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[Axiom-developer] Time for another crazy idea...

From: C Y
Subject: [Axiom-developer] Time for another crazy idea...
Date: Mon, 20 Feb 2006 15:39:01 -0800 (PST)

I know my understanding of categories and domains is massively
imperfect, so perhaps this idea is not worth much, but since it might
be one of those cases where an explanation of why its a bad idea might
be helpful, here we go...

My understanding of Axiom's concept of categories and domains is that
it is similar to and at least somewhat compatible with category and/or
set theory, but it was not explicitly designed to implement and rely
these theories as a foundation.  If that's true, I was wondering what
sort of effort would be involved in tuning Axiom's use of categories to
be in line with category theory mathematics, along the lines of things
like Categories for the Working Mathematician.  If Axiom is already
close to this anyway, perhaps the next step could be taken and Axiom
could relate its category structure directly to research in category
theory, and turn its own core implementation of mathematical
fundamentals into a literate document summarizing the research in those
areas and how it is applied.

Is that a) an insane amount of work and I just don't realize it yet b)
a non-practical idea in terms of having an actual working CAS or c) all
of the above?  I always thought the best way to lead off the Algebra
volumes of Axiom was with a discussion of the fundamental theories of
mathematics encoded in Axiom and the research they are based off of,
but perhaps that's not a good approach for Axiom?

I'm going to finish a unit and dimension implementation before I even
think about tackling something that crazy, but I figured if it's a
really Nutty idea I should find out now ;-)


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