(*4a. empty : tree                    (* an empty tree *) *)
val empty = Empty;                         (* 5/5 points *)
fun empty () = Empty;                      (* 3/5 points *)
fun empty(Empty) = true | empty(_) = false (* 2/5 points *)

(*4b. member : int -> tree -> bool    (* member x t is true if x is in t *) *)
fun member(x)(Empty) = false |
    member(x)(T(_,l,k,r)) = if (x < k) then member(x)(l) else
			    if (x = k) then true else member(x)(r);

(*4c. insert : int -> tree ->  tree    (* insert x t returns a new tree
                                  containing the elements of t union {x} *) *)
(*  The points were divided into two parts, correct insertion into a binary *)
(* tree and correct rebalancing of the red-black tree                       *)
(* Binary Insert: 10/10 points                                              *)
(* Rebalancing:                                                             *)
(*   10/10 points:  a strong resemblence to Okasaki's solution              *)
(*   8/10  points:  otherwise correct rebalancing                           *)
(*   5/10  points:  some problem with rebalancing                           *)