Binary Tree in Elm

BinaryTree.elm

type BinaryTree a = Nil | Node (BinaryTree a) a (BinaryTree a)

insert : comparable -> BinaryTree comparable -> BinaryTree comparable
insert node tree = 
  case tree of 
    Nil -> Node Nil node Nil
    Node left leaf right ->
      if  | leaf == node -> Node left leaf right  
          | leaf <  node -> Node left leaf (insert node right)
          | leaf >  node -> Node (insert node left) leaf right
          
          


isEmpty : BinaryTree a -> Bool
isEmpty tree = 
  case tree of 
    Nil -> True
    _ -> False
    
    
contains : comparable -> BinaryTree comparable -> Bool
contains node tree = 
  case tree of 
    Nil -> False
    Node left leaf right ->
      if | leaf == node -> True
         | leaf <  node -> contains leaf left
         | leaf >  node -> contains leaf right