Data.Stream.Infinite

The type of streams

data Stream a

Constructors

a :> (Stream a) infixr 5

Instances

Monad Stream

Methods

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

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

return :: a -> Stream a

fail :: String -> Stream a

Functor Stream

Methods

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

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

Applicative Stream

Methods

pure :: a -> Stream a

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

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

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

Foldable Stream

Methods

fold :: Monoid m => Stream m -> m

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

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

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

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

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

foldr1 :: (a -> a -> a) -> Stream a -> a

foldl1 :: (a -> a -> a) -> Stream a -> a

toList :: Stream a -> [a]

null :: Stream a -> Bool

length :: Stream a -> Int

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

maximum :: Ord a => Stream a -> a

minimum :: Ord a => Stream a -> a

sum :: Num a => Stream a -> a

product :: Num a => Stream a -> a

Traversable Stream

Methods

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

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

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

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

Distributive Stream

Methods

distribute :: Functor f => f (Stream a) -> Stream (f a)

collect :: Functor f => (a -> Stream b) -> f a -> Stream (f b)

distributeM :: Monad m => m (Stream a) -> Stream (m a)

collectM :: Monad m => (a -> Stream b) -> m a -> Stream (m b)

Representable Stream

Associated Types

type Rep (Stream :: * -> *) :: *

Methods

tabulate :: (Rep Stream -> a) -> Stream a

index :: Stream a -> Rep Stream -> a

Comonad Stream

Methods

extract :: Stream a -> a

duplicate :: Stream a -> Stream (Stream a)

extend :: (Stream a -> b) -> Stream a -> Stream b

ComonadApply Stream

Methods

(<@>) :: Stream (a -> b) -> Stream a -> Stream b

(@>) :: Stream a -> Stream b -> Stream b

(<@) :: Stream a -> Stream b -> Stream a

Traversable1 Stream

Methods

traverse1 :: Apply f => (a -> f b) -> Stream a -> f (Stream b)

sequence1 :: Apply f => Stream (f b) -> f (Stream b)

Apply Stream

Methods

(<.>) :: Stream (a -> b) -> Stream a -> Stream b

(.>) :: Stream a -> Stream b -> Stream b

(<.) :: Stream a -> Stream b -> Stream a

Extend Stream

Methods

duplicated :: Stream a -> Stream (Stream a)

extended :: (Stream a -> b) -> Stream a -> Stream b

Foldable1 Stream

Methods

fold1 :: Semigroup m => Stream m -> m

foldMap1 :: Semigroup m => (a -> m) -> Stream a -> m

Data a => Data (Stream a)

Methods

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

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

toConstr :: Stream a -> Constr

dataTypeOf :: Stream a -> DataType

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

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

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

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

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

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

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

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

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

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

Show a => Show (Stream a)

Methods

showsPrec :: Int -> Stream a -> ShowS

show :: Stream a -> String

showList :: [Stream a] -> ShowS

type Rep Stream

type Rep Stream = Int

Basic functions

tail :: Stream a -> Stream a

Extract the sequence following the head of the stream.

inits :: Stream a -> Stream [a]

The inits function takes a stream xs and returns all the finite prefixes of xs.

Note that this inits is lazier then Data.List.inits:

inits _|_ = [] ::: _|_

while for Data.List.inits:

inits _|_ = _|_

prepend :: Foldable f => f a -> Stream a -> Stream a

Prepend a list to a stream.

concat :: Foldable f => Stream (f a) -> Stream a

Flatten a stream of lists into a stream.

Stream transformations

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

intersperse y xs creates an alternating stream of elements from 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 variant of scanl that has no starting value argument:

scanl1 f [x1, x2, ...] == [x1, 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

iterate f x produces the infinite sequence of repeated applications of f to x.

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

cycle :: NonEmpty a -> Stream a

cycle xs returns the infinite repetition of 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]

take n xs returns the first n elements of xs.

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

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

drop n xs drops the first 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)

splitAt n xs returns a pair consisting of the prefix of 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]

takeWhile p xs returns the longest prefix of the stream xs for which the predicate p holds.

dropWhile :: (a -> Bool) -> Stream a -> Stream a

dropWhile p xs returns the suffix remaining after takeWhile p xs.

Beware: this function may diverge if every element of xs satisfies p, e.g. dropWhile even (repeat 0) will loop.

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

span p xs returns the longest prefix of xs that satisfies p, together with the remainder of the stream.

break :: (a -> Bool) -> Stream a -> ([a], Stream a)

The break p function is equivalent to span not . p.

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

filter p xs, removes any elements from 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" ::: ...

groupBy :: (a -> a -> Bool) -> Stream a -> Stream (NonEmpty a)

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.

elemIndex :: Eq a => a -> Stream a -> Int

The elemIndex function returns the index of the first element in the given stream which is equal (by ==) to the query element,

Beware: elemIndex x xs will diverge if none of the elements of xs equal x.

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.

findIndex :: (a -> Bool) -> Stream a -> Int

The findIndex function takes a predicate and a stream and returns the index of the first element in the stream that satisfies the predicate,

Beware: findIndex p xs will diverge if none of the elements of xs satisfy p.

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.

zipWith :: (a -> b -> c) -> Stream a -> Stream b -> Stream c

The zipWith function generalizes zip. Rather than tupling the functions, the elements are combined using the function passed as the first argument to zipWith.

unzip :: Stream (a, b) -> (Stream a, Stream b)

The unzip function is the inverse of the zip function.

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.

unwords :: Stream String -> Stream Char

The unwords function is an inverse operation to words. It joins words with separating spaces.

lines :: Stream Char -> Stream String

The lines function breaks a stream of characters into a list of strings at newline characters. The resulting strings do not contain newlines.

Beware: if the stream of characters xs does not contain newline characters, accessing the tail of lines xs will loop.

unlines :: Stream String -> Stream Char

The unlines function is an inverse operation to lines. It joins lines, after appending a terminating newline to each.