data Tree a = Empty | Branch a (Tree a) (Tree a)
  deriving (Show, Eq)

isMirror :: Tree a -> Tree a -> Bool
isMirror Empty Empty = True
isMirror (Branch _ l1 r1) (Branch _ l2 r2) = isMirror l1 r2 && isMirror r1 l2
isMirror _ _ = False

symmetric :: (Eq a) => Tree a -> Bool
symmetric Empty = True
symmetric (Branch _ l r) = isMirror l r

add :: (Ord a) => a -> Tree a -> Tree a
add x Empty = Branch x Empty Empty
add x t@(Branch v l r) = case compare x v of
  LT -> Branch v (add x l) r
  GT -> Branch v l (add x r)
  EQ -> t

construct :: (Ord a) => [a] -> Tree a
construct = foldl (flip add) Empty