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Re: FW: data structure vs. mathematical structure (was: [Axiomdeveloper
From: 
Gabriel Dos Reis 
Subject: 
Re: FW: data structure vs. mathematical structure (was: [Axiomdeveloper] Graph theory) 
Date: 
14 Nov 2006 19:19:32 +0100 
"Bill Page" <address@hidden> writes:
 > Bill Page writes:
 >  >  All domains that have SetCategory are required to have a
 >  >  hash into SmallInteger.
 >  >
 >  Gaby wrote:
 >  > That is not a mathematical requirement.
 > 
 > Bill Page wrote;
 >  I would tend to agree but perhaps Kurt Gödel would not have...
 >  ;)
 >

 On November 14, 2006 12:01 AM Gaby wrote:

 > From constructive mathematics point of view, the only things
 > that are required for a set are:
 >
 > (1) say how to build element of a set
 > (2) equality test.
 >

 No, there is a lot more to the mathematics of set than that. It
 would mean that all sets are finite and that is quite far from
 the case.
How do you arrive to that conclusion?
 Rather, sets should be strongly related to types.

 I think the "constructive mathematics" that is most suitable
 to Axiom is probably is probably Intuitionist type theory
 (MartinLöf). See:
In fact, I prefer the definition given by Erret Bishop. See chapters 1
and 2 "his" book
"Constructive Analysis",
Erret Bishop
Douglas Bridges
>From my perspective, it shows a much deeper impact.
 Gaby
 Re: data structure vs. mathematical structure (was: [Axiomdeveloper] Graph theory), Gabriel Dos Reis, 2006/11/13
 FW: data structure vs. mathematical structure (was: [Axiomdeveloper] Graph theory), Bill Page, 2006/11/13
 Re: FW: data structure vs. mathematical structure (was: [Axiomdeveloper] Graph theory), Gabriel Dos Reis, 2006/11/13
 RE: FW: data structure vs. mathematical structure (was: [Axiomdeveloper] Graph theory), Bill Page, 2006/11/13
 Re: FW: data structure vs. mathematical structure (was: [Axiomdeveloper] Graph theory), Gabriel Dos Reis, 2006/11/14
 RE: FW: data structure vs. mathematical structure (was: [Axiomdeveloper] Graph theory), Bill Page, 2006/11/14
 Re: FW: data structure vs. mathematical structure (was: [Axiomdeveloper] Graph theory),
Gabriel Dos Reis <=
 RE: FW: data structure vs. mathematical structure (was: [Axiomdeveloper] Graph theory), Page, Bill, 2006/11/14
 [Axiomdeveloper] Re: FW: data structure vs. mathematical structure, Ralf Hemmecke, 2006/11/14
 [Axiomdeveloper] Re: FW: data structure vs. mathematical structure, Gabriel Dos Reis, 2006/11/14
 [Axiomdeveloper] RE: FW: data structure vs. mathematical structure, Page, Bill, 2006/11/15
 [Axiomdeveloper] Re: FW: data structure vs. mathematical structure, Ralf Hemmecke, 2006/11/15
 Re: [Axiomdeveloper] Re: FW: data structure vs. mathematical structure, Martin Rubey, 2006/11/15
 [Axiomdeveloper] Re: FW: data structure vs. mathematical structure, Gabriel Dos Reis, 2006/11/15
 [Axiomdeveloper] Re: FW: data structure vs. mathematical structure, Ralf Hemmecke, 2006/11/15
 [Axiomdeveloper] Re: FW: data structure vs. mathematical structure, Gabriel Dos Reis, 2006/11/15
 [Axiomdeveloper] Re: FW: data structure vs. mathematical structure, Ralf Hemmecke, 2006/11/15