Given two lists, I can produce a list of all permutations the Cartesian Product of these two lists:
permute :: [a] -> [a] -> [[a]]
permute xs ys = [ [x, y] | x <- xs, y <- ys ]
Example> permute [1,2] [3,4] == [ [1,3], [1,4], [2,3], [2,4] ]
How do I extend permute so that instead of taking two lists, it takes a list (length n) of lists and returns a list of lists (length n)
permute :: [[a]] -> [[a]]
Example> permute [ [1,2], [3,4], [5,6] ]
== [ [1,3,5], [1,3,6], [1,4,5], [1,4,6] ] --etc
I couldn't find anything relevant on Hoogle.. the only function matching the signature was transpose, which doesn't produce the desired output.
Edit: I think the 2-list version of this is essentially the Cartesian Product, but I can't wrap my head around implementing the n-ary Cartesian Product. Any pointers?
Prelude> sequence [[1,2],[3,4],[5,6]]
[[1,3,5],[1,3,6],[1,4,5],[1,4,6],[2,3,5],[2,3,6],[2,4,5],[2,4,6]]