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Re: [Axiom-developer] BINGO, Curiosities with Axiom mathematical structu


From: Ralf Hemmecke
Subject: Re: [Axiom-developer] BINGO, Curiosities with Axiom mathematical structures
Date: Tue, 14 Mar 2006 15:57:33 +0100
User-agent: Thunderbird 1.5 (X11/20051201)

On 03/14/2006 03:39 AM, Page, Bill wrote:
On Monday, March 13, 2006 7:32 PM Gaby wrote:

...
Bill Page writes:

Also, I think you should write:

   square: % -> %;
   default {square(t: %): % == m(t pretend T, t pretend T)
     pretend %

although apparently the compiler does not worry about this
since your representation of the domain MyWord below is the
same as the operation that you pass to MyMonoid.
we should also probably find a way to minimize the "pretend"s :-)


The use of 'pretend' has to do with the issue of representation.
I suppose it would be better to write:

   default {
     Rep == T;
     square(t: %): % == per(m(rep(t), rep(t))
   }

NOOOO.... PLEASE DONT USE ANY REPRESENTATION IN A CATEGORY.

Suppose someone later implements your category and just uses some other representation than T.

Ralf




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