[Axiom-developer] Domains and expressions

[Page, Bill]

I highly recommend the paper:

http://portal.acm.org/citation.cfm?id=1073884.1073921

Domains and expressions: an interface between two approaches
to computer algebra

by

Cosmin E. Oancea, Stephen M. Watt
University of Western Ontario, London, ON, Canada

ABSTRACT

This paper describes a method to use compiled, strongly typed
Aldor domains in the interpreted, expression-oriented Maple
environment. This represents a non-traditional approach to
structuring computer algebra software: using an efficient,
compiled language, designed for writing large complex mathematical
libraries, together with a top-level system based on user-interface
priorities and ease of scripting. We examine what is required to
use Aldor libraries to extend Maple in an effective and natural
way. Since the computational models of Maple and Aldor differ
significantly, new run-time code must implement a non-trivial
semantic correspondence. Our solution allows Aldor functions to
run tightly coupled to the Maple environment, able to directly
and efficiently manipulate Maple data objects. We call the
overall system Alma.

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Although this kind of reminds me of a marriage between a
Hippopotamus and the Elephant's daughter :), I think this
paper is well worth reading and understanding. It presents a
brief but thorough introduction to Aldor domains and categories.
Then it demonstrates how these can be represented in terms of
Maple's object-oriented "modules" and vice-versa. Maple is
presented as an expression-oriented user interface with a
sophisticated scripting language. Aldor on the other hand
provides a high performance strongly-typed compiled language
for writing mathematical libraries. The overall result of this
"marriage" seems quite complex but the examples make it obvious
that it provides a way to fully exploit Aldor within Maple's
un-typed environment.

I think this paper is important from the point of view
of the uni-typed language B# that has been proposed as an
alternative to Axiom's current interpreter.

Regards,
Bill Page.