I'm trying to construct a function all_trees :: [Int] -> [Tree] such that all_trees [1,2,3] will yield [ Leaf 1, Leaf 2, Leaf 3, Branch (Leaf 1) (Leaf 2), Branch (Leaf 1) (Leaf 3), Branch (Leaf 2) (Leaf 1), Branch (Leaf 2) (Leaf 3), Branch (Leaf 3) (Leaf 1), Branch (Leaf 3) (Leaf 2), Branch (Branch (Leaf 1) (Leaf 2)) (Leaf 3), Branch (Branch (Leaf 1) (Leaf 3)) (Leaf 1), Branch (Branch (Leaf 2) (Leaf 1)) (Leaf 3), Branch (Branch (Leaf 2) (Leaf 3)) (Leaf 1), Branch (Branch (Leaf 3) (Leaf 1)) (Leaf 2), Branch (Branch (Leaf 3) (Leaf 2)) (Leaf 1), Branch (Leaf 1) (Branch (Leaf 2) (Leaf 3)), Branch (Leaf 1) (Branch (Leaf 3) (Leaf 2)), Branch (Leaf 2) (Branch (Leaf 1) (Leaf 3)), Branch (Leaf 2) (Branch (Leaf 3) (Leaf 2)), Branch (Leaf 3) (Branch (Leaf 1) (Leaf 2)), Branch (Leaf 3) (Branch (Leaf 2) (Leaf 1)) ] So far I'm not doing too well. Here's what I've got: data Tree = Leaf Int | Branch Tree Tree pick :: [x] -> [(x,[x])] pick = pick_from [] pick_from :: [x] -> [x] -> [(x,[x])] pick_from ks [] = [] pick_from ks [x] = [] pick_from ks xs = (head xs, ks ++ tail xs) : pick_from (ks ++ [head xs]) (tail xs) setup :: [Int] -> [Tree] setup = map Leaf tree2 :: [Tree] -> [Tree] tree2 xs = do (x0,xs0) <- pick xs (x1,xs1) <- pick xs0 return (Branch x0 x1) all_trees ns = (setup ns) ++ (tree2 $ setup ns) Clearly I need another layer of recursion here. (The input list is of arbitrary length.) However, I need to somehow avoid creating duplicate subtrees... (BTW, I'm really impressed with how useful the list monad is for constructing tree2...)