Compare Binary Search Trees

data Tree a = Empty | Node a (Tree a) (Tree a) deriving (Show) data Result a = Equal | NotEqual | RemainsLeft a | RemainsRight a deriving (Show, Eq) cmp Empty Empty = Equal cmp Empty t2 = RemainsRight t2 cmp t1 Empty = RemainsLeft t1 cmp t1@(Node v1 l1 r1) t2@(Node v2 l2 r2) | v1 == v2 = case (cmp l1 l2) of Equal -> (cmp r1 r2) _ -> NotEqual | v1 < v2 = if l2 == Empty then NotEqual else case (cmp t1 l2) of Equal -> RemainsRight (Node v2 Empty r2) NotEqual -> NotEqual RemainsLeft t1' -> cmp t1' (Node v2 Empty r2) RemainsRight l2' -> RemainsRight (Node v2 l2' r2) | otherwise = if l1 == Empty then NotEqual else case (cmp l1 t2) of Equal -> RemainsLeft (Node v1 Empty r1) NotEqual -> NotEqual RemainsLeft l1' -> RemainsLeft (Node v1 l1' r1) RemainsRight t2' -> cmp (Node v1 Empty r1) t2' instance (Ord a) => Eq (Tree a) where t1 == t2 = (cmp t1 t2) == Equal test1 = let t213 = Node 2 (Node 1 Empty Empty) (Node 3 Empty Empty) in let t657 = Node 6 (Node 5 Empty Empty) (Node 7 Empty Empty) in let t1 = Node 4 t213 (Node 8 t657 (Node 9 Empty Empty)) in let t2 = Node 8 (Node 4 t213 t657) (Node 9 Empty Empty) in t1 == t2 test2 = let t213 = Node 2 (Node 1 Empty Empty) (Node 3 Empty Empty) in let t657 = Node 6 (Node 5 Empty Empty) (Node 7 Empty Empty) in let t1 = Node 4 t213 (Node 8 t657 (Node 9 Empty Empty)) in let t2 = Node 8 (Node 4 t213 t657) (Node 9 Empty (Node 10 Empty Empty)) in t1 /= t2