added few more operations

tests/poly/red-black.cd

@@ -38,6 +38,7 @@ let balance ( Unbalanced('a) -> Rtree('a) ; 'b & RBtree('a) -> 'b & RBtree('a) )
   | x -> x
 ;;
 
+
 let balance ( Unbalanced('a) -> Rtree('a) ; 'b\Unbalanced(Any) -> 'b\Unbalanced(Any) )
   | (<black (z)>[ <red (y)>[ <red (x)>[ a b ] c ] d ]
   | <black (z)>[ <red (x)>[ a <red (y)>[ b c ] ] d ]
@@ -47,6 +48,7 @@ let balance ( Unbalanced('a) -> Rtree('a) ; 'b\Unbalanced(Any) -> 'b\Unbalanced(
   | x -> x
 ;;
 
+(*
 type  UTree = <black (Any)>[ <red (Any)>[ <red (Any)>[ Any Any ] Any ] Any ] 
              | <black (Any)>[ <red (Any)>[ Any <red (Any)>[ Any Any ] ] Any ] 
              | <black (Any)>[ Any <red (Any)>[ <red (Any)>[ Any Any ] Any ] ] 
@@ -62,6 +64,11 @@ let balance ( Unbalanced('a) -> Rtree('a) ; 'b\UTree -> 'b\UTree )
         <red (y)>[ <black (x)>[ a b ] <black (z)>[ c d ] ]
   | x -> x
 ;;
+*)
+
+
+(* Here we start the definition of         *)
+(* standard operations for red-black trees *)
 
 let insert (x : 'a) (t : Btree('a)) : Btree('a) =
   let ins_aux ( [] -> Rtree('a);
@@ -75,3 +82,20 @@ let insert (x : 'a) (t : Btree('a)) : Btree('a) =
     in match ins_aux t with
        | <_ (y)>[ a b ] -> <black (y)>[ a b ]
  
+
+let is_empty ( RBtree('a) -> Bool ) | [] -> `true | _ -> `false
+
+
+let member (x : 'a) (t : RBtree('a)) : Bool =
+  match t with
+   | [] -> `false
+   | <_ elem=y>[ left right ] ->
+       (y = x) || ( member x (if x<<y then left else right) ) 
+
+
+let singleton (x : 'a): Btree('a)  = <black elem=x>[ [] [] ]
+
+
+let cardinal ( RBtree('a) -> Int )
+  | [] -> 0
+  | <_ ..>[ l r ] -> cardinal l + cardinal r
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