The type of streams

Move the head of the zipper to the right

Move the head of the zipper to the left

intersperse y xs creates an alternating stream of elements from xs and y.

Interleave two Zippers xs and ys, alternating elements from each list.

[x1,x2,...] `interleave` [y1,y2,...] == [x1,y1,x2,y2,...]
interleave = (<>)

transpose computes the transposition of a stream of streams.

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

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 if you access the taken portion

reverse xs returns the elements of xs in reverse order. xs must be finite.

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

The unzip function is the inverse of the zip function.

Extract the focused element

Cons before the head of the zipper. The head now points to the new element

Move the head of the zipper one step to the right, returning the value we move over.

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.

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

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.

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

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.

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.

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

zip = liftA2 (,)

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

zipWith = liftA2