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

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

Defined in Streaming.Internal

Methods

get :: Stream f m s

put :: s -> Stream f m ()

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

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

Defined in Streaming.Internal

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

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)

Defined in Streaming.Internal

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)

Defined in Streaming.Internal

Methods

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

Functor f => MFunctor (Stream f :: (* -> *) -> * -> *)

Defined in Streaming.Internal

Methods

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

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

Defined in Streaming.Internal

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)

Defined in Streaming.Internal

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)

Defined in Streaming.Internal

Methods

pure :: a -> Stream f m a

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

liftA2 :: (a -> b -> c) -> Stream f m a -> Stream f m b -> Stream f m c

(*>) :: 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)

Defined in Streaming.Internal

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)

Defined in Streaming.Internal

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)

Defined in Streaming.Internal

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)

Defined in Streaming.Internal

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

Defined in Streaming.Internal

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)

Defined in Streaming.Internal

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)

Defined in Streaming.Internal

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)

Defined in Streaming.Internal

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)

Defined in Streaming.Internal

Methods

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

show :: Stream f m r -> String

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

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

Defined in Streaming.Internal

Methods

(<>) :: Stream f m w -> Stream f m w -> Stream f m w

sconcat :: NonEmpty (Stream f m w) -> Stream f m w

stimes :: Integral b => b -> Stream f m w -> Stream f m w

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

Defined in Streaming.Internal

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

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 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.

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

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 :> ())

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_

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

Construct an infinite stream by cycling a finite one

cycles = forever

>>> 

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

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
iterT alg = runIdentityT . iterTM (IdentityT . alg . fmap runIdentityT)

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

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
   

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

Inspecting a stream wrap by wrap

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

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)

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

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.

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.

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

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

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 ()

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

Zipping and unzipping 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

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.

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

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 :: (Functor m, Functor f) => (forall b. m b -> n b) -> Stream f m a -> Stream f n a

The same as hoist, but explicitly named to indicate that it is not entirely safe. In particular, its argument must be a monad morphism.

hoistExposedPost :: (Functor n, Functor f) => (forall b. m b -> n b) -> Stream f m a -> Stream f n a

The same as hoistExposed, but with a Functor constraint on the target rather than the source. This must be used only with a monad morphism.

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

Deprecated: Use maps instead.

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

Deprecated: Use mapsM instead.

destroyExposed :: (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 It permits distinctions that should be hidden, as can be seen from e.g.

isPure stream = destroyExposed (const True) (const False) (const True)

and similar nonsense. The crucial constraint is that the m x -> x argument is an Eilenberg-Moore algebra. See Atkey, "Reasoning about Stream Processing with Effects"

When in doubt, use destroy instead.