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Re: [Axiom-developer] RE: More AxiomUI

From: William Sit
Subject: Re: [Axiom-developer] RE: More AxiomUI
Date: Wed, 22 Jun 2005 11:27:51 -0400

Martin Rubey wrote:
> Currently, the parser of the interpreter and the parser of the compiler are
> different. For example, you cannot define packages, domains or categories in
> the interpreter.

Much I would agree with you that the difference between the two parsers is a
constant headache and certainly makes it harder to go from interpreter to
compiler, I can understand the roles and necessity of both. Being a strongly
typed language, to require a casual user or beginner to declare types for all
identifiers and to use package calls is too much. Other CAS like Maple or
Mathematica are not even typed. 

> In fact, this is also a question of future direction, since I hope very much
> that Aldor will become *the* language for Axiom.

What features of Aldor do you want to add to Axiom?

> Maybe it would make sense to make the type inference as much independent of 
> the
> interpreter as possible. It seems, that quite a few type coercions are defined
> for the interpreter only. Why aren't they in the algebra? One example is the
> coercion from UP to POLY, I think.

First, a direct coercion between two domains of the same category is by design,
I think, not practical. Domains may differ by their mathematical meaning, but
even if they do not, they differ by their data structure (and hence
implementation). When a domain is constructed, it should not be required to be
aware of other domains in the same category (providing coercion would), because
for one thing, it may be the first. Thus such a requirement would require
constant updating of all older domains that in principle are coercible to other
"younger" ones. Note that by the same reasoning, only a younger domain can be
CoercibleTo an older domain, not the other way round. (By making CoercibleTo go
the other way would make "older" become the "younger"). 

Axiom handles this problem with maps. In the polynomial situation, there is
POLYLIFT, which allows one in the compiler programs to map one polynomial of a
domain into another in perhaps some other domain.  I suspect that the
interpreter applies this (mapping facility) to do certain "coercions" that are
not explicitly available (as in CoercibleTo, ConvertibleTo, RetractableTo) and
for some reason, the choice of these maps is not shown in )set mess bot on.


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