module type BINTREE =
sig
  type bin_tree
  val empty : bin_tree
  val member : bin_tree -> int -> bool
  val insert : bin_tree -> int -> bin_tree
end

module Bintree : BINTREE =
struct

  type bin_tree =
    | Empty
    | Node of bin_tree * bin_tree * int

  let empty = Empty

  let rec member (t:bin_tree) (i:int):bool =
    match t with
      | Empty -> false
      | Node (l, r, j) ->
	  if i = j then true
	  else if i < j then (member l i)
	  else (member r i)

  let rec insert (t:bin_tree) (i:int):bin_tree =
    match t with
      | Empty -> Node (Empty, Empty, i)
      | Node (l, r, j) ->
	  if i < j then Node (insert l i, r, j)
	  else Node (l, insert r i, j)

end