Haskell binary search tree

BinTree.hs

module BinTree where

data BinTree a = Leaf 
            | Node (BinTree a) a (BinTree a)

instance Show a => Show (Tree a) where
    show Leaf = "Leaf"
    show (Node lt x rt) = "(" ++ show lt ++ " " ++ show x ++ " " ++ show rt ++ ")"

-- Tree is a Functor
instance Functor BinTree where
 -- fmap :: (a -> b) -> f a -> f b
    fmap f Leaf = Leaf
    fmap f (Node lt x rt) = Node (fmap f lt) (f x) (fmap f rt)
  
-- Tree is an Applicative Functor
instance Applicative BinTree where
 -- pure :: a -> f a
 -- (<*>) :: f (a -> b) -> f a -> f b
    pure x = Node Leaf x Leaf
    Leaf <*> _ = Leaf
    _ <*> Leaf = Leaf
    (Node lf f rf) <*> (Node lt x rt) = Node (lf <*> lt) (f x) (rf <*> rt)
  
-- tree functions
insertTree :: (Ord a, Eq a) => a -> BinTree a -> BinTree a
insertTree a Leaf = Node Leaf a Leaf
insertTree a (Node lt x rt)
    | a == x = Node lt a rt
    | a < x  = Node (insertTree a lt) x rt
    | a > x  = Node lt x (insertTree a rt)
    
searchTree :: (Eq a, Ord a) => a -> BinTree a -> Bool
searchTree a Leaf = False
searchTree a (Node lt x rt)
    | a == x = True
    | a < x  = searchTree a lt
    | a > x  = searchTree a rt