Re: [Axiom-developer] Re: SPAD and Aldor again

[Ralf Hemmecke]

> | I think that will be an important discussion to be had as a project -
> | just how compatible with Aldor we want to stay.
>
> Probably.  I would like to see a discussion about what is necessary to
> support computational mathematics in Axiom, rather than how closely SPAD
> should ressemble another language.

Well, as you know I would rather like to improve the Aldor compiler than 
the SPAD compiler, since that would probably safe some time. But since 
there are no signs that Aldor becomes free, I find Gaby's suggestion 
quite good. Let's discuss, what we want and then design a language that 
fits best. Looking at this Monoid/AbeleanMonoid discussion we had 
before, this language will probably be something else than Aldor and SPAD.

So let me start with a few thoughts.

That Monoid/AbeleanMonoid should be resolved. I want to be able to say 
that the positive integers are a Monoid wrt. + and wrt *.

I would very much like to be able to use any fancy character to denote 
the multiplication of a monoid (not just ASCII). Code should pretty much 
look like actual mathematics. Mathematica and Maple already have some 
kind of that, but it lives in the interpreter. In fact, that would mean 
reducing reduncancy from pamphlets. One would write a mathematical 
formula which would be typeset in the way we like it and at the same 
time be a program.

I would like to define new syntax and use that in a program (nearly) 
exactly as one would do it in a paper.
The literate idea should be pushed to an extreme.

Of course it should also mean to have a way to specify the behaviour of 
algorithms in a formal way so that programs can be checked 
automatically. Proof checkers should, of course, also be written in that 
language.

Yes that is a big dream, but we still have 27 years. ;-)

Ralf