: (Monad m, Functor f, Functor g) => Stream (Sum f g) m r -> Stream f (Stream g m) r

Given a stream on a sum of functors, make it a stream on the left functor, with the streaming on the other functor as the governing monad. This is useful for acting on one or the other functor with a fold, leaving the other material for another treatment. It generalizes partitionEithers, but actually streams properly.

>>> let odd_even = S.maps (S.distinguish even) $ S.each [1..10::Int]
>>> :t separate odd_even
separate odd_even
  :: Monad m => Stream (Of Int) (Stream (Of Int) m) ()

Now, for example, it is convenient to fold on the left and right values separately:

>>> S.toList $ S.toList $ separate odd_even
[2,4,6,8,10] :> ([1,3,5,7,9] :> ())

Or we can write them to separate files or whatever:

>>> runResourceT $ S.writeFile "even.txt" . S.show $ S.writeFile "odd.txt" . S.show $ S.separate odd_even
>>> :! cat even.txt
2
4
6
8
10
>>> :! cat odd.txt
1
3
5
7
9

Of course, in the special case of Stream (Of a) m r, we can achieve the above effects more simply by using copy

>>> S.toList . S.filter even $ S.toList . S.filter odd $ S.copy $ each [1..10::Int]
[2,4,6,8,10] :> ([1,3,5,7,9] :> ())

But separate and unseparate are functor-general.

unseparate :: (Monad m, Functor f, Functor g) => Stream f (Stream g m) r -> Stream (Sum f g) m r

decompose :: (Monad m, Functor f) => Stream (Compose m f) m r -> Stream f m r

Rearrange a succession of layers of the form Compose m (f x).

we could as well define decompose by mapsM:

decompose = mapped getCompose

but mapped is best understood as:

mapped phi = decompose . maps (Compose . phi)

since maps and hoist are the really fundamental operations that preserve the shape of the stream:

maps  :: (Monad m, Functor f) => (forall x. f x -> g x) -> Stream f m r -> Stream g m r
hoist :: (Monad m, Functor f) => (forall a. m a -> n a) -> Stream f m r -> Stream f n r

expand :: (Monad m, Functor f) => (forall a b. (g a -> b) -> f a -> h b) -> Stream f m r -> Stream g (Stream h m) r

If Of had a Comonad instance, then we'd have

copy = expand extend

See expandPost for a version that requires a Functor g instance instead.

expandPost :: (Monad m, Functor g) => (forall a b. (g a -> b) -> f a -> h b) -> Stream f m r -> Stream g (Stream h m) r

If Of had a Comonad instance, then we'd have

copy = expandPost extend

See expand for a version that requires a Functor f instance instead.

Eliminating a Stream

mapsM_ :: (Functor f, Monad m) => (forall x. f x -> m x) -> Stream f m r -> m r

Map each layer to an effect, and run them all.

run :: Monad m => Stream m m r -> m r

Run the effects in a stream that merely layers effects.

streamFold :: (Functor f, Monad m) => (r -> b) -> (m b -> b) -> (f b -> b) -> Stream f m r -> b

streamFold reorders the arguments of destroy to be more akin to foldr It is more convenient to query in ghci to figure out what kind of 'algebra' you need to write.

>>> :t streamFold return join
(Monad m, Functor f) =>
     (f (m a) -> m a) -> Stream f m a -> m a        -- iterT

>>> :t streamFold return (join . lift)
(Monad m, Monad (t m), Functor f, MonadTrans t) =>
     (f (t m a) -> t m a) -> Stream f m a -> t m a  -- iterTM

>>> :t streamFold return effect
(Monad m, Functor f, Functor g) =>
     (f (Stream g m r) -> Stream g m r) -> Stream f m r -> Stream g m r

>>> :t \f -> streamFold return effect (wrap . f)
(Monad m, Functor f, Functor g) =>
     (f (Stream g m a) -> g (Stream g m a))
     -> Stream f m a -> Stream g m a                 -- maps

>>> :t \f -> streamFold return effect (effect . fmap wrap . f)
(Monad m, Functor f, Functor g) =>
     (f (Stream g m a) -> m (g (Stream g m a)))
     -> Stream f m a -> Stream g m a                 -- mapped

    streamFold done eff construct
       = eff . iterT (return . construct . fmap eff) . fmap done

iterTM :: (Functor f, Monad m, MonadTrans t, Monad (t m)) => (f (t m a) -> t m a) -> Stream f m a -> t m a

Specialized fold following the usage of Control.Monad.Trans.Free

iterTM alg = streamFold return (join . lift)
iterTM alg = iterT alg . hoist lift

iterT :: (Functor f, Monad m) => (f (m a) -> m a) -> Stream f m a -> m a

Specialized fold following the usage of Control.Monad.Trans.Free

iterT alg = streamFold return join alg
iterT alg = runIdentityT . iterTM (IdentityT . alg . fmap runIdentityT)

destroy :: (Functor f, Monad m) => Stream f m r -> (f b -> b) -> (m b -> b) -> (r -> b) -> b

Map a stream to its church encoding; compare Data.List.foldr. destroyExposed may be more efficient in some cases when applicable, but it is less safe.

   destroy s construct eff done
     = eff . iterT (return . construct . fmap eff) . fmap done $ s
   

Base functor for streams of individual items

data Of a b

A left-strict pair; the base functor for streams of individual elements.

Constructors

!a :> b infixr 5

Instances

Eq2 Of

Methods

liftEq2 :: (a -> b -> Bool) -> (c -> d -> Bool) -> Of a c -> Of b d -> Bool

Ord2 Of

Methods

liftCompare2 :: (a -> b -> Ordering) -> (c -> d -> Ordering) -> Of a c -> Of b d -> Ordering

Show2 Of

Methods

liftShowsPrec2 :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> (Int -> b -> ShowS) -> ([b] -> ShowS) -> Int -> Of a b -> ShowS

liftShowList2 :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> (Int -> b -> ShowS) -> ([b] -> ShowS) -> [Of a b] -> ShowS

Bifunctor Of

Methods

bimap :: (a -> b) -> (c -> d) -> Of a c -> Of b d

first :: (a -> b) -> Of a c -> Of b c

second :: (b -> c) -> Of a b -> Of a c

Monoid a => Monad (Of a)

Methods

(>>=) :: Of a a -> (a -> Of a b) -> Of a b

(>>) :: Of a a -> Of a b -> Of a b

return :: a -> Of a a

fail :: String -> Of a a

Functor (Of a)

Methods

fmap :: (a -> b) -> Of a a -> Of a b

(<$) :: a -> Of a b -> Of a a

Monoid a => Applicative (Of a)

Methods

pure :: a -> Of a a

(<*>) :: Of a (a -> b) -> Of a a -> Of a b

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

(<*) :: Of a a -> Of a b -> Of a a

Foldable (Of a)

Methods

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

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

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

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

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

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

foldr1 :: (a -> a -> a) -> Of a a -> a

foldl1 :: (a -> a -> a) -> Of a a -> a

toList :: Of a a -> [a]

null :: Of a a -> Bool

length :: Of a a -> Int

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

maximum :: Ord a => Of a a -> a

minimum :: Ord a => Of a a -> a

sum :: Num a => Of a a -> a

product :: Num a => Of a a -> a

Traversable (Of a)

Methods

traverse :: Applicative f => (a -> f b) -> Of a a -> f (Of a b)

sequenceA :: Applicative f => Of a (f a) -> f (Of a a)

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

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

Generic1 (Of a)

Associated Types

type Rep1 (Of a :: * -> *) :: * -> *

Methods

from1 :: Of a a -> Rep1 (Of a) a

to1 :: Rep1 (Of a) a -> Of a a

Eq a => Eq1 (Of a)

Methods

liftEq :: (a -> b -> Bool) -> Of a a -> Of a b -> Bool

Ord a => Ord1 (Of a)

Methods

liftCompare :: (a -> b -> Ordering) -> Of a a -> Of a b -> Ordering

Show a => Show1 (Of a)

Methods

liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> Of a a -> ShowS

liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [Of a a] -> ShowS

(Eq b, Eq a) => Eq (Of a b)

Methods

(==) :: Of a b -> Of a b -> Bool

(/=) :: Of a b -> Of a b -> Bool

(Data b, Data a) => Data (Of a b)

Methods

gfoldl :: (forall d c. Data d => c (d -> c) -> d -> c c) -> (forall g. g -> c g) -> Of a b -> c (Of a b)

gunfold :: (forall c r. Data c => c (c -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Of a b)

toConstr :: Of a b -> Constr

dataTypeOf :: Of a b -> DataType

dataCast1 :: Typeable (* -> *) t => (forall d. Data d => c (t d)) -> Maybe (c (Of a b))

dataCast2 :: Typeable (* -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Of a b))

gmapT :: (forall c. Data c => c -> c) -> Of a b -> Of a b

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Of a b -> r

gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Of a b -> r

gmapQ :: (forall d. Data d => d -> u) -> Of a b -> [u]

gmapQi :: Int -> (forall d. Data d => d -> u) -> Of a b -> u

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Of a b -> m (Of a b)

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Of a b -> m (Of a b)

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Of a b -> m (Of a b)

(Ord b, Ord a) => Ord (Of a b)

Methods

compare :: Of a b -> Of a b -> Ordering

(<) :: Of a b -> Of a b -> Bool

(<=) :: Of a b -> Of a b -> Bool

(>) :: Of a b -> Of a b -> Bool

(>=) :: Of a b -> Of a b -> Bool

max :: Of a b -> Of a b -> Of a b

min :: Of a b -> Of a b -> Of a b

(Read b, Read a) => Read (Of a b)

Methods

readsPrec :: Int -> ReadS (Of a b)

readList :: ReadS [Of a b]

readPrec :: ReadPrec (Of a b)

readListPrec :: ReadPrec [Of a b]

(Show b, Show a) => Show (Of a b)

Methods

showsPrec :: Int -> Of a b -> ShowS

show :: Of a b -> String

showList :: [Of a b] -> ShowS

Generic (Of a b)

Associated Types

type Rep (Of a b) :: * -> *

Methods

from :: Of a b -> Rep (Of a b) x

to :: Rep (Of a b) x -> Of a b

(Monoid a, Monoid b) => Monoid (Of a b)

Methods

mempty :: Of a b

mappend :: Of a b -> Of a b -> Of a b

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

type Rep1 (Of a)

type Rep1 (Of a) = D1 (MetaData "Of" "Data.Functor.Of" "streaming-0.2.0.0-L7KUsrkkM341tk5MlQaig8" False) (C1 (MetaCons ":>" (InfixI RightAssociative 5) False) ((:*:) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) (Rec0 a)) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) Par1)))

type Rep (Of a b)

type Rep (Of a b) = D1 (MetaData "Of" "Data.Functor.Of" "streaming-0.2.0.0-L7KUsrkkM341tk5MlQaig8" False) (C1 (MetaCons ":>" (InfixI RightAssociative 5) False) ((:*:) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) (Rec0 a)) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 b))))

lazily :: Of a b -> (a, b)

Note that lazily, strictly, fst', and mapOf are all so-called natural transformations on the primitive Of a functor If we write

 type f ~~> g = forall x . f x -> g x

then we can restate some types as follows:

 mapOf            :: (a -> b) -> Of a ~~> Of b   -- Bifunctor first
 lazily           ::             Of a ~~> (,) a
 Identity . fst'  ::             Of a ~~> Identity a

Manipulation of a Stream f m r by mapping often turns on recognizing natural transformations of f. Thus maps is far more general the the map of the Streaming.Prelude, which can be defined thus:

 S.map :: (a -> b) -> Stream (Of a) m r -> Stream (Of b) m r
 S.map f = maps (mapOf f)

i.e.

 S.map f = maps (\(a :> x) -> (f a :> x))

This rests on recognizing that mapOf is a natural transformation; note though that it results in such a transformation as well:

 S.map :: (a -> b) -> Stream (Of a) m ~> Stream (Of b) m

Thus we can maps it in turn.

strictly :: (a, b) -> Of a b

Convert a standard Haskell pair into a left-strict pair

re-exports

class MFunctor k t where

A functor in the category of monads, using hoist as the analog of fmap:

hoist (f . g) = hoist f . hoist g

hoist id = id

Minimal complete definition

hoist

Methods

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

Lift a monad morphism from m to n into a monad morphism from (t m) to (t n)

Instances

MFunctor * ListT

Methods

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

MFunctor * Lift

Methods

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

MFunctor * MaybeT

Methods

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

MFunctor * (ErrorT e)

Methods

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

MFunctor * (ExceptT e)

Methods

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

MFunctor * (StateT s)

Methods

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

MFunctor * (StateT s)

Methods

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

MFunctor * (WriterT w)

Methods

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

MFunctor * (WriterT w)

Methods

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

MFunctor * (Backwards *)

Methods

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

MFunctor * (IdentityT *)

Methods

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

Functor f => MFunctor * (Stream f)

Methods

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

MFunctor * (Product * f)

Methods

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

MFunctor * (ReaderT * r)

Methods

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

Functor f => MFunctor * (Compose * * f)

Methods

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

MFunctor * (RWST r w s)

Methods

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

MFunctor * (RWST r w s)

Methods

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

class (MFunctor * t, MonadTrans t) => MMonad t where

A monad in the category of monads, using lift from MonadTrans as the analog of return and embed as the analog of (=<<):

embed lift = id

embed f (lift m) = f m

embed g (embed f t) = embed (\m -> embed g (f m)) t

Minimal complete definition

embed

Methods

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

Embed a newly created MMonad layer within an existing layer

embed is analogous to (=<<)

Instances

MMonad ListT

Methods

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

MMonad MaybeT

Methods

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

Error e => MMonad (ErrorT e)

Methods

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

MMonad (ExceptT e)

Methods

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

Monoid w => MMonad (WriterT w)

Methods

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

Monoid w => MMonad (WriterT w)

Methods

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

MMonad (IdentityT *)

Methods

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

Functor f => MMonad (Stream f)

Methods

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

MMonad (ReaderT * r)

Methods

embed :: Monad n => (forall a. m a -> ReaderT * r n a) -> ReaderT * r m b -> ReaderT * r n b

class MonadTrans t where

The class of monad transformers. Instances should satisfy the following laws, which state that lift is a monad transformation:

• lift . return = return

• lift (m >>= f) = lift m >>= (lift . f)

Minimal complete definition

lift

Methods

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

Lift a computation from the argument monad to the constructed monad.

Instances

MonadTrans ListT

Methods

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

MonadTrans MaybeT

Methods

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

MonadTrans (ErrorT e)

Methods

lift :: Monad m => m a -> ErrorT e m a

MonadTrans (ExceptT e)

Methods

lift :: Monad m => m a -> ExceptT e m a

MonadTrans (StateT s)

Methods

lift :: Monad m => m a -> StateT s m a

MonadTrans (StateT s)

Methods

lift :: Monad m => m a -> StateT s m a

Monoid w => MonadTrans (WriterT w)

Methods

lift :: Monad m => m a -> WriterT w m a

Monoid w => MonadTrans (WriterT w)

Methods

lift :: Monad m => m a -> WriterT w m a

MonadTrans (IdentityT *)

Methods

lift :: Monad m => m a -> IdentityT * m a

Functor f => MonadTrans (Stream f)

Methods

lift :: Monad m => m a -> Stream f m a

MonadTrans (ContT * r)

Methods

lift :: Monad m => m a -> ContT * r m a

MonadTrans (ReaderT * r)

Methods

lift :: Monad m => m a -> ReaderT * r m a

Monoid w => MonadTrans (RWST r w s)

Methods

lift :: Monad m => m a -> RWST r w s m a

Monoid w => MonadTrans (RWST r w s)

Methods

lift :: Monad m => m a -> RWST r w s m a

class Monad m => MonadIO m where

Monads in which IO computations may be embedded. Any monad built by applying a sequence of monad transformers to the IO monad will be an instance of this class.

Instances should satisfy the following laws, which state that liftIO is a transformer of monads:

• liftIO . return = return

• liftIO (m >>= f) = liftIO m >>= (liftIO . f)

Minimal complete definition

liftIO

Methods

liftIO :: IO a -> m a

Lift a computation from the IO monad.

Instances

MonadIO IO

Methods

liftIO :: IO a -> IO a

MonadIO m => MonadIO (ListT m)

Methods

liftIO :: IO a -> ListT m a

MonadIO m => MonadIO (MaybeT m)

Methods

liftIO :: IO a -> MaybeT m a

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

Methods

liftIO :: IO a -> ErrorT e m a

MonadIO m => MonadIO (ExceptT e m)

Methods

liftIO :: IO a -> ExceptT e m a

MonadIO m => MonadIO (StateT s m)

Methods

liftIO :: IO a -> StateT s m a

MonadIO m => MonadIO (StateT s m)

Methods

liftIO :: IO a -> StateT s m a

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

Methods

liftIO :: IO a -> WriterT w m a

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

Methods

liftIO :: IO a -> WriterT w m a

MonadIO m => MonadIO (IdentityT * m)

Methods

liftIO :: IO a -> IdentityT * m a

(MonadIO m, Functor f) => MonadIO (Stream f m)

Methods

liftIO :: IO a -> Stream f m a

MonadIO m => MonadIO (ContT * r m)

Methods

liftIO :: IO a -> ContT * r m a

MonadIO m => MonadIO (ReaderT * r m)

Methods

liftIO :: IO a -> ReaderT * r m a

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

Methods

liftIO :: IO a -> RWST r w s m a

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

Methods

liftIO :: IO a -> RWST r w s m a

newtype Compose k k1 f g a :: forall k k1. (k1 -> *) -> (k -> k1) -> k -> * infixr 9

Right-to-left composition of functors. The composition of applicative functors is always applicative, but the composition of monads is not always a monad.

Constructors

Compose infixr 9

Fields

• getCompose :: f (g a)

Instances

Functor f => MFunctor * (Compose * * f)

Methods

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

(Functor f, Functor g) => Functor (Compose * * f g)

Methods

fmap :: (a -> b) -> Compose * * f g a -> Compose * * f g b

(<$) :: a -> Compose * * f g b -> Compose * * f g a

(Applicative f, Applicative g) => Applicative (Compose * * f g)

Methods

pure :: a -> Compose * * f g a

(<*>) :: Compose * * f g (a -> b) -> Compose * * f g a -> Compose * * f g b

(*>) :: Compose * * f g a -> Compose * * f g b -> Compose * * f g b

(<*) :: Compose * * f g a -> Compose * * f g b -> Compose * * f g 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

(Traversable f, Traversable g) => Traversable (Compose * * f g)

Methods

traverse :: Applicative f => (a -> f b) -> Compose * * f g a -> f (Compose * * f g b)

sequenceA :: Applicative f => Compose * * f g (f a) -> f (Compose * * f g a)

mapM :: Monad m => (a -> m b) -> Compose * * f g a -> m (Compose * * f g b)

sequence :: Monad m => Compose * * f g (m a) -> m (Compose * * f g a)

Functor f => Generic1 (Compose * * f g)

Associated Types

type Rep1 (Compose * * f g :: * -> *) :: * -> *

Methods

from1 :: Compose * * f g a -> Rep1 (Compose * * f g) a

to1 :: Rep1 (Compose * * f g) a -> Compose * * f g a

(Eq1 f, Eq1 g) => Eq1 (Compose * * f g)

Methods

liftEq :: (a -> b -> Bool) -> Compose * * f g a -> Compose * * f g b -> Bool

(Ord1 f, Ord1 g) => Ord1 (Compose * * f g)

Methods

liftCompare :: (a -> b -> Ordering) -> Compose * * f g a -> Compose * * f g b -> Ordering

(Read1 f, Read1 g) => Read1 (Compose * * f g)

Methods

liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (Compose * * f g a)

liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [Compose * * f g a]

(Show1 f, Show1 g) => Show1 (Compose * * f g)

Methods

liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> Compose * * f g a -> ShowS

liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [Compose * * f g a] -> ShowS

(Alternative f, Applicative g) => Alternative (Compose * * f g)

Methods

empty :: Compose * * f g a

(<|>) :: Compose * * f g a -> Compose * * f g a -> Compose * * f g a

some :: Compose * * f g a -> Compose * * f g [a]

many :: Compose * * f g a -> Compose * * f g [a]

(Eq1 f, Eq1 g, Eq a) => Eq (Compose * * f g a)

Methods

(==) :: Compose * * f g a -> Compose * * f g a -> Bool

(/=) :: Compose * * f g a -> Compose * * f g a -> Bool

(Data (f (g a)), Typeable * k, Typeable * k1, Typeable (k1 -> k) g, Typeable (k -> *) f, Typeable k1 a) => Data (Compose k1 k f g a)

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall b. b -> c b) -> Compose k1 k f g a -> c (Compose k1 k f g a)

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Compose k1 k f g a)

toConstr :: Compose k1 k f g a -> Constr

dataTypeOf :: Compose k1 k f g a -> DataType

dataCast1 :: Typeable (* -> *) t => (forall d. Data d => c (t d)) -> Maybe (c (Compose k1 k f g a))

dataCast2 :: Typeable (* -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Compose k1 k f g a))

gmapT :: (forall b. Data b => b -> b) -> Compose k1 k f g a -> Compose k1 k f g a

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Compose k1 k f g a -> r

gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Compose k1 k f g a -> r

gmapQ :: (forall d. Data d => d -> u) -> Compose k1 k f g a -> [u]

gmapQi :: Int -> (forall d. Data d => d -> u) -> Compose k1 k f g a -> u

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Compose k1 k f g a -> m (Compose k1 k f g a)

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Compose k1 k f g a -> m (Compose k1 k f g a)

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Compose k1 k f g a -> m (Compose k1 k f g a)

(Ord1 f, Ord1 g, Ord a) => Ord (Compose * * f g a)

Methods

compare :: Compose * * f g a -> Compose * * f g a -> Ordering

(<) :: Compose * * f g a -> Compose * * f g a -> Bool

(<=) :: Compose * * f g a -> Compose * * f g a -> Bool

(>) :: Compose * * f g a -> Compose * * f g a -> Bool

(>=) :: Compose * * f g a -> Compose * * f g a -> Bool

max :: Compose * * f g a -> Compose * * f g a -> Compose * * f g a

min :: Compose * * f g a -> Compose * * f g a -> Compose * * f g a

(Read1 f, Read1 g, Read a) => Read (Compose * * f g a)

Methods

readsPrec :: Int -> ReadS (Compose * * f g a)

readList :: ReadS [Compose * * f g a]

readPrec :: ReadPrec (Compose * * f g a)

readListPrec :: ReadPrec [Compose * * f g a]

(Show1 f, Show1 g, Show a) => Show (Compose * * f g a)

Methods

showsPrec :: Int -> Compose * * f g a -> ShowS

show :: Compose * * f g a -> String

showList :: [Compose * * f g a] -> ShowS

Generic (Compose k1 k f g a)

Associated Types

type Rep (Compose k1 k f g a) :: * -> *

Methods

from :: Compose k1 k f g a -> Rep (Compose k1 k f g a) x

to :: Rep (Compose k1 k f g a) x -> Compose k1 k f g a

type Rep1 (Compose * * f g)

type Rep1 (Compose * * f g) = D1 (MetaData "Compose" "Data.Functor.Compose" "base" True) (C1 (MetaCons "Compose" PrefixI True) (S1 (MetaSel (Just Symbol "getCompose") NoSourceUnpackedness NoSourceStrictness DecidedLazy) ((:.:) f (Rec1 g))))

type Rep (Compose k1 k f g a)

type Rep (Compose k1 k f g a) = D1 (MetaData "Compose" "Data.Functor.Compose" "base" True) (C1 (MetaCons "Compose" PrefixI True) (S1 (MetaSel (Just Symbol "getCompose") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 (f (g a)))))

data Sum k f g a :: forall k. (k -> *) -> (k -> *) -> k -> *

Lifted sum of functors.

Constructors

InL (f a)

InR (g a)

Instances

(Functor f, Functor g) => Functor (Sum * f g)

Methods

fmap :: (a -> b) -> Sum * f g a -> Sum * f g b

(<$) :: a -> Sum * f g b -> Sum * f g a

(Foldable f, Foldable g) => Foldable (Sum * f g)

Methods

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

(Traversable f, Traversable g) => Traversable (Sum * f g)

Methods

traverse :: Applicative f => (a -> f b) -> Sum * f g a -> f (Sum * f g b)

sequenceA :: Applicative f => Sum * f g (f a) -> f (Sum * f g a)

mapM :: Monad m => (a -> m b) -> Sum * f g a -> m (Sum * f g b)

sequence :: Monad m => Sum * f g (m a) -> m (Sum * f g a)

Generic1 (Sum * f g)

Associated Types

type Rep1 (Sum * f g :: * -> *) :: * -> *

Methods

from1 :: Sum * f g a -> Rep1 (Sum * f g) a

to1 :: Rep1 (Sum * f g) a -> Sum * f g a

(Eq1 f, Eq1 g) => Eq1 (Sum * f g)

Methods

liftEq :: (a -> b -> Bool) -> Sum * f g a -> Sum * f g b -> Bool

(Ord1 f, Ord1 g) => Ord1 (Sum * f g)

Methods

liftCompare :: (a -> b -> Ordering) -> Sum * f g a -> Sum * f g b -> Ordering

(Read1 f, Read1 g) => Read1 (Sum * f g)

Methods

liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (Sum * f g a)

liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [Sum * f g a]

(Show1 f, Show1 g) => Show1 (Sum * f g)

Methods

liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> Sum * f g a -> ShowS

liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [Sum * f g a] -> ShowS

(Eq1 f, Eq1 g, Eq a) => Eq (Sum * f g a)

Methods

(==) :: Sum * f g a -> Sum * f g a -> Bool

(/=) :: Sum * f g a -> Sum * f g a -> Bool

(Data (g a), Data (f a), Typeable * k, Typeable (k -> *) g, Typeable (k -> *) f, Typeable k a) => Data (Sum k f g a)

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall b. b -> c b) -> Sum k f g a -> c (Sum k f g a)

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Sum k f g a)

toConstr :: Sum k f g a -> Constr

dataTypeOf :: Sum k f g a -> DataType

dataCast1 :: Typeable (* -> *) t => (forall d. Data d => c (t d)) -> Maybe (c (Sum k f g a))

dataCast2 :: Typeable (* -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Sum k f g a))

gmapT :: (forall b. Data b => b -> b) -> Sum k f g a -> Sum k f g a

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Sum k f g a -> r

gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Sum k f g a -> r

gmapQ :: (forall d. Data d => d -> u) -> Sum k f g a -> [u]

gmapQi :: Int -> (forall d. Data d => d -> u) -> Sum k f g a -> u

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Sum k f g a -> m (Sum k f g a)

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Sum k f g a -> m (Sum k f g a)

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Sum k f g a -> m (Sum k f g a)

(Ord1 f, Ord1 g, Ord a) => Ord (Sum * f g a)

Methods

compare :: Sum * f g a -> Sum * f g a -> Ordering

(<) :: Sum * f g a -> Sum * f g a -> Bool

(<=) :: Sum * f g a -> Sum * f g a -> Bool

(>) :: Sum * f g a -> Sum * f g a -> Bool

(>=) :: Sum * f g a -> Sum * f g a -> Bool

max :: Sum * f g a -> Sum * f g a -> Sum * f g a

min :: Sum * f g a -> Sum * f g a -> Sum * f g a

(Read1 f, Read1 g, Read a) => Read (Sum * f g a)

Methods

readsPrec :: Int -> ReadS (Sum * f g a)

readList :: ReadS [Sum * f g a]

readPrec :: ReadPrec (Sum * f g a)

readListPrec :: ReadPrec [Sum * f g a]

(Show1 f, Show1 g, Show a) => Show (Sum * f g a)

Methods

showsPrec :: Int -> Sum * f g a -> ShowS

show :: Sum * f g a -> String

showList :: [Sum * f g a] -> ShowS

Generic (Sum k f g a)

Associated Types

type Rep (Sum k f g a) :: * -> *

Methods

from :: Sum k f g a -> Rep (Sum k f g a) x

to :: Rep (Sum k f g a) x -> Sum k f g a

type Rep1 (Sum * f g)

type Rep1 (Sum * f g) = D1 (MetaData "Sum" "Data.Functor.Sum" "base" False) ((:+:) (C1 (MetaCons "InL" PrefixI False) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec1 f))) (C1 (MetaCons "InR" PrefixI False) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec1 g))))

type Rep (Sum k f g a)

type Rep (Sum k f g a) = D1 (MetaData "Sum" "Data.Functor.Sum" "base" False) ((:+:) (C1 (MetaCons "InL" PrefixI False) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 (f a)))) (C1 (MetaCons "InR" PrefixI False) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 (g a)))))

newtype Identity a :: * -> *

Identity functor and monad. (a non-strict monad)

Since: 4.8.0.0

Constructors

Identity

Fields

• runIdentity :: a

Instances

Monad Identity

Methods

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

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

return :: a -> Identity a

fail :: String -> Identity a

Functor Identity

Methods

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

(<$) :: a -> Identity b -> Identity a

MonadFix Identity

Methods

mfix :: (a -> Identity a) -> Identity a

Applicative Identity

Methods

pure :: a -> Identity a

(<*>) :: Identity (a -> b) -> Identity a -> Identity b

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

(<*) :: Identity a -> Identity b -> Identity 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

Traversable Identity

Methods

traverse :: Applicative f => (a -> f b) -> Identity a -> f (Identity b)

sequenceA :: Applicative f => Identity (f a) -> f (Identity a)

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

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

Generic1 Identity

Associated Types

type Rep1 (Identity :: * -> *) :: * -> *

Methods

from1 :: Identity a -> Rep1 Identity a

to1 :: Rep1 Identity a -> Identity a

Eq1 Identity

Methods

liftEq :: (a -> b -> Bool) -> Identity a -> Identity b -> Bool

Ord1 Identity

Methods

liftCompare :: (a -> b -> Ordering) -> Identity a -> Identity b -> Ordering

Read1 Identity

Methods

liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (Identity a)

liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [Identity a]

Show1 Identity

Methods

liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> Identity a -> ShowS

liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [Identity a] -> ShowS

MonadZip Identity

Methods

mzip :: Identity a -> Identity b -> Identity (a, b)

mzipWith :: (a -> b -> c) -> Identity a -> Identity b -> Identity c

munzip :: Identity (a, b) -> (Identity a, Identity b)

Bounded a => Bounded (Identity a)

Methods

minBound :: Identity a

maxBound :: Identity a

Enum a => Enum (Identity a)

Methods

succ :: Identity a -> Identity a

pred :: Identity a -> Identity a

toEnum :: Int -> Identity a

fromEnum :: Identity a -> Int

enumFrom :: Identity a -> [Identity a]

enumFromThen :: Identity a -> Identity a -> [Identity a]

enumFromTo :: Identity a -> Identity a -> [Identity a]

enumFromThenTo :: Identity a -> Identity a -> Identity a -> [Identity a]

Eq a => Eq (Identity a)

Methods

(==) :: Identity a -> Identity a -> Bool

(/=) :: Identity a -> Identity a -> Bool

Floating a => Floating (Identity a)

Methods

pi :: Identity a

exp :: Identity a -> Identity a

log :: Identity a -> Identity a

sqrt :: Identity a -> Identity a

(**) :: Identity a -> Identity a -> Identity a

logBase :: Identity a -> Identity a -> Identity a

sin :: Identity a -> Identity a

cos :: Identity a -> Identity a

tan :: Identity a -> Identity a

asin :: Identity a -> Identity a

acos :: Identity a -> Identity a

atan :: Identity a -> Identity a

sinh :: Identity a -> Identity a

cosh :: Identity a -> Identity a

tanh :: Identity a -> Identity a

asinh :: Identity a -> Identity a

acosh :: Identity a -> Identity a

atanh :: Identity a -> Identity a

log1p :: Identity a -> Identity a

expm1 :: Identity a -> Identity a

log1pexp :: Identity a -> Identity a

log1mexp :: Identity a -> Identity a

Fractional a => Fractional (Identity a)

Methods

(/) :: Identity a -> Identity a -> Identity a

recip :: Identity a -> Identity a

fromRational :: Rational -> Identity a

Integral a => Integral (Identity a)

Methods

quot :: Identity a -> Identity a -> Identity a

rem :: Identity a -> Identity a -> Identity a

div :: Identity a -> Identity a -> Identity a

mod :: Identity a -> Identity a -> Identity a

quotRem :: Identity a -> Identity a -> (Identity a, Identity a)

divMod :: Identity a -> Identity a -> (Identity a, Identity a)

toInteger :: Identity a -> Integer

Data a => Data (Identity a)

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Identity a -> c (Identity a)

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Identity a)

toConstr :: Identity a -> Constr

dataTypeOf :: Identity a -> DataType

dataCast1 :: Typeable (* -> *) t => (forall d. Data d => c (t d)) -> Maybe (c (Identity a))

dataCast2 :: Typeable (* -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Identity a))

gmapT :: (forall b. Data b => b -> b) -> Identity a -> Identity a

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Identity a -> r

gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Identity a -> r

gmapQ :: (forall d. Data d => d -> u) -> Identity a -> [u]

gmapQi :: Int -> (forall d. Data d => d -> u) -> Identity a -> u

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Identity a -> m (Identity a)

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Identity a -> m (Identity a)

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Identity a -> m (Identity a)

Num a => Num (Identity a)

Methods

(+) :: Identity a -> Identity a -> Identity a

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

(*) :: Identity a -> Identity a -> Identity a

negate :: Identity a -> Identity a

abs :: Identity a -> Identity a

signum :: Identity a -> Identity a

fromInteger :: Integer -> Identity a

Ord a => Ord (Identity a)

Methods

compare :: Identity a -> Identity a -> Ordering

(<) :: Identity a -> Identity a -> Bool

(<=) :: Identity a -> Identity a -> Bool

(>) :: Identity a -> Identity a -> Bool

(>=) :: Identity a -> Identity a -> Bool

max :: Identity a -> Identity a -> Identity a

min :: Identity a -> Identity a -> Identity a

Read a => Read (Identity a)

This instance would be equivalent to the derived instances of the Identity newtype if the runIdentity field were removed

Methods

readsPrec :: Int -> ReadS (Identity a)

readList :: ReadS [Identity a]

readPrec :: ReadPrec (Identity a)

readListPrec :: ReadPrec [Identity a]

Real a => Real (Identity a)

Methods

toRational :: Identity a -> Rational

RealFloat a => RealFloat (Identity a)

Methods

floatRadix :: Identity a -> Integer

floatDigits :: Identity a -> Int

floatRange :: Identity a -> (Int, Int)

decodeFloat :: Identity a -> (Integer, Int)

encodeFloat :: Integer -> Int -> Identity a

exponent :: Identity a -> Int

significand :: Identity a -> Identity a

scaleFloat :: Int -> Identity a -> Identity a

isNaN :: Identity a -> Bool

isInfinite :: Identity a -> Bool

isDenormalized :: Identity a -> Bool

isNegativeZero :: Identity a -> Bool

isIEEE :: Identity a -> Bool

atan2 :: Identity a -> Identity a -> Identity a

RealFrac a => RealFrac (Identity a)

Methods

properFraction :: Integral b => Identity a -> (b, Identity a)

truncate :: Integral b => Identity a -> b

round :: Integral b => Identity a -> b

ceiling :: Integral b => Identity a -> b

floor :: Integral b => Identity a -> b

Show a => Show (Identity a)

This instance would be equivalent to the derived instances of the Identity newtype if the runIdentity field were removed

Methods

showsPrec :: Int -> Identity a -> ShowS

show :: Identity a -> String

showList :: [Identity a] -> ShowS

Ix a => Ix (Identity a)

Methods

range :: (Identity a, Identity a) -> [Identity a]

index :: (Identity a, Identity a) -> Identity a -> Int

unsafeIndex :: (Identity a, Identity a) -> Identity a -> Int

inRange :: (Identity a, Identity a) -> Identity a -> Bool

rangeSize :: (Identity a, Identity a) -> Int

unsafeRangeSize :: (Identity a, Identity a) -> Int

IsString a => IsString (Identity a)

Methods

fromString :: String -> Identity a

Generic (Identity a)

Associated Types

type Rep (Identity a) :: * -> *

Methods

from :: Identity a -> Rep (Identity a) x

to :: Rep (Identity a) x -> Identity a

Semigroup a => Semigroup (Identity a)

Methods

(<>) :: Identity a -> Identity a -> Identity a

sconcat :: NonEmpty (Identity a) -> Identity a

stimes :: Integral b => b -> Identity a -> Identity a

Monoid a => Monoid (Identity a)

Methods

mempty :: Identity a

mappend :: Identity a -> Identity a -> Identity a

mconcat :: [Identity a] -> Identity a

Storable a => Storable (Identity a)

Methods

sizeOf :: Identity a -> Int

alignment :: Identity a -> Int

peekElemOff :: Ptr (Identity a) -> Int -> IO (Identity a)

pokeElemOff :: Ptr (Identity a) -> Int -> Identity a -> IO ()

peekByteOff :: Ptr b -> Int -> IO (Identity a)

pokeByteOff :: Ptr b -> Int -> Identity a -> IO ()

peek :: Ptr (Identity a) -> IO (Identity a)

poke :: Ptr (Identity a) -> Identity a -> IO ()

Bits a => Bits (Identity a)

Methods

(.&.) :: Identity a -> Identity a -> Identity a

(.|.) :: Identity a -> Identity a -> Identity a

xor :: Identity a -> Identity a -> Identity a

complement :: Identity a -> Identity a

shift :: Identity a -> Int -> Identity a

rotate :: Identity a -> Int -> Identity a

zeroBits :: Identity a

bit :: Int -> Identity a

setBit :: Identity a -> Int -> Identity a

clearBit :: Identity a -> Int -> Identity a

complementBit :: Identity a -> Int -> Identity a

testBit :: Identity a -> Int -> Bool

bitSizeMaybe :: Identity a -> Maybe Int

bitSize :: Identity a -> Int

isSigned :: Identity a -> Bool

shiftL :: Identity a -> Int -> Identity a

unsafeShiftL :: Identity a -> Int -> Identity a

shiftR :: Identity a -> Int -> Identity a

unsafeShiftR :: Identity a -> Int -> Identity a

rotateL :: Identity a -> Int -> Identity a

rotateR :: Identity a -> Int -> Identity a

popCount :: Identity a -> Int

FiniteBits a => FiniteBits (Identity a)

Methods

finiteBitSize :: Identity a -> Int

countLeadingZeros :: Identity a -> Int

countTrailingZeros :: Identity a -> Int

type Rep1 Identity

type Rep1 Identity = D1 (MetaData "Identity" "Data.Functor.Identity" "base" True) (C1 (MetaCons "Identity" PrefixI True) (S1 (MetaSel (Just Symbol "runIdentity") NoSourceUnpackedness NoSourceStrictness DecidedLazy) Par1))

type Rep (Identity a)

type Rep (Identity a) = D1 (MetaData "Identity" "Data.Functor.Identity" "base" True) (C1 (MetaCons "Identity" PrefixI True) (S1 (MetaSel (Just Symbol "runIdentity") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a)))

class Applicative f => Alternative f where

A monoid on applicative functors.

If defined, some and many should be the least solutions of the equations:

• some v = (:) <$> v <*> many v

• many v = some v <|> pure []

Minimal complete definition

empty, (<|>)

Methods

(<|>) :: f a -> f a -> f a infixl 3

An associative binary operation

Instances

Alternative []

Methods

empty :: [a]

(<|>) :: [a] -> [a] -> [a]

some :: [a] -> [[a]]

many :: [a] -> [[a]]

Alternative Maybe

Methods

empty :: Maybe a

(<|>) :: Maybe a -> Maybe a -> Maybe a

some :: Maybe a -> Maybe [a]

many :: Maybe a -> Maybe [a]

Alternative IO

Methods

empty :: IO a

(<|>) :: IO a -> IO a -> IO a

some :: IO a -> IO [a]

many :: IO a -> IO [a]

Alternative U1

Methods

empty :: U1 a

(<|>) :: U1 a -> U1 a -> U1 a

some :: U1 a -> U1 [a]

many :: U1 a -> U1 [a]

Alternative P

Methods

empty :: P a

(<|>) :: P a -> P a -> P a

some :: P a -> P [a]

many :: P a -> P [a]

Alternative Option

Methods

empty :: Option a

(<|>) :: Option a -> Option a -> Option a

some :: Option a -> Option [a]

many :: Option a -> Option [a]

Alternative ReadPrec

Methods

empty :: ReadPrec a

(<|>) :: ReadPrec a -> ReadPrec a -> ReadPrec a

some :: ReadPrec a -> ReadPrec [a]

many :: ReadPrec a -> ReadPrec [a]

Alternative ReadP

Methods

empty :: ReadP a

(<|>) :: ReadP a -> ReadP a -> ReadP a

some :: ReadP a -> ReadP [a]

many :: ReadP a -> ReadP [a]

Alternative Seq

Methods

empty :: Seq a

(<|>) :: Seq a -> Seq a -> Seq a

some :: Seq a -> Seq [a]

many :: Seq a -> Seq [a]

Alternative f => Alternative (Rec1 f)

Methods

empty :: Rec1 f a

(<|>) :: Rec1 f a -> Rec1 f a -> Rec1 f a

some :: Rec1 f a -> Rec1 f [a]

many :: Rec1 f a -> Rec1 f [a]

MonadPlus m => Alternative (WrappedMonad m)

Methods

empty :: WrappedMonad m a

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

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

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

ArrowPlus a => Alternative (ArrowMonad a)

Methods

empty :: ArrowMonad a a

(<|>) :: ArrowMonad a a -> ArrowMonad a a -> ArrowMonad a a

some :: ArrowMonad a a -> ArrowMonad a [a]

many :: ArrowMonad a a -> ArrowMonad a [a]

Alternative (Proxy *)

Methods

empty :: Proxy * a

(<|>) :: Proxy * a -> Proxy * a -> Proxy * a

some :: Proxy * a -> Proxy * [a]

many :: Proxy * a -> Proxy * [a]

Applicative 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]

Alternative f => Alternative (Lift f)

A combination is Pure only either part is.

Methods

empty :: Lift f a

(<|>) :: Lift f a -> Lift f a -> Lift f a

some :: Lift f a -> Lift f [a]

many :: Lift f a -> Lift f [a]

(Functor m, Monad m) => Alternative (MaybeT m)

Methods

empty :: MaybeT m a

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

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

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

(Alternative f, Alternative g) => Alternative ((:*:) f g)

Methods

empty :: (f :*: g) a

(<|>) :: (f :*: g) a -> (f :*: g) a -> (f :*: g) a

some :: (f :*: g) a -> (f :*: g) [a]

many :: (f :*: g) a -> (f :*: g) [a]

(Alternative f, Applicative g) => Alternative ((:.:) f g)

Methods

empty :: (f :.: g) a

(<|>) :: (f :.: g) a -> (f :.: g) a -> (f :.: g) a

some :: (f :.: g) a -> (f :.: g) [a]

many :: (f :.: g) a -> (f :.: g) [a]

(ArrowZero a, ArrowPlus a) => Alternative (WrappedArrow a b)

Methods

empty :: WrappedArrow a b a

(<|>) :: WrappedArrow a b a -> WrappedArrow a b a -> WrappedArrow a b a

some :: WrappedArrow a b a -> WrappedArrow a b [a]

many :: WrappedArrow a b a -> WrappedArrow a b [a]

Alternative f => Alternative (Alt * f)

Methods

empty :: Alt * f a

(<|>) :: Alt * f a -> Alt * f a -> Alt * f a

some :: Alt * f a -> Alt * f [a]

many :: Alt * f a -> Alt * f [a]

(Functor m, Monad m, Error e) => Alternative (ErrorT e m)

Methods

empty :: ErrorT e m a

(<|>) :: ErrorT e m a -> ErrorT e m a -> ErrorT e m a

some :: ErrorT e m a -> ErrorT e m [a]

many :: ErrorT e m a -> ErrorT e m [a]

(Functor m, Monad m, Monoid e) => Alternative (ExceptT e m)

Methods

empty :: ExceptT e m a

(<|>) :: ExceptT e m a -> ExceptT e m a -> ExceptT e m a

some :: ExceptT e m a -> ExceptT e m [a]

many :: ExceptT e m a -> ExceptT e m [a]

(Functor m, MonadPlus m) => Alternative (StateT s m)

Methods

empty :: StateT s m a

(<|>) :: StateT s m a -> StateT s m a -> StateT s m a

some :: StateT s m a -> StateT s m [a]

many :: StateT s m a -> StateT s m [a]

(Functor m, MonadPlus m) => Alternative (StateT s m)

Methods

empty :: StateT s m a

(<|>) :: StateT s m a -> StateT s m a -> StateT s m a

some :: StateT s m a -> StateT s m [a]

many :: StateT s m a -> StateT s m [a]

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

Methods

empty :: WriterT w m a

(<|>) :: WriterT w m a -> WriterT w m a -> WriterT w m a

some :: WriterT w m a -> WriterT w m [a]

many :: WriterT w m a -> WriterT w m [a]

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

Methods

empty :: WriterT w m a

(<|>) :: WriterT w m a -> WriterT w m a -> WriterT w m a

some :: WriterT w m a -> WriterT w m [a]

many :: WriterT w m a -> WriterT w m [a]

Alternative f => Alternative (Backwards * f)

Try alternatives in the same order as f.

Methods

empty :: Backwards * f a

(<|>) :: Backwards * f a -> Backwards * f a -> Backwards * f a

some :: Backwards * f a -> Backwards * f [a]

many :: Backwards * f a -> Backwards * f [a]

Alternative m => Alternative (IdentityT * m)

Methods

empty :: IdentityT * m a

(<|>) :: IdentityT * m a -> IdentityT * m a -> IdentityT * m a

some :: IdentityT * m a -> IdentityT * m [a]

many :: IdentityT * m a -> IdentityT * m [a]

(Applicative f, Monad m) => Alternative (Stream f m)

The Alternative instance glues streams together stepwise.

empty = never
(<|>) = zipsWith (liftA2 (,))

See also never, untilJust and delays

Methods

empty :: Stream f m a

(<|>) :: Stream f m a -> Stream f m a -> Stream f m a

some :: Stream f m a -> Stream f m [a]

many :: Stream f m a -> Stream f m [a]

Alternative f => Alternative (M1 i c f)

Methods

empty :: M1 i c f a

(<|>) :: M1 i c f a -> M1 i c f a -> M1 i c f a

some :: M1 i c f a -> M1 i c f [a]

many :: M1 i c f a -> M1 i c f [a]

(Alternative f, Alternative g) => Alternative (Product * f g)

Methods

empty :: Product * f g a

(<|>) :: Product * f g a -> Product * f g a -> Product * f g a

some :: Product * f g a -> Product * f g [a]

many :: Product * f g a -> Product * f g [a]

Alternative m => Alternative (ReaderT * r m)

Methods

empty :: ReaderT * r m a

(<|>) :: ReaderT * r m a -> ReaderT * r m a -> ReaderT * r m a

some :: ReaderT * r m a -> ReaderT * r m [a]

many :: ReaderT * r m a -> ReaderT * r m [a]

(Alternative f, Applicative g) => Alternative (Compose * * f g)

Methods

empty :: Compose * * f g a

(<|>) :: Compose * * f g a -> Compose * * f g a -> Compose * * f g a

some :: Compose * * f g a -> Compose * * f g [a]

many :: Compose * * f g a -> Compose * * f g [a]

(Monoid w, Functor m, MonadPlus m) => Alternative (RWST r w s m)

Methods

empty :: RWST r w s m a

(<|>) :: RWST r w s m a -> RWST r w s m a -> RWST r w s m a

some :: RWST r w s m a -> RWST r w s m [a]

many :: RWST r w s m a -> RWST r w s m [a]

(Monoid w, Functor m, MonadPlus m) => Alternative (RWST r w s m)

Methods

empty :: RWST r w s m a

(<|>) :: RWST r w s m a -> RWST r w s m a -> RWST r w s m a

some :: RWST r w s m a -> RWST r w s m [a]

many :: RWST r w s m a -> RWST r w s m [a]

class Bifunctor p where

Formally, the class Bifunctor represents a bifunctor from Hask -> Hask.

Intuitively it is a bifunctor where both the first and second arguments are covariant.

You can define a Bifunctor by either defining bimap or by defining both first and second.

If you supply bimap, you should ensure that:

bimap id id ≡ id

If you supply first and second, ensure:

first id ≡ id
second id ≡ id

If you supply both, you should also ensure:

bimap f g ≡ first f . second g

These ensure by parametricity:

bimap  (f . g) (h . i) ≡ bimap f h . bimap g i
first  (f . g) ≡ first  f . first  g
second (f . g) ≡ second f . second g

Since: 4.8.0.0

Minimal complete definition

bimap | first, second

Methods

bimap :: (a -> b) -> (c -> d) -> p a c -> p b d

Map over both arguments at the same time.

bimap f g ≡ first f . second g

first :: (a -> b) -> p a c -> p b c

Map covariantly over the first argument.

first f ≡ bimap f id

second :: (b -> c) -> p a b -> p a c

Map covariantly over the second argument.

second ≡ bimap id

Instances

Bifunctor Either

Methods

bimap :: (a -> b) -> (c -> d) -> Either a c -> Either b d

first :: (a -> b) -> Either a c -> Either b c

second :: (b -> c) -> Either a b -> Either a c

Bifunctor (,)

Methods

bimap :: (a -> b) -> (c -> d) -> (a, c) -> (b, d)

first :: (a -> b) -> (a, c) -> (b, c)

second :: (b -> c) -> (a, b) -> (a, c)

Bifunctor Arg

Methods

bimap :: (a -> b) -> (c -> d) -> Arg a c -> Arg b d

first :: (a -> b) -> Arg a c -> Arg b c

second :: (b -> c) -> Arg a b -> Arg a c

Bifunctor Of

Methods

bimap :: (a -> b) -> (c -> d) -> Of a c -> Of b d

first :: (a -> b) -> Of a c -> Of b c

second :: (b -> c) -> Of a b -> Of a c

Bifunctor (K1 i)

Methods

bimap :: (a -> b) -> (c -> d) -> K1 i a c -> K1 i b d

first :: (a -> b) -> K1 i a c -> K1 i b c

second :: (b -> c) -> K1 i a b -> K1 i a c

Bifunctor ((,,) x1)

Methods

bimap :: (a -> b) -> (c -> d) -> (x1, a, c) -> (x1, b, d)

first :: (a -> b) -> (x1, a, c) -> (x1, b, c)

second :: (b -> c) -> (x1, a, b) -> (x1, a, c)

Bifunctor (Const *)

Methods

bimap :: (a -> b) -> (c -> d) -> Const * a c -> Const * b d

first :: (a -> b) -> Const * a c -> Const * b c

second :: (b -> c) -> Const * a b -> Const * a c

Bifunctor ((,,,) x1 x2)

Methods

bimap :: (a -> b) -> (c -> d) -> (x1, x2, a, c) -> (x1, x2, b, d)

first :: (a -> b) -> (x1, x2, a, c) -> (x1, x2, b, c)

second :: (b -> c) -> (x1, x2, a, b) -> (x1, x2, a, c)

Bifunctor ((,,,,) x1 x2 x3)

Methods

bimap :: (a -> b) -> (c -> d) -> (x1, x2, x3, a, c) -> (x1, x2, x3, b, d)

first :: (a -> b) -> (x1, x2, x3, a, c) -> (x1, x2, x3, b, c)

second :: (b -> c) -> (x1, x2, x3, a, b) -> (x1, x2, x3, a, c)

Bifunctor ((,,,,,) x1 x2 x3 x4)

Methods

bimap :: (a -> b) -> (c -> d) -> (x1, x2, x3, x4, a, c) -> (x1, x2, x3, x4, b, d)

first :: (a -> b) -> (x1, x2, x3, x4, a, c) -> (x1, x2, x3, x4, b, c)

second :: (b -> c) -> (x1, x2, x3, x4, a, b) -> (x1, x2, x3, x4, a, c)

Bifunctor ((,,,,,,) x1 x2 x3 x4 x5)

Methods

bimap :: (a -> b) -> (c -> d) -> (x1, x2, x3, x4, x5, a, c) -> (x1, x2, x3, x4, x5, b, d)

first :: (a -> b) -> (x1, x2, x3, x4, x5, a, c) -> (x1, x2, x3, x4, x5, b, c)

second :: (b -> c) -> (x1, x2, x3, x4, x5, a, b) -> (x1, x2, x3, x4, x5, a, c)

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

The join function is the conventional monad join operator. It is used to remove one level of monadic structure, projecting its bound argument into the outer level.

liftM :: Monad m => (a1 -> r) -> m a1 -> m r

Promote a function to a monad.

liftM2 :: Monad m => (a1 -> a2 -> r) -> m a1 -> m a2 -> m r

Promote a function to a monad, scanning the monadic arguments from left to right. For example,

   liftM2 (+) [0,1] [0,2] = [0,2,1,3]
   liftM2 (+) (Just 1) Nothing = Nothing

liftA2 :: Applicative f => (a -> b -> c) -> f a -> f b -> f c

Lift a binary function to actions.

liftA3 :: Applicative f => (a -> b -> c -> d) -> f a -> f b -> f c -> f d

Lift a ternary function to actions.

void :: Functor f => f a -> f ()

void value discards or ignores the result of evaluation, such as the return value of an IO action.

Examples

Replace the contents of a Maybe Int with unit:

>>> void Nothing
Nothing
>>> void (Just 3)
Just ()

Replace the contents of an Either Int Int with unit, resulting in an Either Int '()':

>>> void (Left 8675309)
Left 8675309
>>> void (Right 8675309)
Right ()

Replace every element of a list with unit:

>>> void [1,2,3]
[(),(),()]

Replace the second element of a pair with unit:

>>> void (1,2)
(1,())

Discard the result of an IO action:

>>> mapM print [1,2]
1
2
[(),()]
>>> void $ mapM print [1,2]
1
2

(<>) :: Monoid m => m -> m -> m infixr 6

An infix synonym for mappend.

Since: 4.5.0.0