Streaming.Prelude

This names exported by this module are closely modeled on those in Prelude and Data.List, but also on Pipes.Prelude, Pipes.Group and Pipes.Parse. The module may be said to give independent expression to the conception of Producer / Source / Generator manipulation articulated in the latter two modules. Because we dispense with piping and conduiting, the distinction between all of these modules collapses. Some things are lost but much is gained: on the one hand, everything comes much closer to ordinary beginning Haskell programming and, on the other, acquires the plasticity of programming directly with a general free monad type. The leading type, Stream (Of a) m r is chosen to permit an api that is as close as possible to that of Data.List and the Prelude.

Import qualified thus:

import Streaming
import qualified Streaming.Prelude as S

For the examples below, one sometimes needs

import Streaming.Prelude (each, yield, next, mapped, stdoutLn, stdinLn)
import Data.Function ((&))

Other libraries that come up in passing are

import qualified Control.Foldl as L -- cabal install foldl
import qualified Pipes as P
import qualified Pipes.Prelude as P
import qualified System.IO as IO

Here are some correspondences between the types employed here and elsewhere:

              streaming             |            pipes               |       conduit       |  io-streams
-------------------------------------------------------------------------------------------------------------------
Stream (Of a) m ()                  | Producer a m ()                | Source m a          | InputStream a
                                    | ListT m a                      | ConduitM () o m ()  | Generator r ()
-------------------------------------------------------------------------------------------------------------------
Stream (Of a) m r                   | Producer a m r                 | ConduitM () o m r   | Generator a r
-------------------------------------------------------------------------------------------------------------------
Stream (Of a) m (Stream (Of a) m r) | Producer a m (Producer a m r)  |
--------------------------------------------------------------------------------------------------------------------
Stream (Stream (Of a) m) r          | FreeT (Producer a m) m r       |
--------------------------------------------------------------------------------------------------------------------
--------------------------------------------------------------------------------------------------------------------
ByteString m ()                     | Producer ByteString m ()       | Source m ByteString  | InputStream ByteString
--------------------------------------------------------------------------------------------------------------------

Types

data Of a b

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

Constructors

!a :> b infixr 5

Instances

Bifunctor Of

Methods

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

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

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

Eq2 Of

Methods

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

Ord2 Of

Methods

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

Show2 Of

Methods

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

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

Monoid a => Monad (Of a)

Methods

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

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

return :: a -> Of a a

fail :: String -> Of a a

Functor (Of a)

Methods

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

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

Monoid a => Applicative (Of a)

Methods

pure :: a -> Of a a

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

liftA2 :: (a -> b -> c) -> Of a a -> Of a b -> Of a c

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

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

Foldable (Of a)

Methods

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

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

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

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

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

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

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

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

toList :: Of a a -> [a]

null :: Of a a -> Bool

length :: Of a a -> Int

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

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

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

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

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

Traversable (Of a)

Methods

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

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

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

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

Eq a => Eq1 (Of a)

Methods

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

Ord a => Ord1 (Of a)

Methods

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

Show a => Show1 (Of a)

Methods

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

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

Generic1 * (Of a)

Associated Types

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

Methods

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

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

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

Methods

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

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

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

Methods

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

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

toConstr :: Of a b -> Constr

dataTypeOf :: Of a b -> DataType

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

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

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

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

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

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

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

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

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

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

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

Methods

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

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

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

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

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

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

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

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

Methods

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

readList :: ReadS [Of a b]

readPrec :: ReadPrec (Of a b)

readListPrec :: ReadPrec [Of a b]

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

Methods

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

show :: Of a b -> String

showList :: [Of a b] -> ShowS

Generic (Of a b)

Associated Types

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

Methods

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

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

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

Methods

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

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

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

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

Methods

mempty :: Of a b

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

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

type Rep1 * (Of a)

type Rep1 * (Of a) = D1 * (MetaData "Of" "Data.Functor.Of" "streaming-0.2.1.0-k62tIogCS784q9BtifVyf" False) (C1 * (MetaCons ":>" (InfixI RightAssociative 5) False) ((:*:) * (S1 * (MetaSel (Nothing Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) (Rec0 * a)) (S1 * (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) Par1)))

type Rep (Of a b)

type Rep (Of a b) = D1 * (MetaData "Of" "Data.Functor.Of" "streaming-0.2.1.0-k62tIogCS784q9BtifVyf" False) (C1 * (MetaCons ":>" (InfixI RightAssociative 5) False) ((:*:) * (S1 * (MetaSel (Nothing Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) (Rec0 * a)) (S1 * (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 * b))))

Introducing streams of elements

yield :: Monad m => a -> Stream (Of a) m ()

A singleton stream

>>> stdoutLn $ yield "hello"
hello

>>> S.sum $ do {yield 1; yield 2; yield 3}
6

>>> let number = lift (putStrLn "Enter a number:") >> lift readLn >>= yield :: Stream (Of Int) IO ()
>>> S.toList $ do {number; number; number}
Enter a number:
1<Enter>
Enter a number:
2<Enter>
Enter a number:
3<Enter>
[1,2,3] :> ()

each :: (Monad m, Foldable f) => f a -> Stream (Of a) m ()

Stream the elements of a pure, foldable container.

>>> S.print $ each [1..3]
1
2
3

stdinLn :: MonadIO m => Stream (Of String) m ()

View standard input as a Stream (Of String) m r. By contrast, stdoutLn renders a Stream (Of String) m r to standard output. The names follow Pipes.Prelude

>>> stdoutLn stdinLn
hello<Enter>
hello
world<Enter>
world
^CInterrupted.

>>> stdoutLn $ S.map reverse stdinLn
hello<Enter>
olleh
world<Enter>
dlrow
^CInterrupted.

readLn :: (MonadIO m, Read a) => Stream (Of a) m ()

Read values from stdin, ignoring failed parses.

>>> :set -XTypeApplications
>>> S.sum $ S.take 2 (S.readLn @IO @Int)
10<Enter>
12<Enter>
22 :> ()

>>> S.toList $ S.take 2 (S.readLn @IO @Int)
10<Enter>
1@#$%^&*\<Enter>
12<Enter>
[10,12] :> ()

fromHandle :: MonadIO m => Handle -> Stream (Of String) m ()

Read Strings from a Handle using hGetLine

Terminates on end of input

>>> IO.withFile "/usr/share/dict/words" IO.ReadMode $ S.stdoutLn . S.take 3 . S.drop 50000 .  S.fromHandle
deflagrator
deflate
deflation

iterate :: Monad m => (a -> a) -> a -> Stream (Of a) m r

Iterate a pure function from a seed value, streaming the results forever

iterateM :: Monad m => (a -> m a) -> m a -> Stream (Of a) m r

Iterate a monadic function from a seed value, streaming the results forever

repeat :: Monad m => a -> Stream (Of a) m r

Repeat an element ad inf. .

>>> S.print $ S.take 3 $ S.repeat 1
1
1
1

repeatM :: Monad m => m a -> Stream (Of a) m r

Repeat a monadic action ad inf., streaming its results.

>>> S.toList $ S.take 2 $ repeatM getLine
one<Enter>
two<Enter>
["one","two"]

replicate :: Monad m => Int -> a -> Stream (Of a) m ()

Repeat an element several times.

untilRight :: Monad m => m (Either a r) -> Stream (Of a) m r

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

Cycle repeatedly through the layers of a stream, ad inf. This function is functor-general

cycle = forever

>>> rest <- S.print $ S.splitAt 3 $ S.cycle (yield True >> yield False)
True
False
True
>>> S.print $ S.take 3 rest
False
True
False

replicateM :: Monad m => Int -> m a -> Stream (Of a) m ()

Repeat an action several times, streaming its results.

>>> S.print $ S.replicateM 2 getCurrentTime
2015-08-18 00:57:36.124508 UTC
2015-08-18 00:57:36.124785 UTC

enumFrom :: (Monad m, Enum n) => n -> Stream (Of n) m r

An infinite stream of enumerable values, starting from a given value. It is the same as S.iterate succ. Because their return type is polymorphic, enumFrom and enumFromThen (and iterate are useful for example with zip and zipWith, which require the same return type in the zipped streams. With each [1..] the following bit of connect-and-resume would be impossible:

>>> rest <- S.print $ S.zip (S.enumFrom 'a') $ S.splitAt 3 $ S.enumFrom 1
('a',1)
('b',2)
('c',3)
>>> S.print $ S.take 3 rest
4
5
6

enumFromThen :: (Monad m, Enum a) => a -> a -> Stream (Of a) m r

An infinite sequence of enumerable values at a fixed distance, determined by the first and second values. See the discussion of enumFrom

>>> S.print $ S.take 3 $ S.enumFromThen 100 200
100
200
300

unfoldr :: Monad m => (s -> m (Either r (a, s))) -> s -> Stream (Of a) m r

Build a Stream by unfolding steps starting from a seed. In particular note that S.unfoldr S.next = id.

The seed can of course be anything, but this is one natural way to consume a pipes Producer. Consider:

>>> S.stdoutLn $ S.take 2 $ S.unfoldr Pipes.next Pipes.stdinLn
hello<Enter>
hello
goodbye<Enter>
goodbye

>>> S.stdoutLn $ S.unfoldr Pipes.next (Pipes.stdinLn >-> Pipes.take 2)
hello<Enter>
hello
goodbye<Enter>
goodbye

>>> S.effects $ S.unfoldr Pipes.next (Pipes.stdinLn >-> Pipes.take 2 >-> Pipes.stdoutLn)
hello<Enter>
hello
goodbye<Enter>
goodbye

Pipes.unfoldr S.next similarly unfolds a Pipes.Producer from a stream.

Consuming streams of elements

stdoutLn :: MonadIO m => Stream (Of String) m () -> m ()

Write Strings to stdout using putStrLn; terminates on a broken output pipe (The name and implementation are modelled on the Pipes.Prelude stdoutLn).

>>> S.stdoutLn $ S.take 3 $ S.each $ words "one two three four five"
one
two
three

stdoutLn' :: MonadIO m => Stream (Of String) m r -> m r

Write Strings to stdout using putStrLn

Unlike stdoutLn, stdoutLn' does not handle a broken output pipe. Thus it can have a polymorphic return value, rather than (), and this kind of "connect and resume" is possible:

>>> rest <- S.stdoutLn' $ S.show $ S.splitAt 3 (each [1..5])
1
2
3
>>> S.toList rest
[4,5] :> ()

mapM_ :: Monad m => (a -> m b) -> Stream (Of a) m r -> m r

Reduce a stream to its return value with a monadic action.

>>> S.mapM_ Prelude.print $ each [1..3]
1
2
3

>>> rest <- S.mapM_ Prelude.print $ S.splitAt 3 $ each [1..10]
1
2
3
>>> S.sum rest
49 :> ()

print :: (MonadIO m, Show a) => Stream (Of a) m r -> m r

Print the elements of a stream as they arise.

>>> S.print $ S.take 2 S.stdinLn
hello<Enter>
"hello"
world<Enter>
"world"
>>> 

toHandle :: MonadIO m => Handle -> Stream (Of String) m r -> m r

Write a succession of strings to a handle as separate lines.

>>> S.toHandle IO.stdout $ each (words "one two three")
one
two
three

effects :: Monad m => Stream (Of a) m r -> m r

Reduce a stream, performing its actions but ignoring its elements.

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

effects should be understood together with copy and is subject to the rules

S.effects . S.copy       = id
hoist S.effects . S.copy = id

The similar effects and copy operations in Data.ByteString.Streaming obey the same rules.

erase :: Monad m => Stream (Of a) m r -> Stream Identity m r

Remove the elements from a stream of values, retaining the structure of layers.

drained :: (Monad m, Monad (t m), MonadTrans t) => t m (Stream (Of a) m r) -> t m r

Where a transformer returns a stream, run the effects of the stream, keeping the return value. This is usually used at the type

drained :: Monad m => Stream (Of a) m (Stream (Of b) m r) -> Stream (Of a) m r
drained = join . fmap (lift . effects)

Here, for example, we split a stream in two places and throw out the middle segment:

>>> rest <- S.print $ S.drained $ S.splitAt 2 $ S.splitAt 5 $ each [1..7]
1
2
>>> S.print rest
6
7

In particular, we can define versions of take and takeWhile which retrieve the return value of the rest of the stream - and which can thus be used with maps:

take' n = S.drained . S.splitAt n
takeWhile' thus = S.drained . S.span thus

Stream transformers

map :: Monad m => (a -> b) -> Stream (Of a) m r -> Stream (Of b) m r

Standard map on the elements of a stream.

>>> S.stdoutLn $ S.map reverse $ each (words "alpha beta")
ahpla
ateb

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

Replace each element of a stream with the result of a monadic action

>>> S.print $ S.mapM readIORef $ S.chain (\ior -> modifyIORef ior (*100)) $ S.mapM newIORef $ each [1..6]
100
200
300
400
500
600

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

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

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

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

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

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

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

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

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

let noteBeginning text x = putStrLn text >> return text

this puts the is completely functor-general

maps and mapped obey these rules:

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

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

mapped phi = decompose . maps (Compose . phi)

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

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

for :: (Monad m, Functor f) => Stream (Of a) m r -> (a -> Stream f m x) -> Stream f m r

for replaces each element of a stream with an associated stream. Note that the associated stream may layer any functor.

with :: (Monad m, Functor f) => Stream (Of a) m r -> (a -> f x) -> Stream f m r

Replace each element in a stream of individual Haskell values (a Stream (Of a) m r) with an associated functorial step.

for str f  = concats (with str f)
with str f = for str (yields . f)
with str f = maps (\(a:>r) -> r <$ f a) str
with = flip subst
subst = flip with

>>> with (each [1..3]) (yield . show) & intercalates (yield "--") & S.stdoutLn
1
--
2
--
3

subst :: (Monad m, Functor f) => (a -> f x) -> Stream (Of a) m r -> Stream f m r

Replace each element in a stream of individual values with a functorial layer of any sort. subst = flip with and is more convenient in a sequence of compositions that transform a stream.

with = flip subst
for str f = concats $ subst f str
subst f = maps (\(a:>r) -> r <$ f a)
S.concat = concats . subst each

copy :: Monad m => Stream (Of a) m r -> Stream (Of a) (Stream (Of a) m) r

Duplicate the content of stream, so that it can be acted on twice in different ways, but without breaking streaming. Thus, with each [1,2] I might do:

>>> S.print $ each ["one","two"]
"one"
"two"
>>> S.stdoutLn $ each ["one","two"]
one
two

With copy, I can do these simultaneously:

>>> S.print $ S.stdoutLn $ S.copy $ each ["one","two"]
one
"one"
two
"two"

copy should be understood together with effects and is subject to the rules

S.effects . S.copy       = id
hoist S.effects . S.copy = id

The similar operations in Streaming obey the same rules.

Where the actions you are contemplating are each simple folds over the elements, or a selection of elements, then the coupling of the folds is often more straightforwardly effected with Foldl, e.g.

>>> L.purely S.fold (liftA2 (,) L.sum L.product) $ each [1..10]
(55,3628800) :> ()

rather than

>>> S.sum $ S.product . S.copy $ each [1..10]
55 :> (3628800 :> ())

A Control.Foldl fold can be altered to act on a selection of elements by using handles on an appropriate lens. Some such manipulations are simpler and more List-like, using copy:

>>> L.purely S.fold (liftA2 (,) (L.handles (filtered odd) L.sum) (L.handles (filtered even) L.product)) $ each [1..10]
(25,3840) :> ()

becomes

>>> S.sum $ S.filter odd $ S.product $ S.filter even $ S.copy $ each [1..10]
25 :> (3840 :> ())

or using store

>>> S.sum $ S.filter odd $ S.store (S.product . S.filter even) $ each [1..10]
25 :> (3840 :> ())

But anything that fold of a Stream (Of a) m r into e.g. an m (Of b r) that has a constraint on m that is carried over into Stream f m - e.g. Monad, MonadIO, MonadResource, etc. can be used on the stream. Thus, I can fold over different groupings of the original stream:

>>> (S.toList . mapped S.toList . chunksOf 5) $  (S.toList . mapped S.toList . chunksOf 3) $ S.copy $ each [1..10]
[[1,2,3,4,5],[6,7,8,9,10]] :> ([[1,2,3],[4,5,6],[7,8,9],[10]] :> ())

The procedure can be iterated as one pleases, as one can see from this (otherwise unadvisable!) example:

>>> (S.toList . mapped S.toList . chunksOf 4) $ (S.toList . mapped S.toList . chunksOf 3) $ S.copy $ (S.toList . mapped S.toList . chunksOf 2) $ S.copy $ each [1..12]
[[1,2,3,4],[5,6,7,8],[9,10,11,12]] :> ([[1,2,3],[4,5,6],[7,8,9],[10,11,12]] :> ([[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] :> ()))

copy can be considered a special case of expand:

  copy = expand $ p (a :> as) -> a :> p (a :> as)

If Of were an instance of Comonad, then one could write

  copy = expand extend

duplicate :: Monad m => Stream (Of a) m r -> Stream (Of a) (Stream (Of a) m) r

store :: Monad m => (Stream (Of a) (Stream (Of a) m) r -> t) -> Stream (Of a) m r -> t

Store the result of any suitable fold over a stream, keeping the stream for further manipulation. store f = f . copy :

>>> S.print $ S.store S.product $ each [1..4]
1
2
3
4
24 :> ()

>>> S.print $ S.store S.sum $ S.store S.product $ each [1..4]
1
2
3
4
10 :> (24 :> ())

Here the sum (10) and the product (24) have been 'stored' for use when finally we have traversed the stream with print . Needless to say, a second pass is excluded conceptually, so the folds that you apply successively with store are performed simultaneously, and in constant memory -- as they would be if, say, you linked them together with Control.Fold:

>>> L.impurely S.foldM (liftA3 (\a b c -> (b,c)) (L.sink print) (L.generalize L.sum) (L.generalize L.product)) $ each [1..4]
1
2
3
4
(10,24) :> ()

Fusing folds after the fashion of Control.Foldl will generally be a bit faster than the corresponding succession of uses of store, but by constant factor that will be completely dwarfed when any IO is at issue.

But store copy is much/ more powerful, as you can see by reflecting on uses like this:

>>> S.sum $ S.store (S.sum . mapped S.product . chunksOf 2) $ S.store (S.product . mapped S.sum . chunksOf 2 )$ each [1..6]
21 :> (44 :> (231 :> ()))

It will be clear that this cannot be reproduced with any combination of lenses, Control.Fold folds, or the like. (See also the discussion of copy.)

It would conceivable be clearer to import a series of specializations of store. It is intended to be used at types like these:

storeM ::  (forall s m . Monad m => Stream (Of a) m s -> m (Of b s))
        -> (Monad n => Stream (Of a) n r -> Stream (Of a) n (Of b r))
storeM = store

storeMIO :: (forall s m . MonadIO m => Stream (Of a) m s -> m (Of b s))
         -> ( MonadIO n => Stream (Of a) n r -> Stream (Of a) n (Of b r)
storeMIO = store

It is clear from these types that we are just using the general instances:

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

We thus can't be touching the elements of the stream, or the final return value. It is the same with other constraints that Stream (Of a) inherits from the underlying monad, like MonadResource. Thus I can independently filter and write to one file, but nub and write to another, or interact with a database and a logfile and the like:

>>> runResourceT $ (S.writeFile "hello2.txt" . S.nub) $ store (S.writeFile "hello.txt" . S.filter (/= "world")) $ each ["hello", "world", "goodbye", "world"]
>>> :! cat hello.txt
hello
goodbye
>>> :! cat hello2.txt
hello
world
goodbye

chain :: Monad m => (a -> m ()) -> Stream (Of a) m r -> Stream (Of a) m r

Apply an action to all values, re-yielding each

>>> S.product $ S.chain Prelude.print $ S.each [1..5]
1
2
3
4
5
120 :> ()

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

Streams the number of seconds from the beginning of action

Thus, to mark times of user input we might write something like:

>>> S.toList $ S.take 3 $ S.zip S.seconds S.stdinLn
a<Enter>
b<Enter>
c<Enter>
[(0.0,"a"),(1.088711,"b"),(3.7289649999999996,"c")] :> ()

To restrict user input to some number of seconds, we might write:

>>> S.toList $ S.map fst $ S.zip S.stdinLn $ S.takeWhile (< 3) S.seconds
one<Enter>
two<Enter>
three<Enter>
four<Enter>
five<Enter>
["one","two","three","four","five"] :> ()

This of course does not interrupt an action that has already begun.

Like the sequence but streaming. The result type is a stream of a's, but is not accumulated; the effects of the elements of the original stream are interleaved in the resulting stream. Compare:

sequence :: Monad m =>       [m a]           -> m [a]
sequence :: Monad m => Stream (Of (m a)) m r -> Stream (Of a) m r

This obeys the rule

filter :: Monad m => (a -> Bool) -> Stream (Of a) m r -> Stream (Of a) m r

Skip elements of a stream that fail a predicate

filterM :: Monad m => (a -> m Bool) -> Stream (Of a) m r -> Stream (Of a) m r

Skip elements of a stream that fail a monadic test

mapMaybeM :: Monad m => (a -> m (Maybe b)) -> Stream (Of a) m r -> Stream (Of b) m r

Map monadically over a stream, producing a new stream only containing the Just values.

delay :: MonadIO m => Double -> Stream (Of a) m r -> Stream (Of a) m r

Interpolate a delay of n seconds between yields.

intersperse :: Monad m => a -> Stream (Of a) m r -> Stream (Of a) m r

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

End a stream after n elements; the original return value is thus lost. splitAt preserves this information. Note that, like splitAt, this function is functor-general, so that, for example, you can take not just a number of items from a stream of elements, but a number of substreams and the like.

>>> S.toList $ S.take 3 $ each "with"
"wit" :> ()

>>> runResourceT $ S.stdoutLn $ S.take 3 $ S.readFile "stream.hs"
import Streaming
import qualified Streaming.Prelude as S
import Streaming.Prelude (each, next, yield)

takeWhile :: Monad m => (a -> Bool) -> Stream (Of a) m r -> Stream (Of a) m ()

End stream when an element fails a condition; the original return value is lost. By contrast span preserves this information, and is generally more desirable.

S.takeWhile thus = void . S.span thus

To preserve the information - but thus also force the rest of the stream to be developed - write

S.drained . S.span thus

as dropWhile thus is

S.effects . S.span thus

takeWhileM :: Monad m => (a -> m Bool) -> Stream (Of a) m r -> Stream (Of a) m ()

Like takeWhile, but takes a monadic predicate.

drop :: Monad m => Int -> Stream (Of a) m r -> Stream (Of a) m r

Ignore the first n elements of a stream, but carry out the actions

>>> S.toList $ S.drop 2 $  S.replicateM 5 getLine
a<Enter>
b<Enter>
c<Enter>
d<Enter>
e<Enter>
["c","d","e"] :> ()

Because it retains the final return value, drop n is a suitable argument for maps:

>>> S.toList $ concats $ maps (S.drop 4) $ chunksOf 5 $ each [1..20]
[5,10,15,20] :> ()

dropWhile :: Monad m => (a -> Bool) -> Stream (Of a) m r -> Stream (Of a) m r

Ignore elements of a stream until a test succeeds, retaining the rest.

>>> S.print $ S.dropWhile ((< 5) . length) S.stdinLn
one<Enter>
two<Enter>
three<Enter>
"three"
four<Enter>
"four"
^CInterrupted.

concat :: (Monad m, Foldable f) => Stream (Of (f a)) m r -> Stream (Of a) m r

Make a stream of traversable containers into a stream of their separate elements. This is just

concat str = for str each

>>> S.print $ S.concat (each ["xy","z"])
'x'
'y'
'z'

Note that it also has the effect of catMaybes, rights 'map snd' and such-like operations.

>>> S.print $ S.concat $ S.each [Just 1, Nothing, Just 2]
1
2
>>> S.print $  S.concat $ S.each [Right 1, Left "Error!", Right 2]
1
2
>>> S.print $ S.concat $ S.each [('A',1), ('B',2)]
1
2

scan :: Monad m => (x -> a -> x) -> x -> (x -> b) -> Stream (Of a) m r -> Stream (Of b) m r

Strict left scan, streaming, e.g. successive partial results. The seed is yielded first, before any action of finding the next element is performed.

>>> S.print $ S.scan (++) "" id $ each (words "a b c d")
""
"a"
"ab"
"abc"
"abcd"

scan is fitted for use with Control.Foldl, thus:

>>> S.print $ L.purely S.scan L.list $ each [3..5]
[]
[3]
[3,4]
[3,4,5]

scanM :: Monad m => (x -> a -> m x) -> m x -> (x -> m b) -> Stream (Of a) m r -> Stream (Of b) m r

Strict left scan, accepting a monadic function. It can be used with FoldMs from Control.Foldl using impurely. Here we yield a succession of vectors each recording

>>> let v =  L.impurely scanM L.vector $ each [1..4::Int] :: Stream (Of (U.Vector Int)) IO ()
>>> S.print v
fromList []
fromList [1]
fromList [1,2]
fromList [1,2,3]
fromList [1,2,3,4]

scanned :: Monad m => (x -> a -> x) -> x -> (x -> b) -> Stream (Of a) m r -> Stream (Of (a, b)) m r

read :: (Monad m, Read a) => Stream (Of String) m r -> Stream (Of a) m r

Make a stream of strings into a stream of parsed values, skipping bad cases

>>> S.sum_ $ S.read $ S.takeWhile (/= "total") S.stdinLn :: IO Int
1000<Enter>
2000<Enter>
total<Enter>
3000

show :: (Monad m, Show a) => Stream (Of a) m r -> Stream (Of String) m r

cons :: Monad m => a -> Stream (Of a) m r -> Stream (Of a) m r

The natural cons for a Stream (Of a).

cons a stream = yield a >> stream

Useful for interoperation:

Data.Text.foldr S.cons (return ()) :: Text -> Stream (Of Char) m ()
Lazy.foldrChunks S.cons (return ()) :: Lazy.ByteString -> Stream (Of Strict.ByteString) m ()

and so on.

slidingWindow :: Monad m => Int -> Stream (Of a) m b -> Stream (Of (Seq a)) m b

slidingWindow accumulates the first n elements of a stream, update thereafter to form a sliding window of length n. It follows the behavior of the slidingWindow function in conduit-combinators.

>>> S.print $ slidingWindow 4 $ S.each "123456"
fromList "1234"
fromList "2345"
fromList "3456"

Splitting and inspecting streams of elements

next :: Monad m => Stream (Of a) m r -> m (Either r (a, Stream (Of a) m r))

The standard way of inspecting the first item in a stream of elements, if the stream is still 'running'. The Right case contains a Haskell pair, where the more general inspect would return a left-strict pair. There is no reason to prefer inspect since, if the Right case is exposed, the first element in the pair will have been evaluated to whnf.

next :: Monad m => Stream (Of a) m r -> m (Either r (a, Stream (Of a) m r))
inspect :: Monad m => Stream (Of a) m r -> m (Either r (Of a (Stream (Of a) m r)))

Interoperate with pipes producers thus:

Pipes.unfoldr Stream.next :: Stream (Of a) m r -> Producer a m r
Stream.unfoldr Pipes.next :: Producer a m r -> Stream (Of a) m r

Similarly:

IOStreams.unfoldM (fmap (either (const Nothing) Just) . next) :: Stream (Of a) IO b -> IO (InputStream a)
Conduit.unfoldM (fmap (either (const Nothing) Just) . next)   :: Stream (Of a) m r -> Source a m r

But see uncons, which is better fitted to these unfoldMs

uncons :: Monad m => Stream (Of a) m r -> m (Maybe (a, Stream (Of a) m r))

Inspect the first item in a stream of elements, without a return value. uncons provides convenient exit into another streaming type:

IOStreams.unfoldM uncons :: Stream (Of a) IO b -> IO (InputStream a)
Conduit.unfoldM uncons   :: Stream (Of a) m r -> Conduit.Source m a

splitAt :: (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. This function is the same as the splitsAt exported by the Streaming module, but since this module is imported qualified, it can usurp a Prelude name. It specializes to:

 splitAt :: (Monad m, Functor f) => Int -> Stream (Of a) m r -> Stream (Of a) m (Stream (Of a) m r)

split :: (Eq a, Monad m) => a -> Stream (Of a) m r -> Stream (Stream (Of a) m) m r

Split a stream of elements wherever a given element arises. The action is like that of words.

>>> S.stdoutLn $ mapped S.toList $ S.split ' ' $ each "hello world  "
hello
world

breaks :: Monad m => (a -> Bool) -> Stream (Of a) m r -> Stream (Stream (Of a) m) m r

break :: Monad m => (a -> Bool) -> Stream (Of a) m r -> Stream (Of a) m (Stream (Of a) m r)

Break a sequence upon meeting element falls under a predicate, keeping it and the rest of the stream as the return value.

>>> rest <- S.print $ S.break even $ each [1,1,2,3]
1
1
>>> S.print rest
2
3

breakWhen :: Monad m => (x -> a -> x) -> x -> (x -> b) -> (b -> Bool) -> Stream (Of a) m r -> Stream (Of a) m (Stream (Of a) m r)

Yield elements, using a fold to maintain state, until the accumulated value satifies the supplied predicate. The fold will then be short-circuited and the element that breaks it will be put after the break. This function is easiest to use with purely

>>> rest <- each [1..10] & L.purely S.breakWhen L.sum (>10) & S.print
1
2
3
4
>>> S.print rest
5
6
7
8
9
10

span :: Monad m => (a -> Bool) -> Stream (Of a) m r -> Stream (Of a) m (Stream (Of a) m r)

Stream elements until one fails the condition, return the rest.

group :: (Monad m, Eq a) => Stream (Of a) m r -> Stream (Stream (Of a) m) m r

Group successive equal items together

>>> S.toList $ mapped S.toList $ S.group $ each "baaaaad"
["b","aaaaa","d"] :> ()

>>> S.toList $ concats $ maps (S.drained . S.splitAt 1) $ S.group $ each "baaaaaaad"
"bad" :> ()

groupBy :: Monad m => (a -> a -> Bool) -> Stream (Of a) m r -> Stream (Stream (Of a) m) m r

Group elements of a stream in accordance with the supplied comparison.

>>> S.print $ mapped S.toList $ S.groupBy (>=) $ each [1,2,3,1,2,3,4,3,2,4,5,6,7,6,5]
[1]
[2]
[3,1,2,3]
[4,3,2,4]
[5]
[6]
[7,6,5]

Sum and Compose manipulation

distinguish :: (a -> Bool) -> Of a r -> Sum (Of a) (Of a) r

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" :> ()

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

eitherToSum :: Of (Either a b) r -> Sum (Of a) (Of b) r

sumToEither :: Sum (Of a) (Of b) r -> Of (Either a b) r

sumToCompose :: Sum f f r -> Compose (Of Bool) f r

composeToSum :: Compose (Of Bool) f r -> Sum f f r

Folds

Use these to fold the elements of a Stream.

>>> S.fold_ (+) 0 id $ S.each [1..0]
50

The general folds fold, fold_', foldM and foldM_ are arranged for use with Control.Foldl purely and impurely

>>> L.purely fold_ L.sum $ each [1..10]
55
>>> L.purely fold_ (liftA3 (,,) L.sum L.product L.list) $ each [1..10]
(55,3628800,[1,2,3,4,5,6,7,8,9,10])

All functions marked with an underscore omit (e.g. fold_, sum_) the stream's return value in a left-strict pair. They are good for exiting streaming completely, but when you are, e.g. mapped-ing over a Stream (Stream (Of a) m) m r, which is to be compared with [[a]]. Specializing, we have e.g.

 mapped sum :: (Monad m, Num n) => Stream (Stream (Of Int)) IO () -> Stream (Of n) IO ()
 mapped (fold mappend mempty id) :: Stream (Stream (Of Int)) IO () -> Stream (Of Int) IO ()

>>> S.print $ mapped S.sum $ chunksOf 3 $ S.each [1..10]
6
15
24
10

>>> let three_folds = L.purely S.fold (liftA3 (,,) L.sum L.product L.list)
>>> S.print $ mapped three_folds $ chunksOf 3 (each [1..10])
(6,6,[1,2,3])
(15,120,[4,5,6])
(24,504,[7,8,9])
(10,10,[10])

fold :: Monad m => (x -> a -> x) -> x -> (x -> b) -> Stream (Of a) m r -> m (Of b r)

Strict fold of a Stream of elements that preserves the return value. The third parameter will often be id where a fold is written by hand:

>>> S.fold (+) 0 id $ each [1..10]
55 :> ()

>>> S.fold (*) 1 id $ S.fold (+) 0 id $ S.copy $ each [1..10]
3628800 :> (55 :> ())

It can be used to replace a standard Haskell type with one more suited to writing a strict accumulation function. It is also crucial to the Applicative instance for Control.Foldl.Fold We can apply such a fold purely

Control.Foldl.purely S.fold :: Monad m => Fold a b -> Stream (Of a) m r -> m (Of b r)

Thus, specializing a bit:

L.purely S.fold L.sum :: Stream (Of Int) Int r -> m (Of Int r)
mapped (L.purely S.fold L.sum) :: Stream (Stream (Of Int)) IO r -> Stream (Of Int) IO r

Here we use the Applicative instance for Control.Foldl.Fold to stream three-item segments of a stream together with their sums and products.

>>> S.print $ mapped (L.purely S.fold (liftA3 (,,) L.list L.product L.sum)) $ chunksOf 3 $ each [1..10]
([1,2,3],6,6)
([4,5,6],120,15)
([7,8,9],504,24)
([10],10,10)

fold_ :: Monad m => (x -> a -> x) -> x -> (x -> b) -> Stream (Of a) m r -> m b

Strict fold of a Stream of elements, preserving only the result of the fold, not the return value of the stream. The third parameter will often be id where a fold is written by hand:

>>> S.fold_ (+) 0 id $ each [1..10]
55

It can be used to replace a standard Haskell type with one more suited to writing a strict accumulation function. It is also crucial to the Applicative instance for Control.Foldl.Fold

Control.Foldl.purely fold :: Monad m => Fold a b -> Stream (Of a) m () -> m b

foldM :: Monad m => (x -> a -> m x) -> m x -> (x -> m b) -> Stream (Of a) m r -> m (Of b r)

Strict, monadic fold of the elements of a 'Stream (Of a)'

Control.Foldl.impurely foldM' :: Monad m => FoldM a b -> Stream (Of a) m r -> m (b, r)

Thus to accumulate the elements of a stream as a vector, together with a random element we might write:

>>> L.impurely S.foldM (liftA2 (,) L.vector L.random) $ each [1..10::Int] :: IO (Of (U.Vector Int,Maybe Int) ())
([1,2,3,4,5,6,7,8,9,10],Just 9) :> ()

foldM_ :: Monad m => (x -> a -> m x) -> m x -> (x -> m b) -> Stream (Of a) m r -> m b

Strict, monadic fold of the elements of a 'Stream (Of a)'

Control.Foldl.impurely foldM :: Monad m => FoldM a b -> Stream (Of a) m () -> m b

all :: Monad m => (a -> Bool) -> Stream (Of a) m r -> m (Of Bool r)

all_ :: Monad m => (a -> Bool) -> Stream (Of a) m r -> m Bool

any :: Monad m => (a -> Bool) -> Stream (Of a) m r -> m (Of Bool r)

any_ :: Monad m => (a -> Bool) -> Stream (Of a) m r -> m Bool

sum :: (Monad m, Num a) => Stream (Of a) m r -> m (Of a r)

Fold a Stream of numbers into their sum with the return value

 mapped S.sum :: Stream (Stream (Of Int)) m r -> Stream (Of Int) m r

>>> S.sum $ each [1..10]
55 :> ()

>>> (n :> rest)  <- S.sum $ S.splitAt 3 $ each [1..10]
>>> print n
6
>>> (m :> rest') <- S.sum $ S.splitAt 3 rest
>>> print m
15
>>> S.print rest'
7
8
9

sum_ :: (Monad m, Num a) => Stream (Of a) m () -> m a

Fold a Stream of numbers into their sum

product :: (Monad m, Num a) => Stream (Of a) m r -> m (Of a r)

Fold a Stream of numbers into their product with the return value

 maps' product' :: Stream (Stream (Of Int)) m r -> Stream (Of Int) m r

product_ :: (Monad m, Num a) => Stream (Of a) m () -> m a

Fold a Stream of numbers into their product

head :: Monad m => Stream (Of a) m r -> m (Of (Maybe a) r)

head_ :: Monad m => Stream (Of a) m r -> m (Maybe a)

last :: Monad m => Stream (Of a) m r -> m (Of (Maybe a) r)

last_ :: Monad m => Stream (Of a) m r -> m (Maybe a)

elem :: (Monad m, Eq a) => a -> Stream (Of a) m r -> m (Of Bool r)

Exhaust a stream remembering only whether a was an element.

elem_ :: (Monad m, Eq a) => a -> Stream (Of a) m r -> m Bool

notElem :: (Monad m, Eq a) => a -> Stream (Of a) m r -> m (Of Bool r)

Exhaust a stream deciding whether a was an element.

notElem_ :: (Monad m, Eq a) => a -> Stream (Of a) m r -> m Bool

length :: Monad m => Stream (Of a) m r -> m (Of Int r)

Run a stream, keeping its length and its return value.

>>> S.print $ mapped S.length $ chunksOf 3 $ S.each [1..10]
3
3
3
1

length_ :: Monad m => Stream (Of a) m r -> m Int

Run a stream, remembering only its length:

>>> S.length $ S.each [1..10]
10

toList :: Monad m => Stream (Of a) m r -> m (Of [a] r)

Convert an effectful Stream into a list alongside the return value

 mapped toList :: Stream (Stream (Of a)) m r -> Stream (Of [a]) m

Like toList_, toList breaks streaming; unlike toList_ it preserves the return value and thus is frequently useful with e.g. mapped

>>> S.print $ mapped S.toList $ chunksOf 3 $ each [1..9]
[1,2,3]
[4,5,6]
[7,8,9]
>>> S.print $ mapped S.toList $ chunksOf 2 $ S.replicateM 4 getLine
s<Enter>
t<Enter>
["s","t"]
u<Enter>
v<Enter>
["u","v"] 

toList_ :: Monad m => Stream (Of a) m () -> m [a]

Convert an effectful 'Stream (Of a)' into a list of as

Note: Needless to say, this function does not stream properly. It is basically the same as Prelude mapM which, like replicateM, sequence and similar operations on traversable containers is a leading cause of space leaks.

mconcat :: (Monad m, Monoid w) => Stream (Of w) m r -> m (Of w r)

Fold streamed items into their monoidal sum

>>> S.mconcat $ S.take 2 $ S.map (Data.Monoid.Last . Just) (S.stdinLn)
first<Enter>
last<Enter>
Last {getLast = Just "last"} :> ()

mconcat_ :: (Monad m, Monoid w) => Stream (Of w) m r -> m w

minimum :: (Monad m, Ord a) => Stream (Of a) m r -> m (Of (Maybe a) r)

minimum_ :: (Monad m, Ord a) => Stream (Of a) m r -> m (Maybe a)

maximum :: (Monad m, Ord a) => Stream (Of a) m r -> m (Of (Maybe a) r)

maximum_ :: (Monad m, Ord a) => Stream (Of a) m r -> m (Maybe a)

foldrM :: Monad m => (a -> m r -> m r) -> Stream (Of a) m r -> m r

A natural right fold for consuming a stream of elements. See also the more general iterT in the Streaming module and the still more general destroy

foldrT :: (Monad m, MonadTrans t, Monad (t m)) => (a -> t m r -> t m r) -> Stream (Of a) m r -> t m r

A natural right fold for consuming a stream of elements. See also the more general iterTM in the Streaming module and the still more general destroy

foldrT (\a p -> Streaming.yield a >> p) = id
foldrT (\a p -> Pipes.yield a     >> p) :: Monad m => Stream (Of a) m r -> Producer a m r
foldrT (\a p -> Conduit.yield a   >> p) :: Monad m => Stream (Of a) m r -> Conduit a m r

Zips and unzips

zip :: Monad m => Stream (Of a) m r -> Stream (Of b) m r -> Stream (Of (a, b)) m r

Zip two Streamss

zipWith :: Monad m => (a -> b -> c) -> Stream (Of a) m r -> Stream (Of b) m r -> Stream (Of c) m r

Zip two Streamss using the provided combining function

zip3 :: Monad m => Stream (Of a) m r -> Stream (Of b) m r -> Stream (Of c) m r -> Stream (Of (a, b, c)) m r

Zip three streams together

zipWith3 :: Monad m => (a -> b -> c -> d) -> Stream (Of a) m r -> Stream (Of b) m r -> Stream (Of c) m r -> Stream (Of d) m r

Zip three Streams with a combining function

unzip :: Monad m => Stream (Of (a, b)) m r -> Stream (Of a) (Stream (Of b) m) r

The type

Data.List.unzip     :: [(a,b)] -> ([a],[b])

might lead us to expect

Streaming.unzip :: Stream (Of (a,b)) m r -> Stream (Of a) m (Stream (Of b) m r)

which would not stream, since it would have to accumulate the second stream (of bs). Of course, Data.List unzip doesn't stream either.

This unzip does stream, though of course you can spoil this by using e.g. toList:

>>> let xs =  map (\x-> (x,show x)) [1..5::Int]

>>> S.toList $ S.toList $ S.unzip (S.each xs)
["1","2","3","4","5"] :> ([1,2,3,4,5] :> ())

>>> Prelude.unzip xs
([1,2,3,4,5],["1","2","3","4","5"])

Note the difference of order in the results. It may be of some use to think why. The first application of toList was applied to a stream of integers:

>>> :t S.unzip $ S.each xs
S.unzip $ S.each xs :: Monad m => Stream (Of Int) (Stream (Of String) m) ()

Like any fold, toList takes no notice of the monad of effects.

toList :: Monad m => Stream (Of a) m r -> m (Of [a] r)

In the case at hand (since I am in ghci) m = Stream (Of String) IO. So when I apply toList, I exhaust that stream of integers, folding it into a list:

>>> :t S.toList $ S.unzip $ S.each xs
S.toList $ S.unzip $ S.each xs
  :: Monad m => Stream (Of String) m (Of [Int] ())

When I apply toList to this, I reduce everything to an ordinary action in IO, and return a list of strings:

>>> S.toList $ S.toList $ S.unzip (S.each xs)
["1","2","3","4","5"] :> ([1,2,3,4,5] :> ())

unzip can be considered a special case of either unzips or expand:

  unzip = unzips . maps (((a,b) :> x) -> Compose (a :> b :> x))
  unzip = expand $ p ((a,b) :> abs) -> b :> p (a :> abs)

partitionEithers :: Monad m => Stream (Of (Either a b)) m r -> Stream (Of a) (Stream (Of b) m) r

Separate left and right values in distinct streams. (separate is a more powerful, functor-general, equivalent using Sum in place of Either). So, for example, to permit unlimited user input of Ints on condition of only two errors, we might write:

>>> S.toList $ S.print $ S.take 2 $ partitionEithers $ S.map readEither $ S.stdinLn  :: IO (Of [Int] ())
1<Enter>
2<Enter>
qqqqqqqqqq<Enter>
"Prelude.read: no parse"
3<Enter>
rrrrrrrrrr<Enter>
"Prelude.read: no parse"
[1,2,3] :> ()

partitionEithers = separate . maps S.eitherToSum
lefts  = hoist S.effects . partitionEithers
rights = S.effects . partitionEithers
rights = S.concat

partition :: Monad m => (a -> Bool) -> Stream (Of a) m r -> Stream (Of a) (Stream (Of a) m) r

filter p = hoist effects (partition p)

Maybes

These functions discard the Nothings that they encounter. They are analogous to the functions from Data.Maybe that share their names.

catMaybes :: Monad m => Stream (Of (Maybe a)) m r -> Stream (Of a) m r

The catMaybes function takes a Stream of Maybes and returns a Stream of all of the Just values. concat has the same behavior, but is more general; it works for any foldable container type.

mapMaybe :: Monad m => (a -> Maybe b) -> Stream (Of a) m r -> Stream (Of b) m r

The mapMaybe function is a version of map which can throw out elements. In particular, the functional argument returns something of type Maybe b. If this is Nothing, no element is added on to the result Stream. If it is Just b, then b is included in the result Stream.

Pair manipulation

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

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

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

then we can restate some types as follows:

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

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

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

i.e.

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

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

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

Thus we can maps it in turn.

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

Convert a standard Haskell pair into a left-strict pair

fst' :: Of a b -> a

fst' and snd' extract the first and second element of a pair

>>> S.fst' (1:>"hi")
1
>>> S.snd' (1:>"hi")
"hi"

They are contained in the _first and _second lenses, if any lens library is in scope

>>> import Lens.Micro
>>> (1:>"hi") ^. S._first
1
>>> (1:>"hi") ^. S._second
"hi"

snd' :: Of a b -> b

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

Map a function over the first element of an Of pair

>>> S.mapOf even (1:>"hi")
False :> "hi"

mapOf is just first from the Bifunctor instance

>>> first even (1:>"hi")
False :> "hi"

and is contained in the _first lens

>>> import Lens.Micro
>>> over S._first even (1:>"hi")
False :> "hi"

_first :: Functor f => (a -> f a') -> Of a b -> f (Of a' b)

A lens into the first element of a left-strict pair

_second :: Functor f => (b -> f b') -> Of a b -> f (Of a b')

A lens into the second element of a left-strict pair

Interoperation

reread :: Monad m => (s -> m (Maybe a)) -> s -> Stream (Of a) m ()

Read an IORef (Maybe a) or a similar device until it reads Nothing. reread provides convenient exit from the io-streams library

reread readIORef    :: IORef (Maybe a) -> Stream (Of a) IO ()
reread Streams.read :: System.IO.Streams.InputStream a -> Stream (Of a) IO ()

Basic Type

data Stream f m r

Instances

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

Methods

get :: Stream f m s

put :: s -> Stream f m ()

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

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

Methods

ask :: Stream f m r

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

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

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

Methods

throwError :: e -> Stream f m a

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

Functor f => MMonad (Stream f)

Methods

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

Functor f => MonadTrans (Stream f)

Methods

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

Functor f => MFunctor * (Stream f)

Methods

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

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

Methods

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

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

return :: a -> Stream f m a

fail :: String -> Stream f m a

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

Methods

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

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

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

Methods

pure :: a -> Stream f m a

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

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)

Methods

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

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

Methods

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

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

Methods

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

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

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

Methods

liftIO :: IO a -> Stream f m a

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

The Alternative instance glues streams together stepwise.

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

See also never, untilJust and delays

Methods

empty :: Stream f m a

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

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

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

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

Methods

mzero :: Stream f m a

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

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

Methods

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

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

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

Methods

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

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

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

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

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

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

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

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

Methods

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

show :: Stream f m r -> String

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

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

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)

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