 Solution

The recursive Cartesian product is:

cpRec :: [[a]] -> [[a]]
cpRec [] = [[]]
cpRec (xs:xss) = [x:ys | x <- xs, ys <- cpRec xss]

The corresponding right fold is:

cpFold :: [[a]] -> [[a]]
cpFold = foldr step [[]]
  where
    step :: [a] -> [[a]] -> [[a]]
    step xs acc = [x:ys | x <- xs, ys <- acc]

cp :: [[a]] -> [[a]]
cp = cpRec

The base [[]] is essential: there is one way to choose from no factors, namely the empty selection. For a nonempty outer list, choose its first coordinate and prepend it to each selection from the remaining factors. This also proves equality with the right fold by structural induction. An empty factor produces no selections.