# foldr -text +base

foldr, applied to a binary operator, a starting value (typically the right-identity of the operator), and a list, reduces the list using the binary operator, from right to left: > foldr f z [x1, x2, ..., xn] == x1 `f` (x2 `f` ... (xn `f` z)...)
foldr1 is a variant of foldr that has no starting value argument, and thus must be applied to non-empty lists.
Fold over the elements of a structure, associating to the right, but strictly.
Monadic fold over the elements of a structure, associating to the right, i.e. from right to left.
The unfoldr function is a `dual' to foldr: while foldr reduces a list to a summary value, unfoldr builds a list from a seed value. The function takes the element 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 element in a recursive call. For example, > iterate f == unfoldr (\x -> Just (x, f x)) In some cases, unfoldr can undo a foldr operation: > unfoldr f' (foldr f z xs) == xs if the following holds: > f' (f x y) = Just (x,y) > f' z = Nothing A simple use of unfoldr: > unfoldr (\b -> if b == 0 then Nothing else Just (b, b-1)) 10 > [10,9,8,7,6,5,4,3,2,1]