I'm trying to do this from scratch, without the use of a library outside the standard lib. Heres my code:

permutations :: [a] -> [[a]]
permutations (x:xs) = [x] : permutations' xs
    where permutations' (x:xs) = (:) <$> [x] <*> split xs
            split l = [[x] | x <- l]

The problem is that this only produces one fork of the non-deterministic computation. Ideally I'd want

(:) <$> [x] <*> ((:) <$> [x] <*> ((:) <$> [x] <*> ((:) <$> [x] <*> xs)))

But I can't find a way to do this cleanly. My desired result is something like this:

permutations "abc" -> ["abc", "acb", "bac", "bca", "cab", "cba"]

How do I do this?