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

I would prefer the following solutions, using the built-in functions cycle and tails:

rotations xs = take len $ map (take len) $ tails $ cycle xs where
    len = length xs 

For your example [1,2,3,4] the function cycle produces an infinite list [1,2,3,4,1,2,3,4,1,2...]. The function tails generates all possible tails from a given list, here [[1,2,3,4,1,2...],[2,3,4,1,2,3...],[3,4,1,2,3,4...],...]. Now all we need to do is cutting down the "tails"-lists to length 4, and cutting the overall list to length 4, which is done using take. The alias len was introduced to avoid to recalculate length xs several times.