Streaming.Internal

The free monad transformer

The Stream data type is equivalent to FreeT and can represent any effectful succession of steps, where the form of the steps or commands is specified by the first (functor) parameter.

data Stream f m r = Step !(f (Stream f m r)) | Effect (m (Stream f m r)) | Return r

The producer concept uses the simple functor (a,_) - or the stricter Of a _ . Then the news at each step or layer is just: an individual item of type a. Since Stream (Of a) m r is equivalent to Pipe.Producer a m r, much of the pipes Prelude can easily be mirrored in a streaming Prelude. Similarly, a simple Consumer a m r or Parser a m r concept arises when the base functor is (a -> _) . Stream ((->) input) m result consumes input until it returns a result.

To avoid breaking reasoning principles, the constructors should not be used directly. A pattern-match should go by way of inspect - or, in the producer case, next

The constructors are exported by the Internal module.

data Stream f m r

Constructors

Step !(f (Stream f m r))

Effect (m (Stream f m r))

Return r

Instances

(MonadBase b m, Functor f) => MonadBase b (Stream f m)

Functor f => MFunctor (Stream f)

Functor f => MMonad (Stream f)

Functor f => MonadTrans (Stream f)

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

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

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

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

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

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

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

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

(Typeable (* -> *) f, Typeable (* -> *) m, Data r, Data (m (Stream f m r)), Data (f (Stream f m r))) => Data (Stream f m r)

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

Introducing a stream

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

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

Repeat a functorial layer, command or instruct several times.

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

Repeat a functorial layer, command or instruction forever.

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

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

Lift for items in the base functor. Makes a singleton or one-layer succession. It is named by similarity to lift:

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

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

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

destroy a b c (streamBuild psi)  = 

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

Construct an infinite stream by cycling a finite one

cycles = forever

>>> 

Eliminating a stream

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

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.

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 

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)

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

Map a stream directly to its church encoding; compare Data.List.foldr

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 . liftM 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

So for example, when we realize that

>>> :t streamFold return Q.mwrap
(Monad m, Functor f) =>
   (f (Q.ByteString m a) -> Q.ByteString m a)
   -> Stream f m a -> Q.ByteString m a

it is easy to see how to write fromChunks:

>>> streamFold return Q.mwrap (\(a:>b) -> Q.chunk a >>  b)
Monad m => Stream (Of B.ByteString) m a -> Q.ByteString m a -- fromChunks

Inspecting a stream wrap by wrap

inspect :: (Functor f, 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

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)

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)

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

mapped = mapsM 
mapsM phi = decompose . maps (Compose . phi)  

mapped obeys these rules:

mapped return       = id
mapped f . mapped g = mapped (f <=< g)
map f . mapped g    = mapped (liftM f . g)
mapped f . map g    = mapped (f . g)

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

Resort a succession of layers of the form m (f x). Though mapsM is best understood as:

mapsM phi = decompose . maps (Compose . phi)

we could as well define decompose by mapsM:

decompose = mapsM getCompose

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.

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.

Splitting streams

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

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 ()

Zipping and unzipping streams

zipsWith :: (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

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.

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.

>>> 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:

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

We can achieve the above effect more simply in the case of Stream (Of a) m r by using duplicate

>>> S.toList . S.filter even $ S.toList . S.filter odd $ S.duplicate $ 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

Assorted Data.Functor.x help

switch :: Sum f g r -> Sum g f r

Swap the order of functors in a sum of functors.

>>> S.toListM' $ S.print $ separate $ maps S.switch $ maps (S.distinguish (=='a')) $ S.each "banana"
'a'
'a'
'a'
"bnn" :> ()
>>> S.toListM' $ S.print $ separate $ maps (S.distinguish (=='a')) $ S.each "banana"
'b'
'n'
'n'
"aaa" :> ()

ResourceT help

bracketStream :: (Functor f, MonadResource m) => IO a -> (a -> IO ()) -> (a -> Stream f m b) -> Stream f m b

For use in implementation

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

This is akin to the observe of Pipes.Internal . It reeffects the layering in instances of Stream f m r so that it replicates that of FreeT.

hoistExposed :: (Monad m1, Functor f) => (m1 (Stream f m r) -> m (Stream f m r)) -> Stream f m1 r -> Stream f m r

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

mapsMExposed :: (Monad m, Functor f1) => (f1 (Stream f m r) -> m (f (Stream f m r))) -> Stream f1 m r -> Stream f m r

destroyExposed :: (Monad m, Functor f) => Stream f m t -> (f b -> b) -> (m b -> b) -> (t -> b) -> b