How to define a rotates function

Question

How to define a rotates function that generates all rotations of the given list?

For example: rotates [1,2,3,4] =[[1,2,3,4],[2,3,4,1],[3,4,1,2],[4,1,2,3]]

Answer 1

shift (x:xs)  =  xs ++ [x]
rotates xs    =  take (length xs) $ iterate shift xs

iterate f x returns the stream ("infinite list") [x, f x, f (f x), ...]. There are n rotations of an n-element list, so we take the first n of them.