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

[David Casperson]

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:
>
> http://pll.cpsc.ucalgary.ca/charity1/www/home.html
>
> 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.

David
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