[Axiom-math] Re: [fricas-devel] Re: [Aldor-l] Type equivalence of domains in Axiom and Aldor

[Bill Page]

Thanks, Ralf. I like your version better than mine. It makes more
sense than the apparently redundant syntactic change I proposed ...
although I wonder why we should define a local function rather than
just write it inline. Would you agree however that that fact that
Saul's original variant does not compile should be considered a
regression bug in the Aldor compiler?

Regards,
Bill Page.


On 11/23/07, Ralf Hemmecke wrote:
>
> Hello Bill,
>
> I think, I don't like your suggestion.
> I'd rather change it into
>
> define Product(Obj:Category):Category == with {
>          ...
> --        *:(Obj,Obj)->Obj;
>      default {
>          local mult(A:Obj, B:Obj):Obj == {
>                  (
>                      AB:Obj,
>                      pa:AB->A,
>                      pb:AB->B,
>                      product:(X:Obj)->(X->A,X->B)->(X->AB)
>                  ) == Product(A,B);
>                  AB add;
>          }
>          *: (Obj,Obj)->Obj == mult;
>      }
> }
>
> The "default" is like defining an anonymous "add" body which exports
> anything on the left of == that is not declared local. So
>
>    *: (Obj,Obj)->Obj
>
> will get exported by Product(Obj) even if you put a "--" as I did above.
>
> Ralf
>
>
> On 11/08/2007 07:51 PM, Bill Page wrote:
> > Ralf,
> >
> > Here is another version that is slightly more friendly to the #pile
> > syntax (-: no {}  required :-). I presume that the compiler generates
> > the same code...
> >
> > --- Categories.as_orig  2007-11-08 10:09:11.000000000 -0800
> > +++ Categories.as       2007-11-08 10:45:51.000000000 -0800
> > @@ -66,3 +66,3 @@
> >      Product: (A1:Obj,B1:Obj,  A2:Obj,B2:Obj) ->
> > (AB1:Obj,AB2:Obj,(A1->A2,B1->B2)->(AB1->AB2))
> > -    *:(Obj,Obj)->Obj
> > +    *:(Obj,Obj)-> with Obj
> >      default
> > @@ -73,3 +73,3 @@
> >             (ab1,ab2,*)
> > -        (A:Obj)*(B:Obj):Obj ==
> > +        (A:Obj)*(B:Obj): with Obj ==
> >              
> > (AB:Obj,pa:AB->A,pb:AB->B,product:(X:Obj)->(X->A,X->B)->(X->AB))
> > == Product(A,B)
> > @@ -83,3 +83,3 @@
> >      CoProduct: (A1:Obj,B1:Obj, A2:Obj,B2:Obj) ->
> > (AB1:Obj,AB2:Obj,(A2->A1,B2->B1)->(AB2->AB1))
> > -    +:(Obj,Obj)->Obj
> > +    +:(Obj,Obj)-> with Obj
> >      default
> > @@ -90,3 +90,3 @@
> >             (ab1,ab2,+)
> > -        (A:Obj)+(B:Obj):Obj ==
> > +        (A:Obj)+(B:Obj): with Obj ==
> >              
> > (AB:Obj,ia:A->AB,ib:B->AB,product:(X:Obj)->(A->X,B->X)->(AB->X))
> > == CoProduct(A,B)
> > @@ -99,5 +99,5 @@
> >      Product:(A:Obj,n:Integer)   ->
> > (Prod:Obj,Integer->(Prod->A),(X:Obj)->(Tuple (X->A))->(X->Prod))
> > -    ^:(Obj,Integer) -> Obj
> > +    ^:(Obj,Integer) -> with Obj
> >      default
> > -        (A:Obj)^(n:Integer):Obj ==
> > +        (A:Obj)^(n:Integer): with Obj ==
> >             (Prod:Obj,project:Integer->(Prod->A),product:(X:Obj)->(Tuple
> > (X->A))->(X->Prod)) == Product(A,n)
> > @@ -110,5 +110,5 @@
> >      CoProduct:(A:Obj,n:Integer) -> (
> > Sum:Obj,Integer->(A->Sum),(X:Obj)->(Tuple (A->X))->(Sum->X))
> > -    ..:(Obj,Integer) -> Obj
> > +    ..:(Obj,Integer) -> with Obj
> >      default
> > -        (A:Obj)..(n:Integer):Obj ==
> > +        (A:Obj)..(n:Integer): with Obj ==
> >             (Sum:Obj,insert:Integer->(A->Sum),sum:(X:Obj)->(Tuple
> > (A->X))->(Sum->X)) == CoProduct(A,n)
> > address@hidden:~/aldor-src/aldor/install/aldor#
> >
> > ----
> >
> > Regards,
> > Bill Page.
> >
> > On 11/8/07, Bill Page <address@hidden> wrote:
> >> Ralf,
> >>
> >> I think the problem here is that the new version of the Aldor compiler
> >> needs a little more help just be reassured that you really are writing
> >> a function that returns a domain. The empty 'with {}' clause seems to
> >> do the trick.
> >>
> >> Here is a patch to 'Categories.as' that allows it to compile... but I
> >> have not yet compiled the rest so I am not 100% sure that the end
> >> result will be ok. (Also attached as a file.):
> >>
>
>
> --~--~---------~--~----~------------~-------~--~----~
> You received this message because you are subscribed to the Google Groups 
> "FriCAS - computer algebra system" group.
> To post to this group, send email to address@hidden
> To unsubscribe from this group, send email to address@hidden
> For more options, visit this group at 
> http://groups.google.com/group/fricas-devel?hl=en
> -~----------~----~----~----~------~----~------~--~---
>
>