Added comments

tests/poly/red-black.cd

@@ -28,6 +28,9 @@ let balance ( Unbalanced('a) -> Rtree('a) ; 'b\Unbalanced('a) -> 'b\Unbalanced('
 ;;
 ************)
 
+(*                                                                               *)
+(* Version 1: restrict the domain of balance to trees (ie, RBtree | Unbalanced)  *)
+(*                                                                               *)
 
 let balance ( Unbalanced('a) -> Rtree('a) ; 'b & RBtree('a) -> 'b & RBtree('a) )
   | <black (z)>[ <red (y)>[ <red (x)>[ a b ] c ] d ]
@@ -39,6 +42,12 @@ let balance ( Unbalanced('a) -> Rtree('a) ; 'b & RBtree('a) -> 'b & RBtree('a) )
 ;;
 
 
+(*                                                                               *)
+(* Version 2: restrict the first branch to Unbalanced trees whatever             *)
+(*            type it contains                                                   *)
+(*                                                                               *)
+
+
 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 ]
@@ -48,14 +57,19 @@ let balance ( Unbalanced('a) -> Rtree('a) ; 'b\Unbalanced(Any) -> 'b\Unbalanced(
   | x -> x
 ;;
 
-(*
+
+(*                                                                               *)
+(* Version 3: Use the accepted type of the first branch (i.e. UTree)             *)
+(*            to specify the behavious when the second branch is taken           *)
+(*                                                                               *)
+
+
 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 ] ] 
              | <black (Any)>[ Any <red (Any)>[ Any <red (Any)>[ Any Any ] ] ]
 ;;
 
-
 let balance ( Unbalanced('a) -> Rtree('a) ; 'b\UTree -> 'b\UTree )
   | <black (z)>[ <red (y)>[ <red (x)>[ a b ] c ] d ]
   | <black (z)>[ <red (x)>[ a <red (y)>[ b c ] ] d ]
@@ -64,7 +78,7 @@ 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         *)
@@ -83,10 +97,13 @@ let insert (x : 'a) (t : Btree('a)) : Btree('a) =
        | <_ (y)>[ a b ] -> <black (y)>[ a b ]
  
 
-let is_empty ( RBtree('a) -> Bool ) | [] -> `true | _ -> `false
+let is_empty (RBtree('a) -> Bool)  (*better type (Any\[] -> `false ; [] ->`true ) *)
+  | [] -> `true
+  | _ -> `false
 
 
 let member (x : 'a) (t : RBtree('a)) : Bool =
+(* better type: 'a -> ([] -> `false & RBtree('a) -> Bool) *) 
   match t with
    | [] -> `false
    | <_ elem=y>[ left right ] ->
@@ -96,6 +113,6 @@ let member (x : 'a) (t : RBtree('a)) : Bool =
 let singleton (x : 'a): Btree('a)  = <black elem=x>[ [] [] ]
 
 
-let cardinal ( RBtree('a) -> Int )
+let cardinal ( RBtree('a) -> Int )   (* better type: [] -> 0, Any\[] -> [1--*] *)
   | [] -> 0
   | <_ ..>[ l r ] -> cardinal l + cardinal r + 1
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