| Safe Haskell | Safe-Inferred |
|---|---|
| Language | Haskell2010 |
Streaming
Synopsis
- data Stream f m r
- yields :: (Monad m, Functor f) => f r -> Stream f m r
- effect :: (Monad m, Functor f) => m (Stream f m r) -> Stream f m r
- wrap :: (Monad m, Functor f) => f (Stream f m r) -> Stream f m r
- replicates :: (Monad m, Functor f) => Int -> f () -> Stream f m ()
- repeats :: (Monad m, Functor f) => f () -> Stream f m r
- repeatsM :: (Monad m, Functor f) => m (f ()) -> Stream f m r
- unfold :: (Monad m, Functor f) => (s -> m (Either r (f s))) -> s -> Stream f m r
- never :: (Monad m, Applicative f) => Stream f m r
- untilJust :: (Monad m, Applicative f) => m (Maybe r) -> Stream f m r
- streamBuild :: (forall b. (r -> b) -> (m b -> b) -> (f b -> b) -> b) -> Stream f m r
- delays :: (MonadIO m, Applicative f) => Double -> Stream f m r
- maps :: (Monad m, Functor f) => (forall x. f x -> g x) -> Stream f m r -> Stream g m r
- mapsPost :: forall m f g r. (Monad m, Functor g) => (forall x. f x -> g x) -> Stream f m r -> Stream g m r
- mapsM :: (Monad m, Functor f) => (forall x. f x -> m (g x)) -> Stream f m r -> Stream g m r
- 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
- mapped :: (Monad m, Functor f) => (forall x. f x -> m (g x)) -> Stream f m r -> Stream g m r
- mappedPost :: (Monad m, Functor g) => (forall x. f x -> m (g x)) -> Stream f m r -> Stream g m r
- hoistUnexposed :: (Monad m, Functor f) => (forall a. m a -> n a) -> Stream f m r -> Stream f n r
- distribute :: (Monad m, Functor f, MonadTrans t, MFunctor t, Monad (t (Stream f m))) => Stream f (t m) r -> t (Stream f m) r
- groups :: (Monad m, Functor f, Functor g) => Stream (Sum f g) m r -> Stream (Sum (Stream f m) (Stream g m)) m r
- inspect :: Monad m => Stream f m r -> m (Either r (f (Stream f m r)))
- splitsAt :: (Monad m, Functor f) => Int -> Stream f m r -> Stream f m (Stream f m r)
- 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
- concats :: (Monad m, Functor f) => Stream (Stream f m) m r -> Stream f m r
- intercalates :: (Monad m, Monad (t m), MonadTrans t) => t m x -> Stream (t m) m r -> t m r
- cutoff :: (Monad m, Functor f) => Int -> Stream f m r -> Stream f m (Maybe r)
- 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
- 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
- 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
- separate :: (Monad m, Functor f, Functor g) => Stream (Sum f g) m r -> Stream f (Stream g m) r
- 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
- 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
- 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
- mapsM_ :: (Functor f, Monad m) => (forall x. f x -> m x) -> Stream f m r -> m r
- run :: Monad m => Stream m m r -> m r
- streamFold :: (Functor f, Monad m) => (r -> b) -> (m b -> b) -> (f b -> b) -> Stream f m r -> b
- iterTM :: (Functor f, Monad m, MonadTrans t, Monad (t m)) => (f (t m a) -> t m a) -> Stream f m a -> t m a
- iterT :: (Functor f, Monad m) => (f (m a) -> m a) -> Stream f m a -> m a
- destroy :: (Functor f, Monad m) => Stream f m r -> (f b -> b) -> (m b -> b) -> (r -> b) -> b
- data Of a b = !a :> b
- lazily :: Of a b -> (a, b)
- strictly :: (a, b) -> Of a b
- class MFunctor (t :: (Type -> Type) -> k -> Type) where
- class (MFunctor t, MonadTrans t) => MMonad (t :: (Type -> Type) -> Type -> Type) where
- class MonadTrans (t :: (Type -> Type) -> Type -> Type) where
- class Monad m => MonadIO (m :: Type -> Type) where
- newtype Compose (f :: k -> Type) (g :: k1 -> k) (a :: k1) = Compose {
- getCompose :: f (g a)
- data Sum (f :: k -> Type) (g :: k -> Type) (a :: k)
- newtype Identity a = Identity {
- runIdentity :: a
- class Applicative f => Alternative (f :: Type -> Type) where
- (<|>) :: f a -> f a -> f a
- class Bifunctor (p :: Type -> Type -> Type) where
- join :: Monad m => m (m a) -> m a
- liftM :: Monad m => (a1 -> r) -> m a1 -> m r
- liftM2 :: Monad m => (a1 -> a2 -> r) -> m a1 -> m a2 -> m r
- liftA2 :: Applicative f => (a -> b -> c) -> f a -> f b -> f c
- liftA3 :: Applicative f => (a -> b -> c -> d) -> f a -> f b -> f c -> f d
- void :: Functor f => f a -> f ()
- (<>) :: Semigroup a => a -> a -> a
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 rOne 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.
Instances
| (Functor f, MonadState s m) => MonadState s (Stream f m) Source # | |
| (Functor f, MonadReader r m) => MonadReader r (Stream f m) Source # | |
| (Functor f, MonadError e m) => MonadError e (Stream f m) Source # | |
Defined in Streaming.Internal Methods throwError :: e -> Stream f m a # catchError :: Stream f m a -> (e -> Stream f m a) -> Stream f m a # | |
| Functor f => MMonad (Stream f) Source # | |
| Functor f => MonadTrans (Stream f) Source # | |
Defined in Streaming.Internal | |
| Functor f => MFunctor (Stream f :: (Type -> Type) -> Type -> Type) Source # | |
| (Functor f, Monad m) => Monad (Stream f m) Source # | |
| (Functor f, Monad m) => Functor (Stream f m) Source # | Operates covariantly on the stream result, not on its elements: Stream (Of a) m r
^ ^
| `--- This is what |
| (Functor f, MonadFail m) => MonadFail (Stream f m) Source # | |
Defined in Streaming.Internal | |
| (Functor f, Monad m) => Applicative (Stream f m) Source # | |
Defined in Streaming.Internal | |
| (Monad m, Functor f, Eq1 m, Eq1 f) => Eq1 (Stream f m) Source # | |
| (Monad m, Functor f, Ord1 m, Ord1 f) => Ord1 (Stream f m) Source # | |
Defined in Streaming.Internal | |
| (Monad m, Functor f, Show (m ShowSWrapper), Show (f ShowSWrapper)) => Show1 (Stream f m) Source # | |
| (MonadIO m, Functor f) => MonadIO (Stream f m) Source # | |
Defined in Streaming.Internal | |
| (Applicative f, Monad m) => Alternative (Stream f m) Source # | The empty = never (<|>) = zipsWith (liftA2 (,)) |
| (Applicative f, Monad m) => MonadPlus (Stream f m) Source # | |
| (Monad m, Eq (m (Either r (f (Stream f m r))))) => Eq (Stream f m r) Source # | |
| (Monad m, Ord (m (Either r (f (Stream f m r))))) => Ord (Stream f m r) Source # | |
Defined in Streaming.Internal | |
| (Monad m, Show r, Show (m ShowSWrapper), Show (f (Stream f m r))) => Show (Stream f m r) Source # | |
| (Functor f, Monad m, Semigroup w) => Semigroup (Stream f m w) Source # | |
| (Functor f, Monad m, Monoid w) => Monoid (Stream f m w) Source # | |
Constructing a Stream on a given functor
yields :: (Monad m, Functor f) => f r -> Stream f m r Source #
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 Source #
Wrap an effect that returns a stream
effect = join . lift
wrap :: (Monad m, Functor f) => f (Stream f m r) -> Stream f m r Source #
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 () Source #
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 Source #
Repeat a functorial layer (a "command" or "instruction") forever.
repeatsM :: (Monad m, Functor f) => m (f ()) -> Stream f m r Source #
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 Source #
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 Source #
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.stdinLn1<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 fourone<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.
streamBuild :: (forall b. (r -> b) -> (m b -> b) -> (f b -> b) -> b) -> Stream f m r Source #
Reflect a church-encoded stream; cp. GHC.Exts.build
streamFold return_ effect_ step_ (streamBuild psi) = psi return_ effect_ step_
Transforming streams
maps :: (Monad m, Functor f) => (forall x. f x -> g x) -> Stream f m r -> Stream g m r Source #
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 Source #
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 = maps 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 Source #
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 Source #
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 Source #
Map layers of one functor to another with a transformation involving the base monad.
This function is completely functor-general. It is often useful with the more concrete type
mapped :: (forall x. Stream (Of a) IO x -> IO (Of b x)) -> Stream (Stream (Of a) IO) IO r -> Stream (Of b) IO r
to process groups which have been demarcated in an effectful, IO-based
stream by grouping functions like group,
split or breaks. Summary functions
like fold, foldM,
mconcat or toList are often used
to define the transformation argument. For example:
>>>S.toList_ $ S.mapped S.toList $ S.split 'c' (S.each "abcde")["ab","de"]
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 Source #
hoistUnexposed :: (Monad m, Functor f) => (forall a. m a -> n a) -> Stream f m r -> Stream f n r Source #
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 Source #
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 Source #
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))) Source #
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) Source #
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 rest2 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 rest5
chunksOf :: (Monad m, Functor f) => Int -> Stream f m r -> Stream (Stream f m) m r Source #
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 Source #
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 Source #
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
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 Source #
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 Source #
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 Source #
unzips :: (Monad m, Functor f, Functor g) => Stream (Compose f g) m r -> Stream f (Stream g m) r Source #
interleaves :: (Monad m, Applicative h) => Stream h m r -> Stream h m r -> Stream h m r Source #
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 Source #
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_evenseparate 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:
>>>S.writeFile "even.txt" . S.show $ S.writeFile "odd.txt" . S.show $ S.separate odd_even>>>:! cat even.txt2 4 6 8 10>>>:! cat odd.txt1 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 Source #
decompose :: (Monad m, Functor f) => Stream (Compose m f) m r -> Stream f m r Source #
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 Source #
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 Source #
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 Source #
Map each layer to an effect, and run them all.
run :: Monad m => Stream m m r -> m r Source #
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 Source #
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 Source #
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 Source #
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 Source #
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
A left-strict pair; the base functor for streams of individual elements.
Constructors
| !a :> b infixr 5 |
Instances
| Bitraversable Of Source # | Since: 0.2.4.0 |
Defined in Data.Functor.Of Methods bitraverse :: Applicative f => (a -> f c) -> (b -> f d) -> Of a b -> f (Of c d) # | |
| Bifoldable Of Source # | Since: 0.2.4.0 |
| Bifunctor Of Source # | |
| Eq2 Of Source # | |
| Ord2 Of Source # | |
Defined in Data.Functor.Of | |
| Show2 Of Source # | |
| Monoid a => Monad (Of a) Source # | |
| Functor (Of a) Source # | |
| Monoid a => Applicative (Of a) Source # | |
| Foldable (Of a) Source # | |
Defined in Data.Functor.Of Methods fold :: Monoid m => Of a m -> m # foldMap :: Monoid m => (a0 -> m) -> Of a a0 -> m # foldMap' :: Monoid m => (a0 -> m) -> Of a a0 -> m # foldr :: (a0 -> b -> b) -> b -> Of a a0 -> b # foldr' :: (a0 -> b -> b) -> b -> Of a a0 -> b # foldl :: (b -> a0 -> b) -> b -> Of a a0 -> b # foldl' :: (b -> a0 -> b) -> b -> Of a a0 -> b # foldr1 :: (a0 -> a0 -> a0) -> Of a a0 -> a0 # foldl1 :: (a0 -> a0 -> a0) -> Of a a0 -> a0 # elem :: Eq a0 => a0 -> Of a a0 -> Bool # maximum :: Ord a0 => Of a a0 -> a0 # minimum :: Ord a0 => Of a a0 -> a0 # | |
| Traversable (Of a) Source # | |
| Eq a => Eq1 (Of a) Source # | |
| Ord a => Ord1 (Of a) Source # | |
Defined in Data.Functor.Of | |
| Show a => Show1 (Of a) Source # | |
| Generic1 (Of a :: Type -> Type) Source # | |
| (Eq a, Eq b) => Eq (Of a b) Source # | |
| (Data a, Data b) => Data (Of a b) Source # | |
Defined in Data.Functor.Of Methods gfoldl :: (forall d b0. Data d => c (d -> b0) -> d -> c b0) -> (forall g. g -> c g) -> Of a b -> c (Of a b) # gunfold :: (forall b0 r. Data b0 => c (b0 -> 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 b0. Data b0 => b0 -> b0) -> Of a b -> Of a b # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Of a b -> r # gmapQr :: forall r r'. (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 a, Ord b) => Ord (Of a b) Source # | |
| (Read a, Read b) => Read (Of a b) Source # | |
| (Show a, Show b) => Show (Of a b) Source # | |
| Generic (Of a b) Source # | |
| (Semigroup a, Semigroup b) => Semigroup (Of a b) Source # | |
| (Monoid a, Monoid b) => Monoid (Of a b) Source # | |
| type Rep1 (Of a :: Type -> Type) Source # | |
Defined in Data.Functor.Of type Rep1 (Of a :: Type -> Type) = D1 ('MetaData "Of" "Data.Functor.Of" "streaming-0.2.3.1-JmjGcboAIpAA9PomIMwDTs" 'False) (C1 ('MetaCons ":>" ('InfixI 'RightAssociative 5) 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 a) :*: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) Par1)) | |
| type Rep (Of a b) Source # | |
Defined in Data.Functor.Of type Rep (Of a b) = D1 ('MetaData "Of" "Data.Functor.Of" "streaming-0.2.3.1-JmjGcboAIpAA9PomIMwDTs" 'False) (C1 ('MetaCons ":>" ('InfixI 'RightAssociative 5) 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 a) :*: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 b))) | |
lazily :: Of a b -> (a, b) Source #
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.
re-exports
class MFunctor (t :: (Type -> Type) -> k -> Type) 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
Methods
hoist :: forall m n (b :: k). 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)
The first argument to hoist must be a monad morphism, even though the
type system does not enforce this
Instances
| MFunctor Lift | |
| MFunctor MaybeT | |
| MFunctor (IdentityT :: (Type -> Type) -> Type -> Type) | |
| MFunctor (ExceptT e :: (Type -> Type) -> Type -> Type) | |
| MFunctor (ReaderT r :: (Type -> Type) -> Type -> Type) | |
| MFunctor (StateT s :: (Type -> Type) -> Type -> Type) | |
| MFunctor (StateT s :: (Type -> Type) -> Type -> Type) | |
| MFunctor (WriterT w :: (Type -> Type) -> Type -> Type) | |
| MFunctor (WriterT w :: (Type -> Type) -> Type -> Type) | |
| MFunctor (Backwards :: (Type -> Type) -> Type -> Type) | |
| Functor f => MFunctor (Stream f :: (Type -> Type) -> Type -> Type) Source # | |
| MFunctor (Product f :: (Type -> Type) -> Type -> Type) | |
| Functor f => MFunctor (Compose f :: (Type -> Type) -> Type -> Type) | |
| MFunctor (RWST r w s :: (Type -> Type) -> Type -> Type) | |
| MFunctor (RWST r w s :: (Type -> Type) -> Type -> Type) | |
class (MFunctor t, MonadTrans t) => MMonad (t :: (Type -> Type) -> Type -> Type) 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
Methods
embed :: forall (n :: Type -> Type) m b. Monad n => (forall a. m a -> t n a) -> t m b -> t n b #
class MonadTrans (t :: (Type -> Type) -> Type -> Type) where #
The class of monad transformers. Instances should satisfy the
following laws, which state that lift is a monad transformation:
Methods
lift :: Monad m => m a -> t m a #
Lift a computation from the argument monad to the constructed monad.
Instances
| MonadTrans ListT | |
Defined in Control.Monad.Trans.List | |
| MonadTrans MaybeT | |
Defined in Control.Monad.Trans.Maybe | |
| MonadTrans (IdentityT :: (Type -> Type) -> Type -> Type) | |
Defined in Control.Monad.Trans.Identity | |
| MonadTrans (ErrorT e) | |
Defined in Control.Monad.Trans.Error | |
| MonadTrans (ExceptT e) | |
Defined in Control.Monad.Trans.Except | |
| MonadTrans (ReaderT r) | |
Defined in Control.Monad.Trans.Reader | |
| MonadTrans (StateT s) | |
Defined in Control.Monad.Trans.State.Lazy | |
| MonadTrans (StateT s) | |
Defined in Control.Monad.Trans.State.Strict | |
| Monoid w => MonadTrans (WriterT w) | |
Defined in Control.Monad.Trans.Writer.Lazy | |
| Monoid w => MonadTrans (WriterT w) | |
Defined in Control.Monad.Trans.Writer.Strict | |
| Functor f => MonadTrans (Stream f) Source # | |
Defined in Streaming.Internal | |
| MonadTrans (ContT r) | |
Defined in Control.Monad.Trans.Cont | |
| Monoid w => MonadTrans (RWST r w s) | |
Defined in Control.Monad.Trans.RWS.Lazy | |
| Monoid w => MonadTrans (RWST r w s) | |
Defined in Control.Monad.Trans.RWS.Strict | |
class Monad m => MonadIO (m :: Type -> Type) 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:
Instances
newtype Compose (f :: k -> Type) (g :: k1 -> k) (a :: k1) 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
| |
Instances
| Functor f => Generic1 (Compose f g :: k -> Type) | Since: base-4.9.0.0 |
| TestEquality f => TestEquality (Compose f g :: k2 -> Type) | The deduction (via generativity) that if Since: base-4.14.0.0 |
Defined in Data.Functor.Compose | |
| Functor f => MFunctor (Compose f :: (Type -> Type) -> Type -> Type) | |
| (Functor f, Functor g) => Functor (Compose f g) | Since: base-4.9.0.0 |
| (Applicative f, Applicative g) => Applicative (Compose f g) | Since: base-4.9.0.0 |
Defined in Data.Functor.Compose | |
| (Foldable f, Foldable g) => Foldable (Compose f g) | Since: base-4.9.0.0 |
Defined in Data.Functor.Compose Methods fold :: Monoid m => Compose f g m -> m # foldMap :: Monoid m => (a -> m) -> Compose f g a -> m # foldMap' :: Monoid m => (a -> m) -> Compose f g a -> m # foldr :: (a -> b -> b) -> b -> Compose f g a -> b # foldr' :: (a -> b -> b) -> b -> Compose f g a -> b # foldl :: (b -> a -> b) -> b -> Compose f g a -> b # foldl' :: (b -> a -> b) -> b -> Compose f g a -> b # foldr1 :: (a -> a -> a) -> Compose f g a -> a # foldl1 :: (a -> a -> a) -> Compose f g a -> a # toList :: Compose f g a -> [a] # null :: Compose f g a -> Bool # length :: Compose f g a -> Int # elem :: Eq a => a -> Compose f g a -> Bool # maximum :: Ord a => Compose f g a -> a # minimum :: Ord a => Compose f g a -> a # | |
| (Traversable f, Traversable g) => Traversable (Compose f g) | Since: base-4.9.0.0 |
Defined in Data.Functor.Compose | |
| (Eq1 f, Eq1 g) => Eq1 (Compose f g) | Since: base-4.9.0.0 |
| (Ord1 f, Ord1 g) => Ord1 (Compose f g) | Since: base-4.9.0.0 |
Defined in Data.Functor.Compose | |
| (Read1 f, Read1 g) => Read1 (Compose f g) | Since: base-4.9.0.0 |
Defined in Data.Functor.Compose Methods liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (Compose f g a) # liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [Compose f g a] # liftReadPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec (Compose f g a) # liftReadListPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec [Compose f g a] # | |
| (Show1 f, Show1 g) => Show1 (Compose f g) | Since: base-4.9.0.0 |
| (Alternative f, Applicative g) => Alternative (Compose f g) | Since: base-4.9.0.0 |
| (Eq1 f, Eq1 g, Eq a) => Eq (Compose f g a) | Since: base-4.9.0.0 |
| (Typeable a, Typeable f, Typeable g, Typeable k1, Typeable k2, Data (f (g a))) => Data (Compose f g a) | Since: base-4.9.0.0 |
Defined in Data.Functor.Compose Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g0. g0 -> c g0) -> Compose f g a -> c (Compose f g a) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Compose f g a) # toConstr :: Compose f g a -> Constr # dataTypeOf :: Compose f g a -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Compose f g a)) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Compose f g a)) # gmapT :: (forall b. Data b => b -> b) -> Compose f g a -> Compose f g a # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Compose f g a -> r # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Compose f g a -> r # gmapQ :: (forall d. Data d => d -> u) -> Compose f g a -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> Compose f g a -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Compose f g a -> m (Compose f g a) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Compose f g a -> m (Compose f g a) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Compose f g a -> m (Compose f g a) # | |
| (Ord1 f, Ord1 g, Ord a) => Ord (Compose f g a) | Since: base-4.9.0.0 |
Defined in Data.Functor.Compose 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 # | |
| (Read1 f, Read1 g, Read a) => Read (Compose f g a) | Since: base-4.9.0.0 |
| (Show1 f, Show1 g, Show a) => Show (Compose f g a) | Since: base-4.9.0.0 |
| Generic (Compose f g a) | Since: base-4.9.0.0 |
| type Rep1 (Compose f g :: k -> Type) | |
Defined in Data.Functor.Compose | |
| type Rep (Compose f g a) | |
Defined in Data.Functor.Compose | |
data Sum (f :: k -> Type) (g :: k -> Type) (a :: k) #
Lifted sum of functors.
Instances
| Generic1 (Sum f g :: k -> Type) | Since: base-4.9.0.0 |
| (Functor f, Functor g) => Functor (Sum f g) | Since: base-4.9.0.0 |
| (Foldable f, Foldable g) => Foldable (Sum f g) | Since: base-4.9.0.0 |
Defined in Data.Functor.Sum Methods fold :: Monoid m => Sum f g m -> m # foldMap :: Monoid m => (a -> m) -> Sum f g a -> m # foldMap' :: Monoid m => (a -> m) -> Sum f g a -> m # foldr :: (a -> b -> b) -> b -> Sum f g a -> b # foldr' :: (a -> b -> b) -> b -> Sum f g a -> b # foldl :: (b -> a -> b) -> b -> Sum f g a -> b # foldl' :: (b -> a -> b) -> b -> Sum f g a -> b # foldr1 :: (a -> a -> a) -> Sum f g a -> a # foldl1 :: (a -> a -> a) -> Sum f g a -> a # 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 # | |
| (Traversable f, Traversable g) => Traversable (Sum f g) | Since: base-4.9.0.0 |
| (Eq1 f, Eq1 g) => Eq1 (Sum f g) | Since: base-4.9.0.0 |
| (Ord1 f, Ord1 g) => Ord1 (Sum f g) | Since: base-4.9.0.0 |
Defined in Data.Functor.Sum | |
| (Read1 f, Read1 g) => Read1 (Sum f g) | Since: base-4.9.0.0 |
Defined in Data.Functor.Sum | |
| (Show1 f, Show1 g) => Show1 (Sum f g) | Since: base-4.9.0.0 |
| (Eq1 f, Eq1 g, Eq a) => Eq (Sum f g a) | Since: base-4.9.0.0 |
| (Typeable a, Typeable f, Typeable g, Typeable k, Data (f a), Data (g a)) => Data (Sum f g a) | Since: base-4.9.0.0 |
Defined in Data.Functor.Sum Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g0. g0 -> c g0) -> Sum f g a -> c (Sum f g a) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Sum f g a) # toConstr :: Sum f g a -> Constr # dataTypeOf :: Sum f g a -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Sum f g a)) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Sum f g a)) # gmapT :: (forall b. Data b => b -> b) -> Sum f g a -> Sum f g a # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Sum f g a -> r # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Sum f g a -> r # gmapQ :: (forall d. Data d => d -> u) -> Sum f g a -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> Sum f g a -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Sum f g a -> m (Sum f g a) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Sum f g a -> m (Sum f g a) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Sum f g a -> m (Sum f g a) # | |
| (Ord1 f, Ord1 g, Ord a) => Ord (Sum f g a) | Since: base-4.9.0.0 |
| (Read1 f, Read1 g, Read a) => Read (Sum f g a) | Since: base-4.9.0.0 |
| (Show1 f, Show1 g, Show a) => Show (Sum f g a) | Since: base-4.9.0.0 |
| Generic (Sum f g a) | Since: base-4.9.0.0 |
| type Rep1 (Sum f g :: k -> Type) | |
Defined in Data.Functor.Sum type Rep1 (Sum f g :: k -> Type) = D1 ('MetaData "Sum" "Data.Functor.Sum" "base" 'False) (C1 ('MetaCons "InL" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec1 f)) :+: C1 ('MetaCons "InR" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec1 g))) | |
| type Rep (Sum f g a) | |
Defined in Data.Functor.Sum type Rep (Sum f g a) = D1 ('MetaData "Sum" "Data.Functor.Sum" "base" 'False) (C1 ('MetaCons "InL" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (f a))) :+: C1 ('MetaCons "InR" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (g a)))) | |
Identity functor and monad. (a non-strict monad)
Since: base-4.8.0.0
Constructors
| Identity | |
Fields
| |
Instances
| Monad Identity | Since: base-4.8.0.0 |
| Functor Identity | Since: base-4.8.0.0 |
| MonadFix Identity | Since: base-4.8.0.0 |
Defined in Data.Functor.Identity | |
| Applicative Identity | Since: base-4.8.0.0 |
| Foldable Identity | Since: base-4.8.0.0 |
Defined in Data.Functor.Identity Methods fold :: Monoid m => Identity m -> m # foldMap :: Monoid m => (a -> m) -> Identity a -> m # foldMap' :: Monoid m => (a -> m) -> Identity a -> m # foldr :: (a -> b -> b) -> b -> Identity a -> b # foldr' :: (a -> b -> b) -> b -> Identity a -> b # foldl :: (b -> a -> b) -> b -> Identity a -> b # foldl' :: (b -> a -> b) -> b -> Identity a -> b # foldr1 :: (a -> a -> a) -> Identity a -> a # foldl1 :: (a -> a -> a) -> Identity a -> a # elem :: Eq a => a -> Identity a -> Bool # maximum :: Ord a => Identity a -> a # minimum :: Ord a => Identity a -> a # | |
| Traversable Identity | Since: base-4.9.0.0 |
| Eq1 Identity | Since: base-4.9.0.0 |
| Ord1 Identity | Since: base-4.9.0.0 |
Defined in Data.Functor.Classes | |
| Read1 Identity | Since: base-4.9.0.0 |
Defined in Data.Functor.Classes | |
| Show1 Identity | Since: base-4.9.0.0 |
| Bounded a => Bounded (Identity a) | Since: base-4.9.0.0 |
| Enum a => Enum (Identity a) | Since: base-4.9.0.0 |
Defined in Data.Functor.Identity Methods succ :: Identity a -> Identity a # pred :: Identity a -> 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) | Since: base-4.8.0.0 |
| Floating a => Floating (Identity a) | Since: base-4.9.0.0 |
Defined in Data.Functor.Identity Methods 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 # | |
| Fractional a => Fractional (Identity a) | Since: base-4.9.0.0 |
| Integral a => Integral (Identity a) | Since: base-4.9.0.0 |
Defined in Data.Functor.Identity 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) # | |
| Data a => Data (Identity a) | Since: base-4.9.0.0 |
Defined in Data.Data 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 :: forall r r'. (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) | Since: base-4.9.0.0 |
Defined in Data.Functor.Identity | |
| Ord a => Ord (Identity a) | Since: base-4.8.0.0 |
Defined in Data.Functor.Identity | |
| Read a => Read (Identity a) | This instance would be equivalent to the derived instances of the
Since: base-4.8.0.0 |
| Real a => Real (Identity a) | Since: base-4.9.0.0 |
Defined in Data.Functor.Identity Methods toRational :: Identity a -> Rational # | |
| RealFloat a => RealFloat (Identity a) | Since: base-4.9.0.0 |
Defined in Data.Functor.Identity 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 # isInfinite :: Identity a -> Bool # isDenormalized :: Identity a -> Bool # isNegativeZero :: Identity a -> Bool # | |
| RealFrac a => RealFrac (Identity a) | Since: base-4.9.0.0 |
| Show a => Show (Identity a) | This instance would be equivalent to the derived instances of the
Since: base-4.8.0.0 |
| Ix a => Ix (Identity a) | Since: base-4.9.0.0 |
Defined in Data.Functor.Identity 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 # | |
| Generic (Identity a) | Since: base-4.8.0.0 |
| Semigroup a => Semigroup (Identity a) | Since: base-4.9.0.0 |
| Monoid a => Monoid (Identity a) | Since: base-4.9.0.0 |
| Storable a => Storable (Identity a) | Since: base-4.9.0.0 |
Defined in Data.Functor.Identity Methods 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 () # | |
| Bits a => Bits (Identity a) | Since: base-4.9.0.0 |
Defined in Data.Functor.Identity 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 # 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 # | |
| FiniteBits a => FiniteBits (Identity a) | Since: base-4.9.0.0 |
Defined in Data.Functor.Identity Methods finiteBitSize :: Identity a -> Int # countLeadingZeros :: Identity a -> Int # countTrailingZeros :: Identity a -> Int # | |
| Generic1 Identity | Since: base-4.8.0.0 |
| type Rep (Identity a) | |
Defined in Data.Functor.Identity | |
| type Rep1 Identity | |
Defined in Data.Functor.Identity | |
class Applicative f => Alternative (f :: Type -> Type) where #
A monoid on applicative functors.
If defined, some and many should be the least solutions
of the equations:
Instances
class Bifunctor (p :: Type -> Type -> Type) where #
A bifunctor is a type constructor that takes
two type arguments and is a functor in both arguments. That
is, unlike with Functor, a type constructor such as Either
does not need to be partially applied for a Bifunctor
instance, and the methods in this class permit mapping
functions over the Left value or the Right value,
or both at the same time.
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:
bimapidid≡id
If you supply first and second, ensure:
firstid≡idsecondid≡id
If you supply both, you should also ensure:
bimapf g ≡firstf.secondg
These ensure by parametricity:
bimap(f.g) (h.i) ≡bimapf h.bimapg ifirst(f.g) ≡firstf.firstgsecond(f.g) ≡secondf.secondg
Since: base-4.8.0.0
Methods
bimap :: (a -> b) -> (c -> d) -> p a c -> p b d #
Map over both arguments at the same time.
bimapf g ≡firstf.secondg
Examples
>>>bimap toUpper (+1) ('j', 3)('J',4)
>>>bimap toUpper (+1) (Left 'j')Left 'J'
>>>bimap toUpper (+1) (Right 3)Right 4
Instances
| Bifunctor Either | Since: base-4.8.0.0 |
| Bifunctor (,) | Since: base-4.8.0.0 |
| Bifunctor Arg | Since: base-4.9.0.0 |
| Bifunctor Of Source # | |
| Bifunctor ((,,) x1) | Since: base-4.8.0.0 |
| Bifunctor (Const :: Type -> Type -> Type) | Since: base-4.8.0.0 |
| Bifunctor (K1 i :: Type -> Type -> Type) | Since: base-4.9.0.0 |
| Bifunctor ((,,,) x1 x2) | Since: base-4.8.0.0 |
| Bifunctor ((,,,,) x1 x2 x3) | Since: base-4.8.0.0 |
| Bifunctor ((,,,,,) x1 x2 x3 x4) | Since: base-4.8.0.0 |
| Bifunctor ((,,,,,,) x1 x2 x3 x4 x5) | Since: base-4.8.0.0 |
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.
'join bssdo expression
do bs <- bss bs
Examples
A common use of join is to run an IO computation returned from
an STM transaction, since STM transactions
can't perform IO directly. Recall that
atomically :: STM a -> IO a
is used to run STM transactions atomically. So, by
specializing the types of atomically and join to
atomically:: STM (IO b) -> IO (IO b)join:: IO (IO b) -> IO b
we can compose them as
join.atomically:: STM (IO b) -> IO b
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.
Some functors support an implementation of liftA2 that is more
efficient than the default one. In particular, if fmap is an
expensive operation, it is likely better to use liftA2 than to
fmap over the structure and then use <*>.
This became a typeclass method in 4.10.0.0. Prior to that, it was
a function defined in terms of <*> and fmap.
Using ApplicativeDo: 'liftA2 f as bsdo expression
do a <- as b <- bs pure (f a b)
liftA3 :: Applicative f => (a -> b -> c -> d) -> f a -> f b -> f c -> f d #
Lift a ternary function to actions.
Using ApplicativeDo: 'liftA3 f as bs csdo expression
do a <- as b <- bs c <- cs pure (f a b c)
void :: Functor f => f a -> f () #
void valueIO action.
Using ApplicativeDo: 'void asdo expression
do as pure ()
with an inferred Functor constraint.
Examples
Replace the contents of a Maybe Int
>>>void NothingNothing>>>void (Just 3)Just ()
Replace the contents of an Either Int IntEither 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