[Haskell-beginners] partition a list in all possible ways

I'm looking for a function [a] -> [[[a]]] that will partition a list into non-empty pieces in all possible ways. For example f [1,2,3,4] = [[[1],[2],[3],[4]], [[1],[2],[3,4]], [[1],[2,3],[4]], [[1],[2,3,4]], [[1,2],[3],[4]], [[1,2],[3,4]], [[1,2,3],[4]], [[1,2,3,4]]] Perhaps this is a well-known function to experts, but not to me. Hoogle doesn't seem to have anything with this signature. Thanks, Jack