An infinite sequence.

Extract the first element of the sequence.

Extract the sequence following the head of the stream.

Apply a function uniformly over all elements of a sequence.

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

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

repeat x returns a constant stream, where all elements are equal to x.

cycle xs returns the infinite repetition of xs:

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

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

take n xs returns the first n elements of xs.

The splitAt function takes an integer n and a stream xs | and returns a pair consisting of the prefix of xs of length | n and the remaining stream immediately following this prefix.

drop n xs drops the first n elements off the front of the sequence xs.

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

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

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

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

filter p xs, removes any elements from xs that do not satisfy p.

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.

The isPrefix function returns True if the first argument is a prefix of the second.

xs !! n returns the element of the stream xs at index n. Note that the head of the stream has index 0.

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

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

The unzip function is the inverse of the zip function.

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

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

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

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

The listToStream converts an infinite list to a stream. Passing a finite list will result in an error.

The streamToList converts a stream into an infinite list.