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Re: [Axiomdeveloper] Curiosities with Axiom mathematical structures
From: 
Gabriel Dos Reis 
Subject: 
Re: [Axiomdeveloper] Curiosities with Axiom mathematical structures 
Date: 
14 Mar 2006 00:43:08 +0100 
Ralf Hemmecke <address@hidden> writes:
 Dear William,

 On 03/04/2006 05:31 PM, William Sit wrote:
 > Hi Gabe:
 > Gabriel Dos Reis wrote:
 >> William Sit <address@hidden> writes:

 > Agreed in theory, not in practice. We should distinguish two issues: (1)
 > derived operations that depend only on the defining operations should be
 > generically implemented and inherited, and (2) how to handle the notations
 > (equivalently, identifiers in computer science terminology) for the defining
 > operations and derived operations.

 By (1) you probably mean to say something like

 define PrimitiveType: Category == with {
 =: (%, %) > Boolean;
 ~=: (%, %) > Boolean;
 default { (a:%) ~= (b:%):Boolean == ~(a = b); }
 }

 I must say that I liked this idea of "default implementations" when
 I've encountered it. But it also introduces all the complications with
 multiple inheritance.
Inheritance usually does not mary well with genericity, despite the
usual OO propaganda. :(
 Gaby
 Re: [Axiomdeveloper] Curiosities with Axiom mathematical structures, (continued)
 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, Gabriel Dos Reis, 2006/03/13
 Re: [Axiomdeveloper] Curiosities with Axiom mathematical structures, Ralf Hemmecke, 2006/03/08
 Re: [Axiomdeveloper] Curiosities with Axiom mathematical structures, Ralf Hemmecke, 2006/03/08
 Re: [Axiomdeveloper] Curiosities with Axiom mathematical structures, William Sit, 2006/03/09
 Re: [Axiomdeveloper] Curiosities with Axiom mathematical structures, Ralf Hemmecke, 2006/03/09
 Re: [Axiomdeveloper] Curiosities with Axiom mathematical structures, William Sit, 2006/03/10
 RE: [Axiomdeveloper] Curiosities with Axiom mathematical structures, Bill Page, 2006/03/08
 Re: [Axiomdeveloper] Curiosities with Axiom mathematical structures, William Sit, 2006/03/09
 Re: [Axiomdeveloper] Curiosities with Axiom mathematical structures,
Gabriel Dos Reis <=
 Re: [Axiomdeveloper] Curiosities with Axiom mathematical structures, Gabriel Dos Reis, 2006/03/13
 Re: [Axiomdeveloper] Curiosities with Axiom mathematical structures, William Sit, 2006/03/14
 Re: [Axiomdeveloper] Curiosities with Axiom mathematical structures, Martin Rubey, 2006/03/02
 Re: [Axiomdeveloper] Curiosities with Axiom mathematical structures, Gabriel Dos Reis, 2006/03/02
 Re: [Axiomdeveloper] Curiosities with Axiom mathematical structures, Martin Rubey, 2006/03/04
 RE: [Axiomdeveloper] Curiosities with Axiom mathematical structures, Bill Page, 2006/03/04
 RE: [Axiomdeveloper] Curiosities with Axiom mathematical structures, Page, Bill, 2006/03/13