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

[Saul Youssef]

 in 2001.On Nov 8, 2007 10:14 AM, Ralf Hemmecke <address@hidden> wrote:
> Thank you Saul,
>
> First, thank you very much for your code. Under which license is it?
> Public domain, mBSD, GPL, ... ?
>

No problem.  I offer it freely with no restrictions or claims.

> Unfortunately, the compiler has changed a bit.

It might be useful for you just as a sample of odd code that should
work but is structurally different from what you're used to.

>
> woodpecker:~/scratch/Youssef/london>aldor Basics.as
> woodpecker:~/scratch/Youssef/london>aldor Categories.as
>
> #1 (Error) There are 2 meanings for the operator `+'.
>         Meaning 1: (Obj, Obj) -> Obj
>         Meaning 2: (A: Obj, B: Obj) -> (
>                  Obj with
>                ...
> #2 (Error) There are 2 meanings for the operator `..'.
>         Meaning 1: (Obj, Integer) -> Obj
>         Meaning 2: (A: Obj, n: Integer) -> (
>                  Obj with
>            ...
> #3 (Error) There are 2 meanings for the operator `*'.
>         Meaning 1: (Obj, Obj) -> Obj
>         Meaning 2: (A: Obj, B: Obj) -> (
>                  Obj with
>                ...
> #4 (Error) There are 2 meanings for the operator `^'.
>         Meaning 1: (Obj, Integer) -> Obj
>         Meaning 2: (A: Obj, n: Integer) -> (
>                  Obj with
>            ...
>
> In fact, I don't quite know how to resolve that problem.
> Actually, I wonder why I don't see any line numbers here.
>

I haven't a clue about this, but that's why I included the old foam
output in case it's a clue for you.  This stuff was all compiled just
before the London Ontario meeting in 2001.

>
> I guess the commands "ao" and "ai" that I find in "compile" and
> "exercise" mean something like
>
> alias ao=aldor -fao
> alias ai=aldor -G interp
>
> Or did you use other scripts?
>

I'm sure you're right, but I couldn't even tell you for sure at this point.

> >      One of the things that encouraged me at the time was thinking
> > about the simplest Aldor category in the mathematical sense: objects
> > of the category are Aldor domains satisfying
> >
> > Domain: Category == with  # no signatures (my favorite base category
> > for a library)
>
> I wonder why you called it "Domain" and not something else? In some way
> you are right
>
> A: Domain
>
> then says that A is a domain. Sounds not too bad.
>
> Ralf
>

I do think that this is nicer than "DomainCategory", "SetCategory"
etc.  In this style, you typically produce domains by applying domain
constructors  (i.e. "functors") and quotients rather than implementing
them directly, so you might as well then keep the nice names for the
categories.

- Saul