A list of the form fromList xs <> cycle ys where xs and ys are finite lists.

fromList xs is a representation of the list xs, which must be finite.

repeat x is the infinite repetition of a single value.

cycle xs is the infinite repetition of the list xs, which must be finite.

iterate f x is an infinite list of repeated applications of f to x, provided an earlier value is repeated at some point. If no repetition occurs, the computation does not terminate.

unfoldr f z is a list built from a seed value z. The function f takes a seed value and returns Nothing if it is done producing the list or returns Just (a,b), in which case, a is a prepended to the list and b is used as the next seed value in a recursive call. This will not terminate unless one of these evaluations of f returns Nothing or Just (a,b) where b is a previously seen value.

prefix xs is the minimal non-repeating part at the front of xs.

repetend xs is the minimal repeating part of xs, or [] if xs is finite.

map f xs is the list obtained by applying f to each element of xs.

concat xss is the concatenation of all the lists in xss.

concatMap f xs is the concatenation of mapping f over the elements of xs.

concatMap f xs = concat (map f xs)

zip xs ys is a list of corresponding pairs in xs and ys. If one input list is shorter, unmatched elements of the longer list are not included.

zipWith f xs ys is a list of f applied to corresponding elements from xs and ys. If one input list is shorter, unmatched elements of the longer list are not included.

unzip xys in a pair of the list of first components of xys and the list of second components.

filter p xs is the list of elements x of xs for which p x is True.

partition p xs is the list of elements x of xs for which p x is True and the list of those for which it is False.

takeWhile p xs is the longest prefix (possibly empty) of xs of elements that satisfy p.

dropWhile p xs is the remainder of the list after the longest prefix (possibly empty) of xs of elements that satisfy p. If no element satisfies p, the result is an empty list.

span p xs is a pair whose first element is the longest prefix (possibly empty) of xs of elements that satisfy p and whose second element is the remainder of the list. If no element satisfies p, the first list is xs and the second is empty.

take n xs is the prefix of xs of length n, or all of xs if xs is finite and n > length xs.

drop n xs is the suffix of xs after the first n elements, or empty if xs is finite and n > length xs.

splitAt n xs is a pair whose first element is the prefix of xs of length n and whose second element is the remainder of the list.

tails xs is the list of final segments of xs, longest first.

finite xs is True when xs is finite.

elementAt i xs is the element of xs at position i (counting from zero), or Nothing if xs has fewer than i elements.

elemIndex x xs is the index of the first element in xs that is equal (by ==) to x, or Nothing if there is no such element.

find p xs is Just x if x is the first element of xs for which p x is True, or Nothing if there is no such element.

findIndex p xs is Just i if i is the first element x of xs for which p x is True, or Nothing if there is no such element.

any p xs is True if any only if p x is True for any element of xs.

all p xs is True if any only if p x is True for all elements of xs.

maximumBy cmp xs is the greatest element of xs (which must be non-empty) with respect to the comparison function cmp.

minimumBy cmp xs is the least element of xs (which must be non-empty) with respect to the comparison function cmp.

foldMapTake f n xs applies f to the first n elements of xs and combines the results:

foldMapTake f n = foldMap f . take n

but may be significantly faster for some monoids.