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Re: [Axiom-developer] Philosophy...

From: C Y
Subject: Re: [Axiom-developer] Philosophy...
Date: Thu, 22 Sep 2005 08:31:10 -0700 (PDT)

--- Martin Rubey <address@hidden> wrote:
>  > In a sense, Axiom is/was an experiment in the application of
>  > strongly typed programming languages in computer algebra and
>  > to be quite honest and blunt, for the most part the experiment
>  > seems to have failed. :(
> No, most of it has been transformed into MuPad. However, I dare say
> that Aldor is superiour to MuPad's language.

I think the jury is still out on strongly typed issues - such systems
(including Axiom, in some ways) tend to be designed by experts for
experts, and thus it is not surprising that in terms of "market share"
they don't do as well.  I suspect core technical merit has little to do
with such issues, which is quite unfortunate.

I think it is becoming increasingly clear that the Axiom/Aldor issue
needs to be resolved soon.  If serious work with Aldor is to go forward
and not result in fragmenting the Axiom community, the licensing issues
need to be sorted out.  And it sounds from what I've been hearing that
we really, really should be using Aldor if at all possible.

If MuPad is using a lot of the ideas that went into Axiom, a) that's
good and b) we need to do some things significantly different/better
than MuPad to attract a userbase.  Personally, I think this means
trying seriously to merge computer algebra with proof systems, and
creating a computational environment were people can know and prove
that an answer given by the computer is correct.  Just as security is
now the great need in operating system and network design, I think
verifiable correctness and trustable answers and the great frontier for
CAS.  Feature sets have matured quite a bit over the years, so
competing on features isn't enough (IMHO).  If we do that, it's hard to
avoid becoming just another CAS, with a few advantages and a few
disadvantages compared to other systems.  The net result will be people
sticking with what they know. (Maple, Mathematica, what have you.)

There seem to have been a number of efforts to tie Axiom to proof
systems over the years.  I would like to learn more about those
efforts, why they did or didn't work, and why they weren't integrated
into mainstream Axiom. If the difficulties can be overcome, this seems
to me to be the way to make Axiom a) something new and different from
the user point of view and b) the logical choice for a major
theoretical mathematics journal to incorporate into it's system.  Past
archives could be converted to Axiom pamphlet files (when it makes
sense to do so) and we could see if Axiom is up to tracking
mathematical developments over a couple of decades.

Anyway, just some thoughts, for whatever they may be worth.


P.S.  Hey Tim, are there any folks at CMU that are into this kind of
stuff?  Sounds like something that might appeal to them.

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