Ralf Hemmecke wrote:
>
> > Foo(S: Meet(Category(SubDomain(c_1,R)), Category(SubDomain(c_2,R)),
> > ...)) :...
> >
> > where you will need a infinite list of possible conditions.
>
> Not a good example for me. The category of SubDomain(X, p?) does not
> have anything to do with the category of X. Don't you agree?
>
OK, I think you found yet another hole in this concept.
> > Insted, you can write:
> >
> > Foo(S: SubsetCategory(R)):...
>
> I don't see the advantage of this. Suppose you define a Foo like this
> and now you are going to explicitly write the "add" part. Which
> functionality of S can you now actually use inside Foo? You always have
> to wrap things with if's like
>
Actually SubsetCategory has extra argument, so it specifies
subset which is of specific category. However, since for
SubDomain I see no such extra category argument, this breaks
relation between SubDomain and SubsetCategory
> if S has AbelianGroup then ...
>
> because statically you (and the compiler) have no knowledge about the
> category of R.
>
I think that Localize actually presents intened use: in Localize
you know that R is a CommutativeRing, so category of R is
known. I believe that intended use was to pass SubDomain,
like NonZeroInteger to Localize and get (indirectly) rational
numbers. Or one would pass NumbersRelativelyPrimeTo(5) and
get apropriate local ring. AFAICS such defnitions would
allow more static checking than we have now and some dynamic
checks would be inserted automatically by the compiler.
However given current state of both SubDomain and
SubsetCategory this is not going to work.
--
Waldek Hebisch
[EMAIL PROTECTED]
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