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[Axiom-math] Re: [Axiom-developer] POLY INT =\\= UP(x, INT) (was: parti


From: Dylan Thurston
Subject: [Axiom-math] Re: [Axiom-developer] POLY INT =\\= UP(x, INT) (was: partialFraction behavi or in Axiom)
Date: Wed, 8 Oct 2003 19:59:10 +0000 (UTC)
User-agent: slrn/0.9.8.0 (Linux)

On 2003-10-08, Page, Bill <address@hidden> wrote:
> Originally I thought reprogramming (like Aldor) might be
> best, but lately I am thinking that by taking a little more
> care it may be possible for two rather different type
> systems to coexist in AXIOM. Already the AXIOM type system
> contains a number of type definitions which are either
> obsolete or experimental and mostly not documented, e.g.
> NEWPOLY, XPOLY etc.
>
> I am very interested in participating in a joint project
> (with people more knowledgeable about AXIOM then myself!)
> to provide a much more "categorial" type system. ...

Can you say what you mean by a more "categorial" type system?  From my
point of view, the basic AXIOM type system seems reasonable; it's
close to what I came up with myself when trying to design a basic type
system for Haskell, for instance.  I haven't looked much past the
lower levels of the heirarchy, however, and could certainly believe it
needs work; but I don't know that thinking about it as an entire
redesign of the type heirarchy would be helpful.

In the case at hand, the types in question seem eminently reasonable.
The one question in my head is why there's a need for the Polynomial
constructor, polynomials with no specification as to the variables,
given the presence of UP(x, ...) and so forth.  But AXIOM is actually
able to make that cast (from POLY(FRAC INT) to UP(x, FRAC INT))
itself; the problem[1] is that it doesn't think if the cast from
UP(x, INT) to UP(x, FRAC INT) automatically.

This doesn't seem like a problem of the type heirarchy here;  rather,
it's something with the type inference engine.  I don't think it could
be fixed at the level you're thinking of.

Peace,
        Dylan

[1] Apart from the bug of sometimes giving wrong answers, which still
needs to be investigated and fixed.





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