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

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

replicates n = takes n . repeats

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

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

Wrap an effect that returns a stream

effect = join . lift

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 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 :> ())

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

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

Construct an infinite stream by cycling a finite one

cycles = forever

>>> 

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 (liftM 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.

Repeat a

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

Dissolves the segmentation into layers of Stream f m layers.

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

iterT alg = streamFold return join alg

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

iterTM alg = streamFold return (join . lift)

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

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

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

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)

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.

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

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

Run the effects in a stream that merely layers effects.

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

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

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

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

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

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.

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" :> ()

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.