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[Axiom-math] Re: [Aldor-l] Hopf Algebra = Group + Monad

From: David Casperson
Subject: [Axiom-math] Re: [Aldor-l] Hopf Algebra = Group + Monad
Date: Thu, 7 Aug 2008 09:31:47 -0700 (PDT)
User-agent: Alpine 1.00 (OSX 882 2007-12-20)

Bill Page, on 2008-08-07, you wrote:

Date: Thu, 7 Aug 2008 12:25:06 -0400
Subject: Re: [Aldor-l] Hopf Algebra = Group + Monad

On Thu, Aug 7, 2008 at 12:10 PM, David Casperson  wrote:
Hi Bill,

you may want to look at the work of the Charity group at the U of C.

Thanks! I haven't looked at the Charity project for a while:

but "Latest News" and "Download ..." suggests that there has not been
much development since 2000. Is that accurate? Is there work
continuing on this elsewhere?

I suspect that that is accurate.  It still has ideas that I
haven't seen used elsewhere.

Charity is a seriously category theoretical language that is explicitly
aware of co-objects.  It is formally weaker than most programming
languages in that any compiling program terminates.

In the context of co-algebra is seems a little strange to consider
only programs that terminate.

The Charity take on co-objects is stream like.  The object itself
is infinite, but you can only elaborate a first, finite part.
For instance you can express the Ackerman function as a co-object
table, but the indices you elaborate to look up an element are
finite and terminating.

Dr. David Casperson, Assistant Professor     |  address@hidden
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