-- NOTE: this is unfinished and untested

import prelude

data BinTree : Type -> Type where
	Leaf : (A:Type) -> BinTree A
	Node : (A:Type) -> BinTree A -> A -> BinTree A -> BinTree A

contains : (A:Type) -> Ord A -> A -> BinTree A -> Bool
contains _ _ _ (Leaf _) = False
contains A o x (Node _ l y r) 
	| x < y = contains A o x l
	| x > y = contains A o x r
	| otherwise = True

insert : (A:Type) -> Ord A -> A -> BinTree A -> BinTree A
insert A o x (Leaf _) = Node A (Leaf A) x (Leaf A)
insert A o x (Node _ l y r) 
	| x < y = Node A (insert A o x l) y r
	| x > y = Node A l y (insert A o x r)
	| otherwise = Node A l x r