[Axiom-developer] Re: Mostly about MuPad (was: Philosophy... )

[Martin Rubey]

Dear Bill,

unfortunately, I have too little time to answer everything... Especially some
of #1 to #6 need more thinking before I answer.

Bill Page writes:

 > Could you explain what you mean by "statically typed"? I don't think Aldor
 > and Spad could be said to be statically typed either.  I agree that in
 > contrast to Aldor and Spad, Mupad is not "strongly typed". And this is
 > exactly my point.

Hm, I thought that static typing means that the type of a variable is known at
compile time, which is clearly the case in Aldor/Spad but not necessarily in
the Axiom interpreter. As far as I know, it is not the case at all in MuPad.

I don't really know what strongly typed would mean. According to wikipedia,
it's meaning depends on the person using it :-)

 > The "type hierarchy" in MuPad was more or less directly grafted on to MuPad
 > in version 2. Version 1 of MuPad looked almost identical to Maple release 4
 > and had essentially no concept of type at all.  But the structure of these
 > programming languages have diverged greatly in MuPad versions 2 and 3 and
 > Maple from versions 7, 8, 9 and 10. Maple by deliberate design has no
 > concept of type at all (the "assume" facility notwithstanding). Both MuPad
 > and Maple are taking very different paths towards a more complete "object-
 > orientation", and neither are really similar to Axiom.

I find current MuPad quite similar to Axiom. There are domains, categories and
similar stuff, but it seems that Axiom handles this things a lot stricter than
MuPad.

 > >> 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.
 > 
 > I disagree. In spite of what MuPad has borrowed from Axiom, it seems to me
 > that so far MuPad has implemented only a small part of the original concept
 > of the Axiom designers. 

Well, I admit that I don't know MuPad well enough to judge. In any case, I'm
only talking about the design, not the amount of stuff actually implemented...

Martin