Re: Integers and Mathematical Correctness

[Adam Beneschan <adambeneschan@gmail.com>]

On Friday, September 26, 2014 9:59:00 AM UTC-7, AdaMagica wrote:
> On Friday, September 26, 2014 6:38:10 PM UTC+2, Niklas Holsti wrote:
 
> > False. Ada can overload operators on the result type, so you can very 
> > well add
> >
> >    function "/" (Left, Right : Integer) return Rational;
> 
> > and have both"/" visible and used with in-fix notation.
>
> Nah, it's not that easy. The reason is that Integer is defined in Standard, which always has precedence for any use-clause.

The precedence of use clauses is irrelevant.  This (and other rules about visibility and hiding) are used when there are two homographs and the compiler needs to decide which one is meant.  Thus, if you have a type "Integer" defined in Standard, and a type "Integer" defined in some USE'd package, I think the one in Standard would hide the other one, as you say.

However, functions are homographs only if they have the same name, same parameter types, and same return type.  Thus, the function

   function "/" (Left, Right : Integer) return Integer;

defined in Standard cannot hide the function

   function "/" (Left, Right : Integer) return Rational;

defined somewhere else.  The compiler uses the overloading rules, not the USE rules or any such visibility rules, to determine which one is meant.  So if use use / in a context where the result is Rational, it will work fine--the definition in Standard cannot hide it.  If you use it in a context where the compiler can't tell which one is meant, the expression is ambiguous--the rules about USE clauses and such will not help to make it unambiguous.
 
 
> You need a separate integer type
> 
>   type Whole is range ...
>   function "/" (Left, Right: Whole) return Rational;

No, this is not necessary.  Unless the compiler is faulty.

                             -- Adam