[Axiom-developer] Re: categories with parameters and defaults

[Ralf Hemmecke]

On 03/14/2006 07:09 PM, Page, Bill wrote:
> Ralf, 
>
> On Tuesday, March 14, 2006 9:58 AM you wrote:
> > I wrote:
> > > I suppose it would be better to write:
> > >
> > >    default {
> > >      Rep == T;
> > >      square(t: %): % == per(m(rep(t), rep(t))
> > >    }
> > NOOOO.... PLEASE DONT USE ANY REPRESENTATION IN A CATEGORY.
>
> The 'Rep' is not a representation in a category. It is in
> the default implementation of 'square' which is implemented
> in some domain which satisfies this category.
>
> Perhaps you might object that such defaults are best thought
> of as virtual packages. I agree that in SPAD that that is how
> they are implemented. But we still need to worry about
> representation since ultimately they are used in the context
> of some domain which satisfies the corresponding category.
>
> > Suppose someone later implements your category and just
> > uses some other representation than T.
>
> Say what? ;) This default clause is just part of the
> definition of a category where T is a parameter of the category,
> e.g. Martin's 'MyMonoid'. What type T represents depends on how
> this category is "called", e.g. in
>
>   MyMonoid(Integer, *$Integer)
>
> T is Integer, so we have the representation
>
>   Rep == Integer;
>
> In other cases we have other representations

Let me give explicit code...

--- RepInCat.as
#include "aldor"
#include "aldorio"
define CatA(T: Type, foo: T->T): Category == OutputType with {
  foo: () -> %;
  bar: % -> %;
  default {
    Rep == T;
    bar(x: %): % == per foo rep x;
  }
}

DomA: CatA(Integer, -$Integer) == add {
  Rep == List Boolean; import from Rep;
  foo(): % == per [true, false];
  (p: TextWriter) << (x: %): TextWriter == p << rep x;
}

main(): () == {
  import from DomA;
  stdout <<     foo()  << newline; flush!(stdout);
  stdout << bar(foo()) << newline; flush!(stdout);
}
main();
---- end RepInCat.as

By fixing the "Rep" in the category, you require that the compiler has 
to reject the definition of DomA. Currently the Aldor compiler does not 
do that.

And so the above program compiles and yields as output...

aldor -laldor -fx RepInCat.as
RepInCat
[T,F]
Segmentation fault

As expected, right?

If you want the compiler to fix the representation in the category, we 
are back to the multiple inheritance problem.

Ralf