Copyright | (C) 2011 Edward Kmett (C) 2007-2010 Wouter Swierstra Bas van Dijk |
---|---|

License | BSD-style (see the file LICENSE) |

Maintainer | Edward Kmett <ekmett@gmail.com> |

Stability | provisional |

Portability | portable (Haskell 2010) |

Safe Haskell | Trustworthy |

Language | Haskell98 |

- data Stream a = a :> (Stream a)
- tail :: Stream a -> Stream a
- inits :: Stream a -> Stream [a]
- prepend :: Foldable f => f a -> Stream a -> Stream a
- concat :: Foldable f => Stream (f a) -> Stream a
- intersperse :: a -> Stream a -> Stream a
- interleave :: Stream a -> Stream a -> Stream a
- scanl :: (a -> b -> a) -> a -> Stream b -> Stream a
- scanl' :: (a -> b -> a) -> a -> Stream b -> Stream a
- scanl1 :: (a -> a -> a) -> Stream a -> Stream a
- scanl1' :: (a -> a -> a) -> Stream a -> Stream a
- transpose :: Stream (Stream a) -> Stream (Stream a)
- iterate :: (a -> a) -> a -> Stream a
- cycle :: NonEmpty a -> Stream a
- unfold :: (a -> (b, a)) -> a -> Stream b
- take :: Int -> Stream a -> [a]
- drop :: Int -> Stream a -> Stream a
- splitAt :: Int -> Stream a -> ([a], Stream a)
- takeWhile :: (a -> Bool) -> Stream a -> [a]
- dropWhile :: (a -> Bool) -> Stream a -> Stream a
- span :: (a -> Bool) -> Stream a -> ([a], Stream a)
- break :: (a -> Bool) -> Stream a -> ([a], Stream a)
- filter :: (a -> Bool) -> Stream a -> Stream a
- partition :: (a -> Bool) -> Stream a -> (Stream a, Stream a)
- group :: Eq a => Stream a -> Stream (NonEmpty a)
- groupBy :: (a -> a -> Bool) -> Stream a -> Stream (NonEmpty a)
- isPrefixOf :: Eq a => [a] -> Stream a -> Bool
- (!!) :: Stream a -> Int -> a
- elemIndex :: Eq a => a -> Stream a -> Int
- elemIndices :: Eq a => a -> Stream a -> Stream Int
- findIndex :: (a -> Bool) -> Stream a -> Int
- findIndices :: (a -> Bool) -> Stream a -> Stream Int
- zip :: Stream a -> Stream b -> Stream (a, b)
- zipWith :: (a -> b -> c) -> Stream a -> Stream b -> Stream c
- unzip :: Stream (a, b) -> (Stream a, Stream b)
- words :: Stream Char -> Stream String
- unwords :: Stream String -> Stream Char
- lines :: Stream Char -> Stream String
- unlines :: Stream String -> Stream Char

# The type of streams

Monad Stream # | |

Functor Stream # | |

Applicative Stream # | |

Foldable Stream # | |

Traversable Stream # | |

Distributive Stream # | |

Representable Stream # | |

Comonad Stream # | |

ComonadApply Stream # | |

Traversable1 Stream # | |

Apply Stream # | |

Extend Stream # | |

Foldable1 Stream # | |

Data a => Data (Stream a) # | |

Show a => Show (Stream a) # | |

type Rep Stream # | |

# Basic functions

# Stream transformations

intersperse :: a -> Stream a -> Stream a #

creates an alternating stream of
elements from `intersperse`

y xs`xs`

and `y`

.

interleave :: Stream a -> Stream a -> Stream a #

Interleave two Streams `xs`

and `ys`

, alternating elements
from each list.

[x1,x2,...] `interleave` [y1,y2,...] == [x1,y1,x2,y2,...]

scanl :: (a -> b -> a) -> a -> Stream b -> Stream a #

`scanl`

yields a stream of successive reduced values from:

scanl f z [x1, x2, ...] == [z, z `f` x1, (z `f` x1) `f` x2, ...]

scanl' :: (a -> b -> a) -> a -> Stream b -> Stream a #

`scanl`

yields a stream of successive reduced values from:

scanl f z [x1, x2, ...] == [z, z `f` x1, (z `f` x1) `f` x2, ...]

scanl1' :: (a -> a -> a) -> Stream a -> Stream a #

`scanl1'`

is a strict `scanl`

that has no starting value.

transpose :: Stream (Stream a) -> Stream (Stream a) #

`transpose`

computes the transposition of a stream of streams.

# Building streams

iterate :: (a -> a) -> a -> Stream a #

produces the infinite sequence
of repeated applications of `iterate`

f x`f`

to `x`

.

iterate f x = [x, f x, f (f x), ..]

cycle :: NonEmpty a -> Stream a #

returns the infinite repetition of `cycle`

xs`xs`

:

cycle [1,2,3] = Cons 1 (Cons 2 (Cons 3 (Cons 1 (Cons 2 ...

unfold :: (a -> (b, a)) -> a -> Stream b #

The unfold function is similar to the unfold for lists. Note there is no base case: all streams must be infinite.

# Extracting sublists

take :: Int -> Stream a -> [a] #

returns the first `take`

n xs`n`

elements of `xs`

.

*Beware*: passing a negative integer as the first argument will
cause an error.

drop :: Int -> Stream a -> Stream a #

drops the first `drop`

n xs`n`

elements off the front of
the sequence `xs`

.

*Beware*: passing a negative integer as the first argument will
cause an error.

splitAt :: Int -> Stream a -> ([a], Stream a) #

returns a pair consisting of the prefix of
`splitAt`

n xs`xs`

of length `n`

and the remaining stream immediately following
this prefix.

*Beware*: passing a negative integer as the first argument will
cause an error.

takeWhile :: (a -> Bool) -> Stream a -> [a] #

returns the longest prefix of the stream
`takeWhile`

p xs`xs`

for which the predicate `p`

holds.

span :: (a -> Bool) -> Stream a -> ([a], Stream a) #

returns the longest prefix of `span`

p xs`xs`

that satisfies
`p`

, together with the remainder of the stream.

filter :: (a -> Bool) -> Stream a -> Stream a #

, removes any elements from `filter`

p xs`xs`

that do not satisfy `p`

.

*Beware*: this function may diverge if there is no element of
`xs`

that satisfies `p`

, e.g. `filter odd (repeat 0)`

will loop.

partition :: (a -> Bool) -> Stream a -> (Stream a, Stream a) #

The `partition`

function takes a predicate `p`

and a stream
`xs`

, and returns a pair of streams. The first stream corresponds
to the elements of `xs`

for which `p`

holds; the second stream
corresponds to the elements of `xs`

for which `p`

does not hold.

*Beware*: One of the elements of the tuple may be undefined. For
example, `fst (partition even (repeat 0)) == repeat 0`

; on the
other hand `snd (partition even (repeat 0))`

is undefined.

group :: Eq a => Stream a -> Stream (NonEmpty a) #

The `group`

function takes a stream and returns a stream of
lists such that flattening the resulting stream is equal to the
argument. Moreover, each sublist in the resulting stream
contains only equal elements. For example,

group $ cycle "Mississippi" = "M" ::: "i" ::: "ss" ::: "i" ::: "ss" ::: "i" ::: "pp" ::: "i" ::: "M" ::: "i" ::: ...

# Sublist predicates

isPrefixOf :: Eq a => [a] -> Stream a -> Bool #

The `isPrefix`

function returns `True`

if the first argument is
a prefix of the second.

# Indexing streams

(!!) :: Stream a -> Int -> a #

`xs !! n`

returns the element of the stream `xs`

at index
`n`

. Note that the head of the stream has index 0.

*Beware*: passing a negative integer as the first argument will cause
an error.

elemIndices :: Eq a => a -> Stream a -> Stream Int #

The `elemIndices`

function extends `elemIndex`

, by returning the
indices of all elements equal to the query element, in ascending order.

*Beware*: `elemIndices`

`x`

`xs`

will diverge if any suffix of
`xs`

does not contain `x`

.

findIndices :: (a -> Bool) -> Stream a -> Stream Int #

The `findIndices`

function extends `findIndex`

, by returning the
indices of all elements satisfying the predicate, in ascending
order.

*Beware*: `findIndices`

`p`

`xs`

will diverge if all the elements
of any suffix of `xs`

fails to satisfy `p`

.

# Zipping and unzipping streams

zip :: Stream a -> Stream b -> Stream (a, b) #

The `zip`

function takes two streams and returns a list of
corresponding pairs.

# Functions on streams of characters

words :: Stream Char -> Stream String #

The `words`

function breaks a stream of characters into a
stream of words, which were delimited by white space.

*Beware*: if the stream of characters `xs`

does not contain white
space, accessing the tail of `words xs`

will loop.