Re: [Axiom-developer] Curiosities with Axiom mathematical structures

[William Sit]

Ralf Hemmecke wrote:
> 
> Well, it seems that my "where" invention was not explained clearly
> enough. What I meant by
> 
>    MyMonoid where {
>      0: % == 1;
>      +: (%, %) -> % == *;
>      ntimes: (%, Integer) -> % == power;
>    }
> 
> was that this construct actually defines a category that exports
>      0: %;
>      +: (%, %) -> %;
>      ntimes: (%, Integer) -> %;
> and at the same time declares those functions to be just other names for
> 1, *, and power in the structure MyMonoid. It all boils down to
> declaring a category
> 
>    with {
>      0: %;
>      +: (%, %) -> %;
>      ntimes: (%, Integer) -> %;
>    }
> 
> but somehow with the name MyMonoid attached to it. Or saying it in
> another way. It is like defining MultiplicativeMonoid and AdditiveMonoid
>   and giving them the same name MyMonoid. I don't anymore think that
> such "renaming" has much advantage. (However, I was not so convinced
> before the discussion started.)
> 
> BTW, in my "where" syntax I though quite a bit whether I should write
> 
>    + == *
> 
> or
> 
>    * == +
> 
> Unfortunately, my choice led you to think it is a category default.

I was just following Aldor syntax, not knowing you were inventing something new.
So it is all "clear" now :-).
 
> Oh, now I am a bit puzzled. Didn't I read the name "William Sit" on one
> the first pages of the original Axiom book (by Jenks&Sutor)? I always
> thought you are one of the designers. No?
> 

I must then correct your wrong impression. I came to Axiom quite late in the
game, around 1987-88, when spad was running on an IBM 360 (or may be it was
7090) in 16MB memory space. Later that moved to the RT. Spad was well developed
by then Steven Watts was already working on the Aldor compiler (called A#). The
designers were no longer fixing spad compiler bugs (unless it is really
serious).

My name got into the Axiom book through the generosity of the authors (Robert
Sutor and Richard Jenks). I made only a few pages of contribution on ordinary
differential polynomial rings in the book. So, I am only an Axiom user (and a
limited one at that).

William