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Re: [Axiomdeveloper] BINGO, Curiosities with Axiom mathematical structu
From: 
Gabriel Dos Reis 
Subject: 
Re: [Axiomdeveloper] BINGO, Curiosities with Axiom mathematical structures 
Date: 
14 Mar 2006 01:32:04 +0100 
"Bill Page" <address@hidden> writes:
 Martin,

 I think you have a rather beautiful idea... but I see some
 problems.

 On March 9, 2006 11:08 AM you wrote:
 >
 > I am satisfied now:
 > 
 > #include "axiom"
 >
 > MyMonoid(T: Type, m: (T, T) > T): Category == with {
 > square: T> T;
 > default {square(t: T): T == m(t, t)}
 > }

 This definition of the category MyMonoid looks quite strange
 because it does not export any binary operation!

 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 :)
 Gaby
 Re: [Axiomdeveloper] Curiosities with Axiom mathematical structures, (continued)
 Re: [Axiomdeveloper] Curiosities with Axiom mathematical structures, Martin Rubey, 2006/03/08
 Re: [Axiomdeveloper] Curiosities with Axiom mathematical structures, Ralf Hemmecke, 2006/03/09
 Re: [Axiomdeveloper] Curiosities with Axiom mathematical structures, Martin Rubey, 2006/03/09
 [Axiomdeveloper] BINGO, Curiosities with Axiom mathematical structures, Martin Rubey, 2006/03/09
 Re: [Axiomdeveloper] BINGO,Curiosities with Axiom mathematical structures, William Sit, 2006/03/09
 Re: [Axiomdeveloper] BINGO, Curiosities with Axiom mathematical structures, Ralf Hemmecke, 2006/03/10
 Re: [Axiomdeveloper] BINGO,Curiosities with Axiom mathematical structures, William Sit, 2006/03/10
 Re: [Axiomdeveloper] BINGO, Curiosities with Axiom mathematical structures, Gabriel Dos Reis, 2006/03/13
 RE: [Axiomdeveloper] BINGO, Curiosities with Axiom mathematical structures, Bill Page, 2006/03/09
 Re: [Axiomdeveloper] BINGO,Curiosities with Axiom mathematical structures, William Sit, 2006/03/10
 Re: [Axiomdeveloper] BINGO, Curiosities with Axiom mathematical structures,
Gabriel Dos Reis <=
 [Axiomdeveloper] Re: BINGO, Curiosities with Axiom mathematical structures, Martin Rubey, 2006/03/10
 Re: [Axiomdeveloper] Curiosities with Axiom mathematical structures, Ralf Hemmecke, 2006/03/09
 RE: [Axiomdeveloper] Curiosities with Axiom mathematical structures, Bill Page, 2006/03/10
 Re: [Axiomdeveloper] Curiosities with Axiom mathematical structures, Gabriel Dos Reis, 2006/03/13
 Re: [Axiomdeveloper] Curiosities with Axiom mathematical structures, Ralf Hemmecke, 2006/03/14
 Re: [Axiomdeveloper] Curiosities with Axiom mathematical structures, William Sit, 2006/03/10
 [Axiomdeveloper] Re: BINGO, Curiosities with Axiom mathematical structures, Ralf Hemmecke, 2006/03/10
 RE: [Axiomdeveloper] Re: BINGO, Curiosities with Axiom mathematical structures, Bill Page, 2006/03/11
 Re: [Axiomdeveloper] Re: BINGO, Curiosities with Axiom mathematical structures, Martin Rubey, 2006/03/11
 Re: [Axiomdeveloper] Re: BINGO, Curiosities with Axiom mathematical structures, Gabriel Dos Reis, 2006/03/13