streamly-0.7.0: Beautiful Streaming, Concurrent and Reactive Composition

Copyright (c) 2017 Harendra Kumar BSD3 streamly@composewell.com experimental GHC None Haskell2010

Streamly.Prelude

Description

This module is designed to be imported qualified:

import qualified Streamly.Prelude as S


Functions with the suffix M are general functions that work on monadic arguments. The corresponding functions without the suffix M work on pure arguments and can in general be derived from their monadic versions but are provided for convenience and for consistency with other pure APIs in the base package.

In many cases, short definitions of the combinators are provided in the documentation for illustration. The actual implementation may differ for performance reasons.

Functions having a MonadAsync constraint work concurrently when used with appropriate stream type combinator. Please be careful to not use parallely with infinite streams.

Deconstruction and folds accept a SerialT type instead of a polymorphic type to ensure that streams always have a concrete monomorphic type by default, reducing type errors. In case you want to use any other type of stream you can use one of the type combinators provided in the Streamly module to convert the stream type.

Synopsis

# Construction

## Primitives

Primitives to construct a stream from pure values or monadic actions. All other stream construction and generation combinators described later can be expressed in terms of these primitives. However, the special versions provided in this module can be much more efficient in most cases. Users can create custom combinators using these primitives.

nil :: IsStream t => t m a Source #

An empty stream.

> toList nil
[]


Since: 0.1.0

cons :: IsStream t => a -> t m a -> t m a infixr 5 Source #

Construct a stream by adding a pure value at the head of an existing stream. For serial streams this is the same as (return a) consM r but more efficient. For concurrent streams this is not concurrent whereas consM is concurrent. For example:

> toList $1 cons 2 cons 3 cons nil [1,2,3]  Since: 0.1.0 (.:) :: IsStream t => a -> t m a -> t m a infixr 5 Source # Operator equivalent of cons. > toList$ 1 .: 2 .: 3 .: nil
[1,2,3]


Since: 0.1.1

consM :: (IsStream t, MonadAsync m) => m a -> t m a -> t m a infixr 5 Source #

Constructs a stream by adding a monadic action at the head of an existing stream. For example:

> toList $getLine consM getLine consM nil hello world ["hello","world"]  Concurrent (do not use parallely to construct infinite streams) Since: 0.2.0 (|:) :: (IsStream t, MonadAsync m) => m a -> t m a -> t m a infixr 5 Source # Operator equivalent of consM. We can read it as "parallel colon" to remember that | comes before :. > toList$ getLine |: getLine |: nil
hello
world
["hello","world"]

let delay = threadDelay 1000000 >> print 1
drain $serially$ delay |: delay |: delay |: nil
drain $parallely$ delay |: delay |: delay |: nil


Concurrent (do not use parallely to construct infinite streams)

Since: 0.2.0

## From Values

Generate a monadic stream from a seed value or values.

yield :: IsStream t => a -> t m a Source #

yield a = a cons nil


Create a singleton stream from a pure value.

The following holds in monadic streams, but not in Zip streams:

yield = pure
yield = yieldM . pure


In Zip applicative streams yield is not the same as pure because in that case pure is equivalent to repeat instead. yield and pure are equally efficient, in other cases yield may be slightly more efficient than the other equivalent definitions.

Since: 0.4.0

yieldM :: (Monad m, IsStream t) => m a -> t m a Source #

yieldM m = m consM nil


Create a singleton stream from a monadic action.

> toList $yieldM getLine hello ["hello"]  Since: 0.4.0 repeat :: (IsStream t, Monad m) => a -> t m a Source # Generate an infinite stream by repeating a pure value. Since: 0.4.0 repeatM :: (IsStream t, MonadAsync m) => m a -> t m a Source # repeatM = fix . consM repeatM = cycle1 . yieldM  Generate a stream by repeatedly executing a monadic action forever. drain$ serially $S.take 10$ S.repeatM $(threadDelay 1000000 >> print 1) drain$ asyncly  $S.take 10$ S.repeatM $(threadDelay 1000000 >> print 1)  Concurrent, infinite (do not use with parallely) Since: 0.2.0 replicate :: (IsStream t, Monad m) => Int -> a -> t m a Source # replicate = take n . repeat  Generate a stream of length n by repeating a value n times. Since: 0.6.0 replicateM :: (IsStream t, MonadAsync m) => Int -> m a -> t m a Source # replicateM = take n . repeatM  Generate a stream by performing a monadic action n times. Same as: drain$ serially $S.replicateM 10$ (threadDelay 1000000 >> print 1)
drain $asyncly$ S.replicateM 10 $(threadDelay 1000000 >> print 1)  Concurrent Since: 0.1.1 ## Enumeration We can use the Enum type class to enumerate a type producing a list and then convert it to a stream: fromList$ enumFromThen from then


However, this is not particularly efficient. The Enumerable type class provides corresponding functions that generate a stream instead of a list, efficiently.

class Enum a => Enumerable a where Source #

Types that can be enumerated as a stream. The operations in this type class are equivalent to those in the Enum type class, except that these generate a stream instead of a list. Use the functions in Streamly.Streams.Enumeration module to define new instances.

Since: 0.6.0

Methods

enumerateFrom :: (IsStream t, Monad m) => a -> t m a Source #

enumerateFrom from generates a stream starting with the element from, enumerating up to maxBound when the type is Bounded or generating an infinite stream when the type is not Bounded.

> S.toList $S.take 4$ S.enumerateFrom (0 :: Int)
[0,1,2,3]


For Fractional types, enumeration is numerically stable. However, no overflow or underflow checks are performed.

> S.toList $S.take 4$ S.enumerateFrom 1.1
[1.1,2.1,3.1,4.1]


Since: 0.6.0

enumerateFromTo :: (IsStream t, Monad m) => a -> a -> t m a Source #

Generate a finite stream starting with the element from, enumerating the type up to the value to. If to is smaller than from then an empty stream is returned.

> S.toList $S.enumerateFromTo 0 4 [0,1,2,3,4]  For Fractional types, the last element is equal to the specified to value after rounding to the nearest integral value. > S.toList$ S.enumerateFromTo 1.1 4
[1.1,2.1,3.1,4.1]
> S.toList $S.enumerateFromTo 1.1 4.6 [1.1,2.1,3.1,4.1,5.1]  Since: 0.6.0 enumerateFromThen :: (IsStream t, Monad m) => a -> a -> t m a Source # enumerateFromThen from then generates a stream whose first element is from, the second element is then and the successive elements are in increments of then - from. Enumeration can occur downwards or upwards depending on whether then comes before or after from. For Bounded types the stream ends when maxBound is reached, for unbounded types it keeps enumerating infinitely. > S.toList$ S.take 4 $S.enumerateFromThen 0 2 [0,2,4,6] > S.toList$ S.take 4 $S.enumerateFromThen 0 (-2) [0,-2,-4,-6]  Since: 0.6.0 enumerateFromThenTo :: (IsStream t, Monad m) => a -> a -> a -> t m a Source # enumerateFromThenTo from then to generates a finite stream whose first element is from, the second element is then and the successive elements are in increments of then - from up to to. Enumeration can occur downwards or upwards depending on whether then comes before or after from. > S.toList$ S.enumerateFromThenTo 0 2 6
[0,2,4,6]
> S.toList $S.enumerateFromThenTo 0 (-2) (-6) [0,-2,-4,-6]  Since: 0.6.0 Instances  Source # Instance detailsDefined in Streamly.Streams.Enumeration MethodsenumerateFrom :: (IsStream t, Monad m) => Bool -> t m Bool Source #enumerateFromTo :: (IsStream t, Monad m) => Bool -> Bool -> t m Bool Source #enumerateFromThen :: (IsStream t, Monad m) => Bool -> Bool -> t m Bool Source #enumerateFromThenTo :: (IsStream t, Monad m) => Bool -> Bool -> Bool -> t m Bool Source # Source # Instance detailsDefined in Streamly.Streams.Enumeration MethodsenumerateFrom :: (IsStream t, Monad m) => Char -> t m Char Source #enumerateFromTo :: (IsStream t, Monad m) => Char -> Char -> t m Char Source #enumerateFromThen :: (IsStream t, Monad m) => Char -> Char -> t m Char Source #enumerateFromThenTo :: (IsStream t, Monad m) => Char -> Char -> Char -> t m Char Source # Source # Instance detailsDefined in Streamly.Streams.Enumeration MethodsenumerateFrom :: (IsStream t, Monad m) => Double -> t m Double Source #enumerateFromTo :: (IsStream t, Monad m) => Double -> Double -> t m Double Source #enumerateFromThen :: (IsStream t, Monad m) => Double -> Double -> t m Double Source #enumerateFromThenTo :: (IsStream t, Monad m) => Double -> Double -> Double -> t m Double Source # Source # Instance detailsDefined in Streamly.Streams.Enumeration MethodsenumerateFrom :: (IsStream t, Monad m) => Float -> t m Float Source #enumerateFromTo :: (IsStream t, Monad m) => Float -> Float -> t m Float Source #enumerateFromThen :: (IsStream t, Monad m) => Float -> Float -> t m Float Source #enumerateFromThenTo :: (IsStream t, Monad m) => Float -> Float -> Float -> t m Float Source # Source # Instance detailsDefined in Streamly.Streams.Enumeration MethodsenumerateFrom :: (IsStream t, Monad m) => Int -> t m Int Source #enumerateFromTo :: (IsStream t, Monad m) => Int -> Int -> t m Int Source #enumerateFromThen :: (IsStream t, Monad m) => Int -> Int -> t m Int Source #enumerateFromThenTo :: (IsStream t, Monad m) => Int -> Int -> Int -> t m Int Source # Source # Instance detailsDefined in Streamly.Streams.Enumeration MethodsenumerateFrom :: (IsStream t, Monad m) => Int8 -> t m Int8 Source #enumerateFromTo :: (IsStream t, Monad m) => Int8 -> Int8 -> t m Int8 Source #enumerateFromThen :: (IsStream t, Monad m) => Int8 -> Int8 -> t m Int8 Source #enumerateFromThenTo :: (IsStream t, Monad m) => Int8 -> Int8 -> Int8 -> t m Int8 Source # Source # Instance detailsDefined in Streamly.Streams.Enumeration MethodsenumerateFrom :: (IsStream t, Monad m) => Int16 -> t m Int16 Source #enumerateFromTo :: (IsStream t, Monad m) => Int16 -> Int16 -> t m Int16 Source #enumerateFromThen :: (IsStream t, Monad m) => Int16 -> Int16 -> t m Int16 Source #enumerateFromThenTo :: (IsStream t, Monad m) => Int16 -> Int16 -> Int16 -> t m Int16 Source # Source # Instance detailsDefined in Streamly.Streams.Enumeration MethodsenumerateFrom :: (IsStream t, Monad m) => Int32 -> t m Int32 Source #enumerateFromTo :: (IsStream t, Monad m) => Int32 -> Int32 -> t m Int32 Source #enumerateFromThen :: (IsStream t, Monad m) => Int32 -> Int32 -> t m Int32 Source #enumerateFromThenTo :: (IsStream t, Monad m) => Int32 -> Int32 -> Int32 -> t m Int32 Source # Source # Instance detailsDefined in Streamly.Streams.Enumeration MethodsenumerateFrom :: (IsStream t, Monad m) => Int64 -> t m Int64 Source #enumerateFromTo :: (IsStream t, Monad m) => Int64 -> Int64 -> t m Int64 Source #enumerateFromThen :: (IsStream t, Monad m) => Int64 -> Int64 -> t m Int64 Source #enumerateFromThenTo :: (IsStream t, Monad m) => Int64 -> Int64 -> Int64 -> t m Int64 Source # Source # Instance detailsDefined in Streamly.Streams.Enumeration MethodsenumerateFrom :: (IsStream t, Monad m) => Integer -> t m Integer Source #enumerateFromTo :: (IsStream t, Monad m) => Integer -> Integer -> t m Integer Source #enumerateFromThen :: (IsStream t, Monad m) => Integer -> Integer -> t m Integer Source #enumerateFromThenTo :: (IsStream t, Monad m) => Integer -> Integer -> Integer -> t m Integer Source # Source # Instance detailsDefined in Streamly.Streams.Enumeration MethodsenumerateFrom :: (IsStream t, Monad m) => Natural -> t m Natural Source #enumerateFromTo :: (IsStream t, Monad m) => Natural -> Natural -> t m Natural Source #enumerateFromThen :: (IsStream t, Monad m) => Natural -> Natural -> t m Natural Source #enumerateFromThenTo :: (IsStream t, Monad m) => Natural -> Natural -> Natural -> t m Natural Source # Source # Instance detailsDefined in Streamly.Streams.Enumeration MethodsenumerateFrom :: (IsStream t, Monad m) => Ordering -> t m Ordering Source #enumerateFromTo :: (IsStream t, Monad m) => Ordering -> Ordering -> t m Ordering Source #enumerateFromThen :: (IsStream t, Monad m) => Ordering -> Ordering -> t m Ordering Source #enumerateFromThenTo :: (IsStream t, Monad m) => Ordering -> Ordering -> Ordering -> t m Ordering Source # Source # Instance detailsDefined in Streamly.Streams.Enumeration MethodsenumerateFrom :: (IsStream t, Monad m) => Word -> t m Word Source #enumerateFromTo :: (IsStream t, Monad m) => Word -> Word -> t m Word Source #enumerateFromThen :: (IsStream t, Monad m) => Word -> Word -> t m Word Source #enumerateFromThenTo :: (IsStream t, Monad m) => Word -> Word -> Word -> t m Word Source # Source # Instance detailsDefined in Streamly.Streams.Enumeration MethodsenumerateFrom :: (IsStream t, Monad m) => Word8 -> t m Word8 Source #enumerateFromTo :: (IsStream t, Monad m) => Word8 -> Word8 -> t m Word8 Source #enumerateFromThen :: (IsStream t, Monad m) => Word8 -> Word8 -> t m Word8 Source #enumerateFromThenTo :: (IsStream t, Monad m) => Word8 -> Word8 -> Word8 -> t m Word8 Source # Source # Instance detailsDefined in Streamly.Streams.Enumeration MethodsenumerateFrom :: (IsStream t, Monad m) => Word16 -> t m Word16 Source #enumerateFromTo :: (IsStream t, Monad m) => Word16 -> Word16 -> t m Word16 Source #enumerateFromThen :: (IsStream t, Monad m) => Word16 -> Word16 -> t m Word16 Source #enumerateFromThenTo :: (IsStream t, Monad m) => Word16 -> Word16 -> Word16 -> t m Word16 Source # Source # Instance detailsDefined in Streamly.Streams.Enumeration MethodsenumerateFrom :: (IsStream t, Monad m) => Word32 -> t m Word32 Source #enumerateFromTo :: (IsStream t, Monad m) => Word32 -> Word32 -> t m Word32 Source #enumerateFromThen :: (IsStream t, Monad m) => Word32 -> Word32 -> t m Word32 Source #enumerateFromThenTo :: (IsStream t, Monad m) => Word32 -> Word32 -> Word32 -> t m Word32 Source # Source # Instance detailsDefined in Streamly.Streams.Enumeration MethodsenumerateFrom :: (IsStream t, Monad m) => Word64 -> t m Word64 Source #enumerateFromTo :: (IsStream t, Monad m) => Word64 -> Word64 -> t m Word64 Source #enumerateFromThen :: (IsStream t, Monad m) => Word64 -> Word64 -> t m Word64 Source #enumerateFromThenTo :: (IsStream t, Monad m) => Word64 -> Word64 -> Word64 -> t m Word64 Source # Source # Instance detailsDefined in Streamly.Streams.Enumeration MethodsenumerateFrom :: (IsStream t, Monad m) => () -> t m () Source #enumerateFromTo :: (IsStream t, Monad m) => () -> () -> t m () Source #enumerateFromThen :: (IsStream t, Monad m) => () -> () -> t m () Source #enumerateFromThenTo :: (IsStream t, Monad m) => () -> () -> () -> t m () Source # Integral a => Enumerable (Ratio a) Source # Instance detailsDefined in Streamly.Streams.Enumeration MethodsenumerateFrom :: (IsStream t, Monad m) => Ratio a -> t m (Ratio a) Source #enumerateFromTo :: (IsStream t, Monad m) => Ratio a -> Ratio a -> t m (Ratio a) Source #enumerateFromThen :: (IsStream t, Monad m) => Ratio a -> Ratio a -> t m (Ratio a) Source #enumerateFromThenTo :: (IsStream t, Monad m) => Ratio a -> Ratio a -> Ratio a -> t m (Ratio a) Source # HasResolution a => Enumerable (Fixed a) Source # Instance detailsDefined in Streamly.Streams.Enumeration MethodsenumerateFrom :: (IsStream t, Monad m) => Fixed a -> t m (Fixed a) Source #enumerateFromTo :: (IsStream t, Monad m) => Fixed a -> Fixed a -> t m (Fixed a) Source #enumerateFromThen :: (IsStream t, Monad m) => Fixed a -> Fixed a -> t m (Fixed a) Source #enumerateFromThenTo :: (IsStream t, Monad m) => Fixed a -> Fixed a -> Fixed a -> t m (Fixed a) Source # Enumerable a => Enumerable (Identity a) Source # Instance detailsDefined in Streamly.Streams.Enumeration MethodsenumerateFrom :: (IsStream t, Monad m) => Identity a -> t m (Identity a) Source #enumerateFromTo :: (IsStream t, Monad m) => Identity a -> Identity a -> t m (Identity a) Source #enumerateFromThen :: (IsStream t, Monad m) => Identity a -> Identity a -> t m (Identity a) Source #enumerateFromThenTo :: (IsStream t, Monad m) => Identity a -> Identity a -> Identity a -> t m (Identity a) Source # enumerate :: (IsStream t, Monad m, Bounded a, Enumerable a) => t m a Source # enumerate = enumerateFrom minBound Enumerate a Bounded type from its minBound to maxBound Since: 0.6.0 enumerateTo :: (IsStream t, Monad m, Bounded a, Enumerable a) => a -> t m a Source # enumerateTo = enumerateFromTo minBound Enumerate a Bounded type from its minBound to specified value. Since: 0.6.0 ## From Generators Generate a monadic stream from a seed value and a generator function. unfoldr :: (Monad m, IsStream t) => (b -> Maybe (a, b)) -> b -> t m a Source # unfoldr step s = case step s of Nothing -> nil Just (a, b) -> a cons unfoldr step b  Build a stream by unfolding a pure step function step starting from a seed s. The step function returns the next element in the stream and the next seed value. When it is done it returns Nothing and the stream ends. For example, let f b = if b > 3 then Nothing else Just (b, b + 1) in toList$ unfoldr f 0

[0,1,2,3]


Since: 0.1.0

unfoldrM :: (IsStream t, MonadAsync m) => (b -> m (Maybe (a, b))) -> b -> t m a Source #

Build a stream by unfolding a monadic step function starting from a seed. The step function returns the next element in the stream and the next seed value. When it is done it returns Nothing and the stream ends. For example,

let f b =
if b > 3
then return Nothing
else print b >> return (Just (b, b + 1))
in drain $unfoldrM f 0   0 1 2 3  When run concurrently, the next unfold step can run concurrently with the processing of the output of the previous step. Note that more than one step cannot run concurrently as the next step depends on the output of the previous step. (asyncly$ S.unfoldrM (\n -> liftIO (threadDelay 1000000) >> return (Just (n, n + 1))) 0)
& S.foldlM' (\_ a -> threadDelay 1000000 >> print a) ()


Concurrent

Since: 0.1.0

unfold :: (IsStream t, Monad m) => Unfold m a b -> a -> t m b Source #

Convert an Unfold into a stream by supplying it an input seed.

>>> unfold UF.replicateM 10 (putStrLn "hello")


Since: 0.7.0

iterate :: IsStream t => (a -> a) -> a -> t m a Source #

iterate f x = x cons iterate f x


Generate an infinite stream with x as the first element and each successive element derived by applying the function f on the previous element.

> S.toList $S.take 5$ S.iterate (+1) 1
[1,2,3,4,5]


Since: 0.1.2

iterateM :: (IsStream t, MonadAsync m) => (a -> m a) -> m a -> t m a Source #

iterateM f m = m >>= a -> return a consM iterateM f (f a)


Generate an infinite stream with the first element generated by the action m and each successive element derived by applying the monadic function f on the previous element.

When run concurrently, the next iteration can run concurrently with the processing of the previous iteration. Note that more than one iteration cannot run concurrently as the next iteration depends on the output of the previous iteration.

drain $serially$ S.take 10 $S.iterateM (\x -> threadDelay 1000000 >> print x >> return (x + 1)) (return 0) drain$ asyncly  $S.take 10$ S.iterateM
(\x -> threadDelay 1000000 >> print x >> return (x + 1)) (return 0)


Concurrent

Since: 0.7.0 (signature change)

Since: 0.1.2

fromIndices :: (IsStream t, Monad m) => (Int -> a) -> t m a Source #

fromIndices f = let g i = f i cons g (i + 1) in g 0


Generate an infinite stream, whose values are the output of a function f applied on the corresponding index. Index starts at 0.

> S.toList $S.take 5$ S.fromIndices id
[0,1,2,3,4]


Since: 0.6.0

fromIndicesM :: (IsStream t, MonadAsync m) => (Int -> m a) -> t m a Source #

fromIndicesM f = let g i = f i consM g (i + 1) in g 0


Generate an infinite stream, whose values are the output of a monadic function f applied on the corresponding index. Index starts at 0.

Concurrent

Since: 0.6.0

## From Containers

Convert an input structure, container or source into a stream. All of these can be expressed in terms of primitives.

fromList :: (Monad m, IsStream t) => [a] -> t m a Source #

fromList = foldr cons nil


Construct a stream from a list of pure values. This is more efficient than fromFoldable for serial streams.

Since: 0.4.0

fromListM :: (MonadAsync m, IsStream t) => [m a] -> t m a Source #

fromListM = foldr consM nil


Construct a stream from a list of monadic actions. This is more efficient than fromFoldableM for serial streams.

Since: 0.4.0

fromFoldable :: (IsStream t, Foldable f) => f a -> t m a Source #

fromFoldable = foldr cons nil


Construct a stream from a Foldable containing pure values:

Since: 0.2.0

fromFoldableM :: (IsStream t, MonadAsync m, Foldable f) => f (m a) -> t m a Source #

fromFoldableM = foldr consM nil


Construct a stream from a Foldable containing monadic actions.

drain $serially$ S.fromFoldableM $replicateM 10 (threadDelay 1000000 >> print 1) drain$ asyncly  $S.fromFoldableM$ replicateM 10 (threadDelay 1000000 >> print 1)


Concurrent (do not use with parallely on infinite containers)

Since: 0.3.0

# Elimination

## Deconstruction

It is easy to express all the folds in terms of the uncons primitive, however the specific implementations provided later are generally more efficient.

uncons :: (IsStream t, Monad m) => SerialT m a -> m (Maybe (a, t m a)) Source #

Decompose a stream into its head and tail. If the stream is empty, returns Nothing. If the stream is non-empty, returns Just (a, ma), where a is the head of the stream and ma its tail.

This is a brute force primitive. Avoid using it as long as possible, use it when no other combinator can do the job. This can be used to do pretty much anything in an imperative manner, as it just breaks down the stream into individual elements and we can loop over them as we deem fit. For example, this can be used to convert a streamly stream into other stream types.

Since: 0.1.0

tail :: (IsStream t, Monad m) => SerialT m a -> m (Maybe (t m a)) Source #

tail = fmap (fmap snd) . uncons

Extract all but the first element of the stream, if any.

Since: 0.1.1

init :: (IsStream t, Monad m) => SerialT m a -> m (Maybe (t m a)) Source #

Extract all but the last element of the stream, if any.

Since: 0.5.0

## Folding

In imperative terms a fold can be considered as a loop over the stream that reduces the stream to a single value. Left and right folds use a fold function f and an identity element z (zero) to recursively deconstruct a structure and then combine and reduce the values or transform and reconstruct a new container.

In general, a right fold is suitable for transforming and reconstructing a right associated structure (e.g. cons lists and streamly streams) and a left fold is suitable for reducing a right associated structure. The behavior of right and left folds are described in detail in the individual fold's documentation. To illustrate the two folds for cons lists:

foldr :: (a -> b -> b) -> b -> [a] -> b
foldr f z [] = z
foldr f z (x:xs) = x f foldr f z xs

foldl :: (b -> a -> b) -> b -> [a] -> b
foldl f z [] = z
foldl f z (x:xs) = foldl f (z f x) xs

foldr is conceptually equivalent to:

foldr f z [] = z
foldr f z [x] = f x z
foldr f z xs = foldr f (foldr f z (tail xs)) [head xs]

foldl is conceptually equivalent to:

foldl f z [] = z
foldl f z [x] = f z x
foldl f z xs = foldl f (foldl f z (init xs)) [last xs]

Left and right folds are duals of each other.

foldr f z xs = foldl (flip f) z (reverse xs)
foldl f z xs = foldr (flip f) z (reverse xs)


More generally:

foldr f z xs = foldl g id xs z where g k x = k . f x
foldl f z xs = foldr g id xs z where g x k = k . flip f x


## Right Folds

Let's take a closer look at the foldr definition for lists, as given earlier:

foldr f z (x:xs) = x f foldr f z xs


foldr invokes the fold step function f as f x (foldr f z xs). At each invocation of f, foldr gives us the next element in the input container x and a recursive expression foldr f z xs representing the yet unbuilt (lazy thunk) part of the output.

When f x xs is lazy in xs it can consume the input one element at a time in FIFO order to build a lazy output expression. For example,

f x remaining = show x : remaining

take 2 $foldr f [] (1:2:undefined) would consume the input lazily on demand, consuming only first two elements and resulting in ["1", "2"]. f can terminate recursion by not evaluating the remaining part: f 2 remaining = show 2 : [] f x remaining = show x : remaining f would terminate recursion whenever it sees element 2 in the input. Therefore, take 2$ foldr f [] (1:2:undefined) would work without any problem.

On the other hand, if f a b is strict in b it would end up consuming the whole input right away and expanding the recursive expression b (i.e. foldr f z xs) fully before it yields an output expression, resulting in the following right associated expression:

foldr f z xs == x1 f (x2 f ...(xn f z))


For example,

f x remaining = x + remaining

With this definition, foldr f 0 [1..1000], would recurse completely until it reaches the terminating case ... f (1000 f 0), and then start reducing the whole expression from right to left, therefore, consuming the input elements in LIFO order. Thus, such an evaluation would require memory proportional to the size of input. Try out foldr (+) 0 (map (\x -> trace (show x) x) [1..10]).

Notice the order of the arguments to the step function f a b. It follows the order of a and b in the right associative recursive expression generated by expanding a f b.

A right fold is a pull fold, the step function is the puller, it can pull more data from the input container by using its second argument in the output expression or terminate pulling by not using it. As a corollary:

1. a step function which is lazy in its second argument (usually functions or constructors that build a lazy structure e.g. (:)) can pull lazily on demand.
2. a step function strict in its second argument (usually reducers e.g. (+)) would end up pulling all of its input and buffer it in memory before potentially reducing it.

A right fold is suitable for lazy reconstructions e.g. transformation, mapping, filtering of right associated input structures (e.g. cons lists). Whereas a left fold is suitable for reductions (e.g. summing a stream of numbers) of right associated structures. Note that these roles will reverse for left associated structures (e.g. snoc lists). Most of our observations here assume right associated structures, lists being the canonical example.

1. A lazy FIFO style pull using a right fold allows pulling a potentially infinite input stream lazily, perform transformations on it, and reconstruct a new structure without having to buffer the whole structure. In contrast, a left fold would buffer the entire structure before the reconstructed structure can be consumed.
2. Even if buffering the entire input structure is ok, we need to keep in mind that a right fold reconstructs structures in a FIFO style, whereas a left fold reconstructs in a LIFO style, thereby reversing the order of elements..
3. A right fold has termination control and therefore can terminate early without going throught the entire input, a left fold cannot terminate without consuming all of its input. For example, a right fold implementation of or can terminate as soon as it finds the first True element, whereas a left fold would necessarily go through the entire input irrespective of that.
4. Reduction (e.g. using (+) on a stream of numbers) using a right fold occurs in a LIFO style, which means that the entire input gets buffered before reduction starts. Whereas with a strict left fold reductions occur incrementally in FIFO style. Therefore, a strict left fold is more suitable for reductions.

foldrM :: Monad m => (a -> m b -> m b) -> m b -> SerialT m a -> m b Source #

Right associative/lazy pull fold. foldrM build final stream constructs an output structure using the step function build. build is invoked with the next input element and the remaining (lazy) tail of the output structure. It builds a lazy output expression using the two. When the "tail structure" in the output expression is evaluated it calls build again thus lazily consuming the input stream until either the output expression built by build is free of the "tail" or the input is exhausted in which case final is used as the terminating case for the output structure. For more details see the description in the previous section.

Example, determine if any element is odd in a stream:

>>> S.foldrM (\x xs -> if odd x then return True else xs) (return False) $S.fromList (2:4:5:undefined) > True  Since: 0.7.0 (signature changed) Since: 0.2.0 (signature changed) Since: 0.1.0 foldr :: Monad m => (a -> b -> b) -> b -> SerialT m a -> m b Source # Right fold, lazy for lazy monads and pure streams, and strict for strict monads. Please avoid using this routine in strict monads like IO unless you need a strict right fold. This is provided only for use in lazy monads (e.g. Identity) or pure streams. Note that with this signature it is not possible to implement a lazy foldr when the monad m is strict. In that case it would be strict in its accumulator and therefore would necessarily consume all its input. Since: 0.1.0 ## Left Folds Note that the observations below about the behavior of a left fold assume that we are working on a right associated structure like cons lists and streamly streams. If we are working on a left associated structure (e.g. snoc lists) the roles of right and left folds would reverse. Let's take a closer look at the foldl definition for lists given above: foldl f z (x:xs) = foldl f (z f x) xs  foldl calls itself recursively, in each call it invokes f as f z x providing it with the result accumulated till now z (the state) and the next element from the input container. First call to f is supplied with the initial value of the accumulator z and each subsequent call uses the output of the previous call to f z x. > foldl' (+) 0 [1,2,3] 6 The recursive call at the head of the output expression is bound to be evaluated until recursion terminates, therefore, a left fold always consumes the whole input container. The following would result in an error, even though the fold is not using the values at all: > foldl' (\_ _ -> 0) 0 (1:undefined) *** Exception: Prelude.undefined As foldl recurses, it builds the left associated expression shown below. Notice, the order of the arguments to the step function f b a. It follows the left associative recursive expression generated by expanding b f a. foldl f z xs == (((z f x1) f x2) ...) f xn  The strict left fold foldl' forces the reduction of its argument z f x before using it, therefore it never builds the whole expression in memory. Thus, z f x1 would get reduced to z1 and then z1 f x2 would get reduced to z2 and so on, incrementally reducing the expression from left to right as it recurses, consuming the input in FIFO order. Try out foldl' (+) 0 (map (\x -> trace (show x) x) [1..10]) to see how it works. For example: > S.foldl' (+) 0$ S.fromList [1,2,3,4]
10

0 + 1 = 1
1 + 2 = 3
3 + 3 = 6
6 + 4 = 10


However, foldl' evaluates the accumulator only to WHNF. It may further help if the step function uses a strict data structure as accumulator to improve performance and to keep the expression fully reduced at all times during the fold.

A left fold can also build a new structure instead of reducing one if a constructor is used as a fold step. However, it may not be very useful because it will consume the whole input and construct the new structure in memory before we can consume it. Thus the whole structure gets buffered in memory. When the list constructor is used it would build a new list in reverse (LIFO) order:

$S.takeWhile (\(_,x) -> x <= 10)$ S.postscan ((,) <$> FL.last <*> avg) (S.enumerateFromTo 1.0 100.0)   [1.0,2.0,3.0,4.0,5.0,6.0,7.0,8.0,9.0,10.0,11.0,12.0,13.0,14.0,15.0,16.0,17.0,18.0,19.0]  fold :: Monad m => Fold m a b -> SerialT m a -> m b Source # Fold a stream using the supplied left fold. >>> S.fold FL.sum (S.enumerateFromTo 1 100) 5050  Since: 0.7.0 ## Full Folds Folds that are guaranteed to evaluate the whole stream. drain :: Monad m => SerialT m a -> m () Source # drain = mapM_ (\_ -> return ()) Run a stream, discarding the results. By default it interprets the stream as SerialT, to run other types of streams use the type adapting combinators for example drain . asyncly. Since: 0.7.0 last :: Monad m => SerialT m a -> m (Maybe a) Source # Extract the last element of the stream, if any. last xs = xs !! (length xs - 1) Since: 0.1.1 length :: Monad m => SerialT m a -> m Int Source # Determine the length of the stream. Since: 0.1.0 sum :: (Monad m, Num a) => SerialT m a -> m a Source # Determine the sum of all elements of a stream of numbers. Returns 0 when the stream is empty. Note that this is not numerically stable for floating point numbers. Since: 0.1.0 product :: (Monad m, Num a) => SerialT m a -> m a Source # Determine the product of all elements of a stream of numbers. Returns 1 when the stream is empty. Since: 0.1.1 maximumBy :: Monad m => (a -> a -> Ordering) -> SerialT m a -> m (Maybe a) Source # Determine the maximum element in a stream using the supplied comparison function. Since: 0.6.0 maximum :: (Monad m, Ord a) => SerialT m a -> m (Maybe a) Source # maximum = maximumBy compare  Determine the maximum element in a stream. Since: 0.1.0 minimumBy :: Monad m => (a -> a -> Ordering) -> SerialT m a -> m (Maybe a) Source # Determine the minimum element in a stream using the supplied comparison function. Since: 0.6.0 minimum :: (Monad m, Ord a) => SerialT m a -> m (Maybe a) Source # minimum = minimumBy compare  Determine the minimum element in a stream. Since: 0.1.0 the :: (Eq a, Monad m) => SerialT m a -> m (Maybe a) Source # Ensures that all the elements of the stream are identical and then returns that unique element. Since: 0.6.0 ## Lazy Folds Folds that generate a lazy structure. Note that the generated structure may not be lazy if the underlying monad is strict. toList :: Monad m => SerialT m a -> m [a] Source # toList = S.foldr (:) []  Convert a stream into a list in the underlying monad. The list can be consumed lazily in a lazy monad (e.g. Identity). In a strict monad (e.g. IO) the whole list is generated and buffered before it can be consumed. Warning! working on large lists accumulated as buffers in memory could be very inefficient, consider using Streamly.Array instead. Since: 0.1.0 ## Partial Folds Folds that may terminate before evaluating the whole stream. These folds strictly evaluate the stream until the result is determined. drainN :: Monad m => Int -> SerialT m a -> m () Source # drainN n = drain . take n Run maximum up to n iterations of a stream. Since: 0.7.0 drainWhile :: Monad m => (a -> Bool) -> SerialT m a -> m () Source # drainWhile p = drain . takeWhile p Run a stream as long as the predicate holds true. Since: 0.7.0 (!!) :: Monad m => SerialT m a -> Int -> m (Maybe a) Source # Lookup the element at the given index. Since: 0.6.0 head :: Monad m => SerialT m a -> m (Maybe a) Source # Extract the first element of the stream, if any. head = (!! 0) Since: 0.1.0 findM :: Monad m => (a -> m Bool) -> SerialT m a -> m (Maybe a) Source # Returns the first element that satisfies the given predicate. Since: 0.6.0 find :: Monad m => (a -> Bool) -> SerialT m a -> m (Maybe a) Source # Like findM but with a non-monadic predicate. find p = findM (return . p) Since: 0.5.0 lookup :: (Monad m, Eq a) => a -> SerialT m (a, b) -> m (Maybe b) Source # In a stream of (key-value) pairs (a, b), return the value b of the first pair where the key equals the given value a. lookup = snd <$> find ((==) . fst)

Since: 0.5.0

findIndex :: Monad m => (a -> Bool) -> SerialT m a -> m (Maybe Int) Source #

Returns the first index that satisfies the given predicate.

Since: 0.5.0

elemIndex :: (Monad m, Eq a) => a -> SerialT m a -> m (Maybe Int) Source #

Returns the first index where a given value is found in the stream.

elemIndex a = findIndex (== a)

Since: 0.5.0

null :: Monad m => SerialT m a -> m Bool Source #

Determine whether the stream is empty.

Since: 0.1.1

elem :: (Monad m, Eq a) => a -> SerialT m a -> m Bool Source #

Determine whether an element is present in the stream.

Since: 0.1.0

notElem :: (Monad m, Eq a) => a -> SerialT m a -> m Bool Source #

Determine whether an element is not present in the stream.

Since: 0.1.0

all :: Monad m => (a -> Bool) -> SerialT m a -> m Bool Source #

Determine whether all elements of a stream satisfy a predicate.

Since: 0.1.0

any :: Monad m => (a -> Bool) -> SerialT m a -> m Bool Source #

Determine whether any of the elements of a stream satisfy a predicate.

Since: 0.1.0

and :: Monad m => SerialT m Bool -> m Bool Source #

Determines if all elements of a boolean stream are True.

Since: 0.5.0

or :: Monad m => SerialT m Bool -> m Bool Source #

Determines whether at least one element of a boolean stream is True.

Since: 0.5.0

## Multi-Stream folds

eqBy :: (IsStream t, Monad m) => (a -> b -> Bool) -> t m a -> t m b -> m Bool Source #

Compare two streams for equality using an equality function.

Since: 0.6.0

cmpBy :: (IsStream t, Monad m) => (a -> b -> Ordering) -> t m a -> t m b -> m Ordering Source #

Compare two streams lexicographically using a comparison function.

Since: 0.6.0

isPrefixOf :: (Eq a, IsStream t, Monad m) => t m a -> t m a -> m Bool Source #

Returns True if the first stream is the same as or a prefix of the second. A stream is a prefix of itself.

> S.isPrefixOf (S.fromList "hello") (S.fromList "hello" :: SerialT IO Char)
True


Since: 0.6.0

isSubsequenceOf :: (Eq a, IsStream t, Monad m) => t m a -> t m a -> m Bool Source #

Returns True if all the elements of the first stream occur, in order, in the second stream. The elements do not have to occur consecutively. A stream is a subsequence of itself.

> S.isSubsequenceOf (S.fromList "hlo") (S.fromList "hello" :: SerialT IO Char)
True


Since: 0.6.0

stripPrefix :: (Eq a, IsStream t, Monad m) => t m a -> t m a -> m (Maybe (t m a)) Source #

Drops the given prefix from a stream. Returns Nothing if the stream does not start with the given prefix. Returns Just nil when the prefix is the same as the stream.

Since: 0.6.0

# Transformation

## Mapping

In imperative terms a map operation can be considered as a loop over the stream that transforms the stream into another stream by performing an operation on each element of the stream.

map is the least powerful transformation operation with strictest guarantees. A map, (1) is a stateless loop which means that no state is allowed to be carried from one iteration to another, therefore, operations on different elements are guaranteed to not affect each other, (2) is a strictly one-to-one transformation of stream elements which means it guarantees that no elements can be added or removed from the stream, it can merely transform them.

map :: (IsStream t, Monad m) => (a -> b) -> t m a -> t m b Source #

map = fmap


Same as fmap.

> S.toList $S.map (+1)$ S.fromList [1,2,3]
[2,3,4]


Since: 0.4.0

sequence :: (IsStream t, MonadAsync m) => t m (m a) -> t m a Source #

sequence = mapM id


Replace the elements of a stream of monadic actions with the outputs of those actions.

> drain $S.sequence$ S.fromList [putStr "a", putStr "b", putStrLn "c"]
abc

drain $S.replicateM 10 (return$ threadDelay 1000000 >> print 1)
& (serially . S.sequence)

drain $S.replicateM 10 (return$ threadDelay 1000000 >> print 1)
& (asyncly . S.sequence)


Concurrent (do not use with parallely on infinite streams)

Since: 0.1.0

mapM :: (IsStream t, MonadAsync m) => (a -> m b) -> t m a -> t m b Source #

mapM f = sequence . map f


Apply a monadic function to each element of the stream and replace it with the output of the resulting action.

> drain $S.mapM putStr$ S.fromList ["a", "b", "c"]
abc

drain $S.replicateM 10 (return 1) & (serially . S.mapM (\x -> threadDelay 1000000 >> print x)) drain$ S.replicateM 10 (return 1)
& (asyncly . S.mapM (\x -> threadDelay 1000000 >> print x))


Concurrent (do not use with parallely on infinite streams)

Since: 0.1.0

## Special Maps

mapM_ :: Monad m => (a -> m b) -> SerialT m a -> m () Source #

mapM_ = drain . mapM

Apply a monadic action to each element of the stream and discard the output of the action. This is not really a pure transformation operation but a transformation followed by fold.

Since: 0.1.0

trace :: (IsStream t, MonadAsync m) => (a -> m b) -> t m a -> t m a Source #

Apply a monadic function to each element flowing through the stream and discard the results.

> S.drain $S.trace print (S.enumerateFromTo 1 2) 1 2  Compare with tap. Since: 0.7.0 tap :: (IsStream t, Monad m) => Fold m a b -> t m a -> t m a Source # Tap the data flowing through a stream into a Fold. For example, you may add a tap to log the contents flowing through the stream. The fold is used only for effects, its result is discarded.  Fold m a b | -----stream m a ---------------stream m a-----  > S.drain$ S.tap (FL.drainBy print) (S.enumerateFromTo 1 2)
1
2


Compare with trace.

Since: 0.7.0

## Scanning

A scan is more powerful than map. While a map is a stateless loop, a scan is a stateful loop which means that a state can be shared across all the loop iterations, therefore, future iterations can be impacted by the state changes made by the past iterations. A scan yields the state of the loop after each iteration. Like a map, a postscan or prescan does not add or remove elements in the stream, it just transforms them. However, a scan adds one extra element to the stream.

A left associative scan, also known as a prefix sum, can be thought of as a stream transformation consisting of left folds of all prefixes of a stream. Another way of thinking about it is that it streams all the intermediate values of the accumulator while applying a left fold on the input stream. A right associative scan, on the other hand, can be thought of as a stream consisting of right folds of all the suffixes of a stream.

The following equations hold for lists:

scanl f z xs == map (foldl f z) $inits xs scanr f z xs == map (foldr f z)$ tails xs
> scanl (+) 0 [1,2,3,4]
0                 = 0
0 + 1             = 1
0 + 1 + 2         = 3
0 + 1 + 2 + 3     = 6
0 + 1 + 2 + 3 + 4 = 10

> scanr (+) 0 [1,2,3,4]
1 + 2 + 3 + 4 + 0 = 10
2 + 3 + 4 + 0 = 9
3 + 4 + 0 = 7
4 + 0 = 4
0 = 0


Left and right scans are duals:

scanr f z xs ==  reverse $scanl (flip f) z (reverse xs) scanl f z xs == reverse$ scanr (flip f) z (reverse xs)

A scan is a stateful map i.e. a combination of map and fold:

map f xs =           tail $scanl (\_ x -> f x) z xs map f xs = reverse$ head $scanr (\_ x -> f x) z xs foldl f z xs = last$ scanl f z xs
foldr f z xs = head $scanr f z xs ## Left scans scanl' :: (IsStream t, Monad m) => (b -> a -> b) -> b -> t m a -> t m b Source # Strict left scan. Like map, scanl' too is a one to one transformation, however it adds an extra element. > S.toList$ S.scanl' (+) 0 $fromList [1,2,3,4] [0,1,3,6,10]  > S.toList$ S.scanl' (flip (:)) [] $S.fromList [1,2,3,4] [[],[1],[2,1],[3,2,1],[4,3,2,1]]  The output of scanl' is the initial value of the accumulator followed by all the intermediate steps and the final result of foldl'. By streaming the accumulated state after each fold step, we can share the state across multiple stages of stream composition. Each stage can modify or extend the state, do some processing with it and emit it for the next stage, thus modularizing the stream processing. This can be useful in stateful or event-driven programming. Consider the following monolithic example, computing the sum and the product of the elements in a stream in one go using a foldl': > S.foldl' (\(s, p) x -> (s + x, p * x)) (0,1)$ S.fromList [1,2,3,4]
(10,24)


Using scanl' we can make it modular by computing the sum in the first stage and passing it down to the next stage for computing the product:

>   S.foldl' (\(_, p) (s, x) -> (s, p * x)) (0,1)
$S.scanl' (\(s, _) x -> (s + x, x)) (0,1)$ S.fromList [1,2,3,4]
(10,24)


IMPORTANT: scanl' evaluates the accumulator to WHNF. To avoid building lazy expressions inside the accumulator, it is recommended that a strict data structure is used for accumulator.

Since: 0.2.0

scanlM' :: (IsStream t, Monad m) => (b -> a -> m b) -> b -> t m a -> t m b Source #

Like scanl' but with a monadic fold function.

Since: 0.4.0

postscanl' :: (IsStream t, Monad m) => (b -> a -> b) -> b -> t m a -> t m b Source #

Like scanl' but does not stream the initial value of the accumulator.

postscanl' f z xs = S.drop 1 $S.scanl' f z xs Since: 0.7.0 postscanlM' :: (IsStream t, Monad m) => (b -> a -> m b) -> b -> t m a -> t m b Source # Like postscanl' but with a monadic step function. Since: 0.7.0 scanl1' :: (IsStream t, Monad m) => (a -> a -> a) -> t m a -> t m a Source # Like scanl' but for a non-empty stream. The first element of the stream is used as the initial value of the accumulator. Does nothing if the stream is empty. > S.toList$ S.scanl1 (+) $fromList [1,2,3,4] [1,3,6,10]  Since: 0.6.0 scanl1M' :: (IsStream t, Monad m) => (a -> a -> m a) -> t m a -> t m a Source # Like scanl1' but with a monadic step function. Since: 0.6.0 ## Scan Using Fold scan :: (IsStream t, Monad m) => Fold m a b -> t m a -> t m b Source # Scan a stream using the given monadic fold. Since: 0.7.0 postscan :: (IsStream t, Monad m) => Fold m a b -> t m a -> t m b Source # Postscan a stream using the given monadic fold. Since: 0.7.0 ## Filtering Remove some elements from the stream based on a predicate. In imperative terms a filter over a stream corresponds to a loop with a continue clause for the cases when the predicate fails. filter :: (IsStream t, Monad m) => (a -> Bool) -> t m a -> t m a Source # Include only those elements that pass a predicate. Since: 0.1.0 filterM :: (IsStream t, Monad m) => (a -> m Bool) -> t m a -> t m a Source # Same as filter but with a monadic predicate. Since: 0.4.0 ## Mapping Filters Mapping along with filtering mapMaybe :: (IsStream t, Monad m) => (a -> Maybe b) -> t m a -> t m b Source # Map a Maybe returning function to a stream, filter out the Nothing elements, and return a stream of values extracted from Just. Equivalent to: mapMaybe f = S.map fromJust . S.filter isJust . S.map f  Since: 0.3.0 mapMaybeM :: (IsStream t, MonadAsync m, Functor (t m)) => (a -> m (Maybe b)) -> t m a -> t m b Source # Like mapMaybe but maps a monadic function. Equivalent to: mapMaybeM f = S.map fromJust . S.filter isJust . S.mapM f  Concurrent (do not use with parallely on infinite streams) Since: 0.3.0 ## Deleting Elements Deleting elements is a special case of de-interleaving streams. deleteBy :: (IsStream t, Monad m) => (a -> a -> Bool) -> a -> t m a -> t m a Source # Deletes the first occurence of the element in the stream that satisfies the given equality predicate. > S.toList$ S.deleteBy (==) 3 $S.fromList [1,3,3,5] [1,3,5]  Since: 0.6.0 uniq :: (Eq a, IsStream t, Monad m) => t m a -> t m a Source # Drop repeated elements that are adjacent to each other. Since: 0.6.0 ## Inserting Elements Inserting elements is a special case of interleaving/merging streams. insertBy :: (IsStream t, Monad m) => (a -> a -> Ordering) -> a -> t m a -> t m a Source # insertBy cmp elem stream inserts elem before the first element in stream that is less than elem when compared using cmp. insertBy cmp x = mergeBy cmp (yield x)  > S.toList$ S.insertBy compare 2 $S.fromList [1,3,5] [1,2,3,5]  Since: 0.6.0 intersperseM :: (IsStream t, MonadAsync m) => m a -> t m a -> t m a Source # Generate a stream by performing a monadic action between consecutive elements of the given stream. Concurrent (do not use with parallely on infinite streams) > S.toList$ S.intersperseM (return ',') $S.fromList "hello" "h,e,l,l,o"  Since: 0.5.0 intersperse :: (IsStream t, MonadAsync m) => a -> t m a -> t m a Source # Generate a stream by inserting a given element between consecutive elements of the given stream. > S.toList$ S.intersperse ',' $S.fromList "hello" "h,e,l,l,o"  Since: 0.7.0 ## Indexing Indexing can be considered as a special type of zipping where we zip a stream with an index stream. indexed :: (IsStream t, Monad m) => t m a -> t m (Int, a) Source # indexed = S.postscanl' (\(i, _) x -> (i + 1, x)) (-1,undefined) indexed = S.zipWith (,) (S.enumerateFrom 0) Pair each element in a stream with its index, starting from index 0. > S.toList$ S.indexed $S.fromList "hello" [(0,h),(1,e),(2,l),(3,l),(4,o)]  Since: 0.6.0 indexedR :: (IsStream t, Monad m) => Int -> t m a -> t m (Int, a) Source # indexedR n = S.postscanl' (\(i, _) x -> (i - 1, x)) (n + 1,undefined) indexedR n = S.zipWith (,) (S.enumerateFromThen n (n - 1)) Pair each element in a stream with its index, starting from the given index n and counting down. > S.toList$ S.indexedR 10 $S.fromList "hello" [(10,h),(9,e),(8,l),(7,l),(6,o)]  Since: 0.6.0 ## Reordering Elements reverse :: (IsStream t, Monad m) => t m a -> t m a Source # Returns the elements of the stream in reverse order. The stream must be finite. Note that this necessarily buffers the entire stream in memory. Since 0.7.0 (Monad m constraint) Since: 0.1.1 ## Trimming Take or remove elements from one or both ends of a stream. take :: (IsStream t, Monad m) => Int -> t m a -> t m a Source # Take first n elements from the stream and discard the rest. Since: 0.1.0 takeWhile :: (IsStream t, Monad m) => (a -> Bool) -> t m a -> t m a Source # End the stream as soon as the predicate fails on an element. Since: 0.1.0 takeWhileM :: (IsStream t, Monad m) => (a -> m Bool) -> t m a -> t m a Source # Same as takeWhile but with a monadic predicate. Since: 0.4.0 drop :: (IsStream t, Monad m) => Int -> t m a -> t m a Source # Discard first n elements from the stream and take the rest. Since: 0.1.0 dropWhile :: (IsStream t, Monad m) => (a -> Bool) -> t m a -> t m a Source # Drop elements in the stream as long as the predicate succeeds and then take the rest of the stream. Since: 0.1.0 dropWhileM :: (IsStream t, Monad m) => (a -> m Bool) -> t m a -> t m a Source # Same as dropWhile but with a monadic predicate. Since: 0.4.0 ## Slicing Streams can be sliced into segments in space or in time. We use the term chunk to refer to a spatial length of the stream (spatial window) and the term session to refer to a length in time (time window). chunksOf :: (IsStream t, Monad m) => Int -> Fold m a b -> t m a -> t m b Source # Group the input stream into groups of n elements each and then fold each group using the provided fold function. > S.toList$ S.chunksOf 2 FL.sum (S.enumerateFromTo 1 10)
[3,7,11,15,19]

This can be considered as an n-fold version of ltake where we apply ltake repeatedly on the leftover stream until the stream exhausts.

Since: 0.7.0

intervalsOf :: (IsStream t, MonadAsync m) => Double -> Fold m a b -> t m a -> t m b Source #

Group the input stream into windows of n second each and then fold each group using the provided fold function.

Since: 0.7.0

## Searching

Finding the presence or location of an element, a sequence of elements or another stream within a stream.

findIndices :: (IsStream t, Monad m) => (a -> Bool) -> t m a -> t m Int Source #

Find all the indices where the element in the stream satisfies the given predicate.

Since: 0.5.0

elemIndices :: (IsStream t, Eq a, Monad m) => a -> t m a -> t m Int Source #

Find all the indices where the value of the element in the stream is equal to the given value.

Since: 0.5.0

## Splitting

In general we can express splitting in terms of parser combinators. These are some common use functions for convenience and efficiency. While parsers can fail these functions are designed to transform a stream without failure with a predefined behavior for all cases.

In general, there are three possible ways of combining stream segments with a separator. The separator could be prefixed to each segment, suffixed to each segment, or it could be infixed between segments. intersperse and intercalate operations are examples of infixed combining whereas unlines is an example of suffixed combining. When we split a stream with separators we can split in three different ways, each being an opposite of the three ways of combining.

Splitting may keep the separator or drop it. Depending on how we split, the separator may be kept attached to the stream segments in prefix or suffix position or as a separate element in infix position. Combinators like splitOn that use On in their names drop the separator and combinators that use With in their names keep the separator. When a segment is missing it is considered as empty, therefore, we never encounter an error in parsing.

splitOn :: (IsStream t, Monad m) => (a -> Bool) -> Fold m a b -> t m a -> t m b Source #

Split on an infixed separator element, dropping the separator. Splits the stream on separator elements determined by the supplied predicate, separator is considered as infixed between two segments, if one side of the separator is missing then it is parsed as an empty stream. The supplied Fold is applied on the split segments. With - representing non-separator elements and . as separator, splitOn splits as follows:

"--.--" => "--" "--"
"--."   => "--" ""
".--"   => ""   "--"


splitOn (== x) is an inverse of intercalate (S.yield x)

Let's use the following definition for illustration:

splitOn' p xs = S.toList $S.splitOn p (FL.toList) (S.fromList xs) >>> splitOn' (== '.') "" [""]  >>> splitOn' (== '.') "." ["",""]  >>> splitOn' (== '.') ".a" > ["","a"]  >>> splitOn' (== '.') "a." > ["a",""]  >>> splitOn' (== '.') "a.b" > ["a","b"]  >>> splitOn' (== '.') "a..b" > ["a","","b"]  Since: 0.7.0 splitOnSuffix :: (IsStream t, Monad m) => (a -> Bool) -> Fold m a b -> t m a -> t m b Source # Like splitOn but the separator is considered as suffixed to the segments in the stream. A missing suffix at the end is allowed. A separator at the beginning is parsed as empty segment. With - representing elements and . as separator, splitOnSuffix splits as follows:  "--.--." => "--" "--" "--.--" => "--" "--" ".--." => "" "--"  splitOnSuffix' p xs = S.toList$ S.splitSuffixBy p (FL.toList) (S.fromList xs)
>>> splitOnSuffix' (== '.') ""
[]

>>> splitOnSuffix' (== '.') "."
[""]

>>> splitOnSuffix' (== '.') "a"
["a"]

>>> splitOnSuffix' (== '.') ".a"
> ["","a"]

>>> splitOnSuffix' (== '.') "a."
> ["a"]

>>> splitOnSuffix' (== '.') "a.b"
> ["a","b"]

>>> splitOnSuffix' (== '.') "a.b."
> ["a","b"]

>>> splitOnSuffix' (== '.') "a..b.."
> ["a","","b",""]

lines = splitOnSuffix (== '\n')

Since: 0.7.0

splitWithSuffix :: (IsStream t, Monad m) => (a -> Bool) -> Fold m a b -> t m a -> t m b Source #

Like splitOnSuffix but keeps the suffix attached to the resulting splits.

splitWithSuffix' p xs = S.toList $S.splitWithSuffix p (FL.toList) (S.fromList xs) >>> splitWithSuffix' (== '.') "" []  >>> splitWithSuffix' (== '.') "." ["."]  >>> splitWithSuffix' (== '.') "a" ["a"]  >>> splitWithSuffix' (== '.') ".a" > [".","a"]  >>> splitWithSuffix' (== '.') "a." > ["a."]  >>> splitWithSuffix' (== '.') "a.b" > ["a.","b"]  >>> splitWithSuffix' (== '.') "a.b." > ["a.","b."]  >>> splitWithSuffix' (== '.') "a..b.." > ["a.",".","b.","."]  Since: 0.7.0 wordsBy :: (IsStream t, Monad m) => (a -> Bool) -> Fold m a b -> t m a -> t m b Source # Like splitOn after stripping leading, trailing, and repeated separators. Therefore, ".a..b." with . as the separator would be parsed as ["a","b"]. In other words, its like parsing words from whitespace separated text. wordsBy' p xs = S.toList$ S.wordsBy p (FL.toList) (S.fromList xs)
>>> wordsBy' (== ',') ""
> []

>>> wordsBy' (== ',') ","
> []

>>> wordsBy' (== ',') ",a,,b,"
> ["a","b"]

words = wordsBy isSpace

Since: 0.7.0

## Grouping

Splitting a stream by combining multiple contiguous elements into groups using some criterion.

groups :: (IsStream t, Monad m, Eq a) => Fold m a b -> t m a -> t m b Source #

groups = groupsBy (==)
groups = groupsByRolling (==)

Groups contiguous spans of equal elements together in individual groups.

>>> S.toList $S.groups FL.toList$ S.fromList [1,1,2,2]
> [[1,1],[2,2]]


Since: 0.7.0

groupsBy :: (IsStream t, Monad m) => (a -> a -> Bool) -> Fold m a b -> t m a -> t m b Source #

groupsBy cmp f $S.fromList [a,b,c,...] assigns the element a to the first group, if a cmp b is True then b is also assigned to the same group. If a cmp c is True then c is also assigned to the same group and so on. When the comparison fails a new group is started. Each group is folded using the fold f and the result of the fold is emitted in the output stream. >>> S.toList$ S.groupsBy (>) FL.toList $S.fromList [1,3,7,0,2,5] > [[1,3,7],[0,2,5]]  Since: 0.7.0 groupsByRolling :: (IsStream t, Monad m) => (a -> a -> Bool) -> Fold m a b -> t m a -> t m b Source # Unlike groupsBy this function performs a rolling comparison of two successive elements in the input stream. groupsByRolling cmp f$ S.fromList [a,b,c,...] assigns the element a to the first group, if a cmp b is True then b is also assigned to the same group. If b cmp c is True then c is also assigned to the same group and so on. When the comparison fails a new group is started. Each group is folded using the fold f.

>>> S.toList $S.groupsByRolling (\a b -> a + 1 == b) FL.toList$ S.fromList [1,2,3,7,8,9]
> [[1,2,3],[7,8,9]]


Since: 0.7.0

# Combining Streams

New streams can be constructed by appending, merging or zipping existing streams.

## Appending

Streams form a Semigroup and a Monoid under the append operation. Appending can be considered as a generalization of the cons operation to consing a stream to a stream.

-------Stream m a------|-------Stream m a------|=>----Stream m a---


>> S.toList $S.fromList [1,2] <> S.fromList [3,4] [1,2,3,4] >> S.toList$ fold $[S.fromList [1,2], S.fromList [3,4]] [1,2,3,4]  ## Merging Streams form a commutative semigroup under the merge operation. Merging can be considered as a generalization of inserting an element in a stream to interleaving a stream with another stream. -------Stream m a------| |=>----Stream m a--- -------Stream m a------|  mergeBy :: (IsStream t, Monad m) => (a -> a -> Ordering) -> t m a -> t m a -> t m a Source # Merge two streams using a comparison function. The head elements of both the streams are compared and the smaller of the two elements is emitted, if both elements are equal then the element from the first stream is used first. If the streams are sorted in ascending order, the resulting stream would also remain sorted in ascending order. > S.toList$ S.mergeBy compare (S.fromList [1,3,5]) (S.fromList [2,4,6,8])
[1,2,3,4,5,6,8]


Since: 0.6.0

mergeByM :: (IsStream t, Monad m) => (a -> a -> m Ordering) -> t m a -> t m a -> t m a Source #

Like mergeBy but with a monadic comparison function.

Merge two streams randomly:

> randomly _ _ = randomIO >>= x -> return $if x then LT else GT > S.toList$ S.mergeByM randomly (S.fromList [1,1,1,1]) (S.fromList [2,2,2,2])
[2,1,2,2,2,1,1,1]


Merge two streams in a proportion of 2:1:

proportionately m n = do
ref <- newIORef $cycle$ concat [replicate m LT, replicate n GT]
return $\_ _ -> do r <- readIORef ref writeIORef ref$ tail r
return $head r main = do f <- proportionately 2 1 xs <- S.toList$ S.mergeByM f (S.fromList [1,1,1,1,1,1]) (S.fromList [2,2,2])
print xs

[1,1,2,1,1,2,1,1,2]


Since: 0.6.0

mergeAsyncBy :: (IsStream t, MonadAsync m) => (a -> a -> Ordering) -> t m a -> t m a -> t m a Source #

Like mergeBy but merges concurrently (i.e. both the elements being merged are generated concurrently).

Since: 0.6.0

mergeAsyncByM :: (IsStream t, MonadAsync m) => (a -> a -> m Ordering) -> t m a -> t m a -> t m a Source #

Like mergeByM but merges concurrently (i.e. both the elements being merged are generated concurrently).

Since: 0.6.0

## Zipping

-------Stream m a------|
|=>----Stream m c---
-------Stream m b------|


zipWith :: (IsStream t, Monad m) => (a -> b -> c) -> t m a -> t m b -> t m c Source #

Zip two streams serially using a pure zipping function.

> S.toList $S.zipWith (+) (S.fromList [1,2,3]) (S.fromList [4,5,6]) [5,7,9]  Since: 0.1.0 zipWithM :: (IsStream t, Monad m) => (a -> b -> m c) -> t m a -> t m b -> t m c Source # Like zipWith but using a monadic zipping function. Since: 0.4.0 zipAsyncWith :: (IsStream t, MonadAsync m) => (a -> b -> c) -> t m a -> t m b -> t m c Source # Like zipWith but zips concurrently i.e. both the streams being zipped are generated concurrently. Since: 0.1.0 zipAsyncWithM :: (IsStream t, MonadAsync m) => (a -> b -> m c) -> t m a -> t m b -> t m c Source # Like zipWithM but zips concurrently i.e. both the streams being zipped are generated concurrently. Since: 0.4.0 ## Folding Streams of Streams Stream operations like map and filter represent loop processing in imperative programming terms. Similarly, the imperative concept of nested loops are represented by streams of streams. The concatMap operation represents nested looping. A concatMap operation loops over the input stream and then for each element of the input stream generates another stream and then loops over that inner stream as well producing effects and generating a single output stream. The Monad instances of different stream types provide a more convenient way of writing nested loops. Note that the monad bind operation is just flip concatMap. One dimension loops are just a special case of nested loops. For example, concatMap can degenerate to a simple map operation: map f m = S.concatMap (\x -> S.yield (f x)) m Similarly, concatMap can perform filtering by mapping an element to a nil stream: filter p m = S.concatMap (\x -> if p x then S.yield x else S.nil) m concatMapWith :: IsStream t => (forall c. t m c -> t m c -> t m c) -> (a -> t m b) -> t m a -> t m b Source # concatMapWith merge map stream is a two dimensional looping combinator. The first argument specifies a merge or concat function that is used to merge the streams generated by applying the second argument i.e. the map function to each element of the input stream. The concat function could be serial, parallel, async, ahead or any other zip or merge function and the second argument could be any stream generation function using a seed. Compare foldMapWith Since: 0.7.0 concatMap :: (IsStream t, Monad m) => (a -> t m b) -> t m a -> t m b Source # Map a stream producing function on each element of the stream and then flatten the results into a single stream. concatMap = concatMapWith serial concatMap f = concatMapM (return . f)  Since: 0.6.0 concatMapM :: (IsStream t, Monad m) => (a -> m (t m b)) -> t m a -> t m b Source # Map a stream producing monadic function on each element of the stream and then flatten the results into a single stream. Since the stream generation function is monadic, unlike concatMap, it can produce an effect at the beginning of each iteration of the inner loop. Since: 0.6.0 concatUnfold :: (IsStream t, Monad m) => Unfold m a b -> t m a -> t m b Source # Like concatMap but uses an Unfold for stream generation. Unlike concatMap this can fuse the Unfold code with the inner loop and therefore provide many times better performance. Since: 0.7.0 # Exceptions before :: (IsStream t, Monad m) => m b -> t m a -> t m a Source # Run a side effect before the stream yields its first element. Since: 0.7.0 after :: (IsStream t, Monad m) => m b -> t m a -> t m a Source # Run a side effect whenever the stream stops normally. Since: 0.7.0 bracket :: (IsStream t, MonadCatch m) => m b -> (b -> m c) -> (b -> t m a) -> t m a Source # Run the first action before the stream starts and remember its output, generate a stream using the output, run the second action using the remembered value as an argument whenever the stream ends normally or due to an exception. Since: 0.7.0 onException :: (IsStream t, MonadCatch m) => m b -> t m a -> t m a Source # Run a side effect whenever the stream aborts due to an exception. Since: 0.7.0 finally :: (IsStream t, MonadCatch m) => m b -> t m a -> t m a Source # Run a side effect whenever the stream stops normally or aborts due to an exception. Since: 0.7.0 handle :: (IsStream t, MonadCatch m, Exception e) => (e -> t m a) -> t m a -> t m a Source # When evaluating a stream if an exception occurs, stream evaluation aborts and the specified exception handler is run with the exception as argument. Since: 0.7.0 # Deprecated once :: (Monad m, IsStream t) => m a -> t m a Source # Deprecated: Please use yieldM instead. Same as yieldM Since: 0.2.0 each :: (IsStream t, Foldable f) => f a -> t m a Source # Deprecated: Please use fromFoldable instead. Same as fromFoldable. Since: 0.1.0 scanx :: (IsStream t, Monad m) => (x -> a -> x) -> x -> (x -> b) -> t m a -> t m b Source # Deprecated: Please use scanl followed by map instead. Strict left scan with an extraction function. Like scanl', but applies a user supplied extraction function (the third argument) at each step. This is designed to work with the foldl library. The suffix x is a mnemonic for extraction. Since: 0.7.0 (Monad m constraint) Since 0.2.0 foldx :: Monad m => (x -> a -> x) -> x -> (x -> b) -> SerialT m a -> m b Source # Deprecated: Please use foldl' followed by fmap instead. Strict left fold with an extraction function. Like the standard strict left fold, but applies a user supplied extraction function (the third argument) to the folded value at the end. This is designed to work with the foldl library. The suffix x is a mnemonic for extraction. Since: 0.2.0 foldxM :: Monad m => (x -> a -> m x) -> m x -> (x -> m b) -> SerialT m a -> m b Source # Deprecated: Please use foldlM' followed by fmap instead. Like foldx, but with a monadic step function. Since: 0.2.0 foldr1 :: Monad m => (a -> a -> a) -> SerialT m a -> m (Maybe a) Source # Deprecated: Use foldrM instead. Lazy right fold for non-empty streams, using first element as the starting value. Returns Nothing if the stream is empty. Since: 0.5.0 runStream :: Monad m => SerialT m a -> m () Source # Deprecated: Please use "drain" instead Run a stream, discarding the results. By default it interprets the stream as SerialT, to run other types of streams use the type adapting combinators for example runStream . asyncly. Since: 0.2.0 runN :: Monad m => Int -> SerialT m a -> m () Source # Deprecated: Please use "drainN" instead runN n = runStream . take n Run maximum up to n iterations of a stream. Since: 0.6.0 runWhile :: Monad m => (a -> Bool) -> SerialT m a -> m () Source # Deprecated: Please use "drainWhile" instead runWhile p = runStream . takeWhile p Run a stream as long as the predicate holds true. Since: 0.6.0 fromHandle :: (IsStream t, MonadIO m) => Handle -> t m String Source # Deprecated: Please use Streamly.FileSystem.Handle module (see the changelog) Read lines from an IO Handle into a stream of Strings. Since: 0.1.0 toHandle :: MonadIO m => Handle -> SerialT m String -> m () Source # Deprecated: Please use Streamly.FileSystem.Handle module (see the changelog) toHandle h = S.mapM_$ hPutStrLn h


Write a stream of Strings to an IO Handle.

Since: 0.1.0