"fold" in Haskell? -

write function of higher order ateach f xs applying default function f each element of list xs.

ateach succ [1 5] = [2,3,4,5,6] ateach length ["haskell", "go", "forward"] = [7,5,8] 

as dave4420 pointed out, ateach seems standard map function (please clarify if not). if case, have different ways implement it, e.g.:

-- direct recursion ateach _ [] = [] ateach f (x:xs) = ???   -- list comprehension ateach f xs = [??? | x <- xs]  --using fold ateach f = foldr ??? [] 

i don't want spoil fun, can try fill out ???.