Re: Ada self-referential operators

[ncohen@watson.ibm.com (Norman H. Cohen)]

In article <D3nsJJ.6qz@swlvx2.msd.ray.com>, jgv@swl.msd.ray.com (John
Volan) writes:

|> Realize that the relationship between "=" and "/=" is *unique* within
|> Ada.

Sad but true.  I wish the ordering operators worked analogously:  For two
operands of a given type T and a result of type Boolean, you would be
allowed to define (or override a predefinition) of exactly one of "<",
">", "<=", or ">=", and the others would be implicitly defined for you.
If the programmer chose to define "<", the others would be implicitly
defined as follows:

   function ">" (Left, Right: T) return Boolean is
   begin
      return Right < Left;
   end ">";

   function "<=" (Left, Right: T) return Boolean is
   begin
      return Left < Right or Left = Right;
   end "<=";

   function ">=" (Left, Right: T) return Boolean is
   begin
      return Right < Left or Right = Left;
   end ">=";

If the programmer chose to define "<=", the others would be implicitly
defined as follows:

   function "<" (Left, Right: T) return Boolean is
   begin
      return Left <= Right and Left /= Right;
   end "<";

   function ">" (Left, Right: T) return Boolean is
   begin
      return Right <= Left and Right /= Left;
   end ">=";

   function ">=" (Left, Right: T) return Boolean is
   begin
      return Right <= Left;
   end ">=";

This would only be allowed for types with an "=" operator (nonlimited
types and limited types with programmer-defined "=").

(For some relations it may be most straightforward to define "<"
explicitly, but for others, such as set containment, it is more
straightforward to define "<=" explicitly.  Note that we do NOT define
A>=B, for example, to be equivalent to not(A<B).  That relationship does
not hold for partial orders such as the set containment relation.)

The advantages of this approach would be:

   - Guaranteed consistency among the ordering operators.
   - Avoidance of tedious, redundant work to provide a complete set of
       ordering operators.
   - Ability to declare a single ordering operator to a generic formal
       function but to have operator clearest in a given context
       available anywhere in the generic template.

--
Norman H. Cohen    ncohen@watson.ibm.com