import Test.QuickCheck

------------------------------------------------------------------

-- A binary tree structure:
data Tree a = Leaf a | Node (Tree a) (Tree a)

tree123 :: Tree Int
tree123 = Node (Leaf 1)
               (Node (Leaf 2)
                     (Leaf 3))

-- Returns the height of a binary tree:
height :: Tree a -> Int
height (Leaf x)     = 0
height (Node t1 t2) = 1 + max (height t1) (height t2)

prop_height_nonnegative :: Tree Int -> Bool
prop_height_nonnegative t = height t >= 0


-- Tests with polymorphic operations:
prop_append_commutative :: [Int] -> [Int] -> Bool
prop_append_commutative xs ys = xs ++ ys == ys ++ xs