main :: [sys_message]
main = [Stdout (lay [show (f example)
                    | f <- [preorder,inorder,postorder,levelorder]])]

example :: tree num
example = Node 1 (Node 2 (Node 4 (leaf 7) Nilt)
                         (leaf 5))
                 (Node 3 (Node 6 (leaf 8) (leaf 9)) Nilt)

tree * ::= Nilt | Node * (tree *) (tree *)

leaf :: *->tree *
leaf k = Node k Nilt Nilt

preorder :: tree *->[*]
preorder Nilt         = []
preorder (Node v l r) = v : preorder l ++ preorder r

inorder :: tree *->[*]
inorder Nilt         = []
inorder (Node v l r) = inorder l ++ v : inorder r

postorder :: tree *->[*]
postorder Nilt         = []
postorder (Node v l r) = postorder l ++ postorder r ++ [v]

levelorder :: tree *->[*]
levelorder t = f [t]
               where f []              = []
                     f (Nilt:xs)       = f xs
                     f (Node v l r:xs) = v : f (xs++[l,r])