Re: Difference between Axiom/Aldor and the rest of the world

Hi Martin and Bill,

I understand your point. You realized you need a well defined
(general) language, and Aldor is it's implementation. This is much
better than Maple/Mathematica, I agree.

I am just addressing the technological point of view - you have a nice
language, tuned to the purpose of the CAS. This is certainly one way
to go.

There is certainly another way to go however, and that is the way I
took - don't reinvent some language, just take already working
language with a specification and a working (open source)
implementation. And a large userbase.

I think those are quite philosophical questions and it's not clear
which approach is better. So you just need to make some decision, and
I did one (with good arguments), you did another (with good
arguments).

Ondrej


On 27 Mar 2007 09:19:39 +0200, Martin Rubey <[email protected]> wrote:
> Dear Bill, Ondrej,
>
> I'd like to make two differences between the extension languages of Maple,
> Mathematica, MuPAD on one hand, and Aldor on the other hand very clear.
>
> Aldor has semantics which are very well explained (in great detail, see the
> "Aldor Compiler User Guide"), and are reduced to very few important
> concepts. Most importantly: Types are first class objects and every object has
> a type. This implies, for example, that the result of a function may be a type,
> as is the case with the "Fraction" constructor, or the "Polynomial" constructor
> in Axiom.
>
> The current implementation of Aldor is quite good at following those
> semantics. Really, with Aldor one should distinguish between the implementation
> and the language. It is quite clear what is a bug and what is a feature,
> although, of course, there are some borderline cases.
>
> In other words, the definition of Aldor does *not* go like "Aldor is the
> language implemented by the current Aldor compiler", but rather "Aldor is the
> language as described in the Aldor Compiler User Guide", and there is an
> implementation that tries hard to follow this guide.
>
> If you look at it this way, you can *really* say that SPAD is version 1 of the
> Aldor compiler, although this is not true historically. There are astonishingly
> few semantic differences and some syntactic differences, but mostly, SPAD
> implements simply a subset of what is described in the Aldor Compiler User
> Guide.
>
> I left out Maxima on purpose, since I believe that the "true" Maxima extension
> language is Ansi Common Lisp, although the current group of developers thinks
> otherwise.
>
> If you can come up with a semantic description of Mathematica's extension
> language, please tell Richard Fateman, since he tried but failed. :-)
>
> -------------------------------------------------------------------------------
>
> Concerning simplification, I'd like to add that this is really a
> non-concept. The real concept behind it is "normal form" or "canonical form",
> or at least, "test for zero".  And in fact, Axiom is very strong in those
> domains very you have one of those things.  And that's exactly why I'd like to
> have my hierarchy "rational - ... - differentially algebraic functions"
> implemented in Axiom, since they all allow test for zero, and an incredible
> amount of functions occurring in practice falls into one of these
> domains. Although, the example you gave for the limit computation does not, as
> far as I can see.
>
>
>
> All the best,
>
> Martin
>
>