[Axiom-mail] Re: Axiom and OpenMath/MathML

[Bill Page]

On Mon, 9 Dec 2002 20:40:27 -0500 Bill Page
address@hidden wrote:
> >
> >> C Y wrote:
> >> You might want to read 
> >> http://www.cs.berkeley.edu/~fateman/papers/openmathcrit.pdf
> >> to see some of his objections to OpenMath.
> >
>..
> In most respects I think Fateman is simply wrong ...

In case I gave the impression that I think Richard Fateman
is wrong on all points in the above document, I want to
add that there *are* some things that he says that I do
agree with - it's just that these have little to do with
OpenMath. For example, in section 8 he talks about issues
of scope and binding: "The fact that binding, evaluation,
substitution and related concepts have been so mangled by
computer algebra systems (for example Maple and
Mathematica) should have served as object lessons to
OpenMath designers. Instead of standing on the shoulders
of those who have gone before, we are standing on their
toes.". I like that statement and I agree with it fully
having struggled with Maple's arcane evaluation rules
and variables bindings for almost 10 years. New versions
of Maple have done very little to improve the situation.
Axiom and Aldor on the other hand seem to have got it
right from the beginnning.

It is not clear to me, however how this relates to the
goals of OpenMath per se.

In section 9 he discusses new interfaces to computer
algebra systems based on HTTP and dynamic HTML
(e.g. CL-HTTP). Coupled with MathML, I think this approach
has a great deal of promise both as a local graphical
user interface and in remote access to computer algebra
systems via the web. Certainly given the current state of
Axiom's GUI, this should be seriously considered.

The problem of session variables and multi-threading in
systems designed for simultaneous remote access by many
users is a significant one. Even in the single user case,
the current worksheet/server interface provided by Maple,
for example, often leads to situations where the contents
of the worksheet does not reflect the state of the
calculation engine. This problem was solved many years
ago with the original spreadsheet programs so that changes
in one part of a worksheet automatically (or on demand)
resulted in the rest of the worksheet being updated.

With respect to improving web interfaces to computer
algebra systems Fateman writes: "I can not say for sure,
but I expect that OpenMath would not help.". I agree but
here again he seems to be simply attaching a strawman.

Finally, in his conclusion he writes: "Once some truly
significant program makes essential use of OpenMath - so
essential and with so remarkable a significance that many
other programs will speak OpenMath simply to use it - then
there is a chance of validating the ideas [of OpenMath]."
Perhaps open source Axiom could be this truly significant
program?

Regards,
Bill Page.