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[Axiom-developer] Re: rep, per, Rep in SPAD/Aldor
From: |
Ralf Hemmecke |
Subject: |
[Axiom-developer] Re: rep, per, Rep in SPAD/Aldor |
Date: |
Sat, 14 Jul 2007 09:16:45 +0200 |
User-agent: |
Thunderbird 2.0.0.4 (X11/20070604) |
Gaby,
just a short reply. As I said, I agree that Rep is an important issue.
It would actually be good to hear what Stephen Watt has to say about
that issue. I'd like to learn about the original intentions.
Secondly, what we want to convey with `rep' is not that one can take
object foo, restrict its interpretation at type T and then do an
`on faith interpretation of its sequence of bytes representation as
an object at type U'. Rather, what we want to say is that object foo
at type T is the result of a (hopefully injective) mapping from U and we
are interested in its pre-image.
I don't know that I understand that paragraph. If I understand that
correctly, then (U = Rep, T = %)
per: Rep -> % injective map
In general we have card(Rep)>=card(%). (If this would not always be
true then I don't know.)
rep: % -> Rep the "inverse" of per
If x is from % then rep(x) should be an element from Rep such that
per(rep x) = x. Since there might be several such elements, rep should
choose one, and since we want rep to be a function, it should always
choose the same element from the preimage of per.
Gaby, what you were saying is that Rep and % (in an abstract setting)
need not be represented by the same string of bytes in memory. That is
my interpretation of your paragraph. Abstractly seen, this seems to be
OK, but from an efficiency point of view, it is probably always good if
rep and per actually do nothing than changing the view on the same
string of bytes in memory. But, I agree, that decision should be left to
the compiler.
Ralf
- Re: [Axiom-developer] Unions in Spad, (continued)
- Re: [Axiom-developer] Unions in Spad, Ralf Hemmecke, 2007/07/13
- Re: [Axiom-developer] Unions in Spad, Ralf Hemmecke, 2007/07/13
- Re: [Axiom-developer] Unions in Spad, Ralf Hemmecke, 2007/07/13
- Re: [Axiom-developer] Unions in Spad, Stephen Wilson, 2007/07/13
- Re: [Axiom-developer] Unions in Spad, Stephen Wilson, 2007/07/13
- Re: [Axiom-developer] Unions in Spad, Gabriel Dos Reis, 2007/07/13
- rep, per, Rep in SPAD/Aldor, was: Re: [Axiom-developer] Unions in Spad, Ralf Hemmecke, 2007/07/13
- Re: rep, per, Rep in SPAD/Aldor, was: Re: [Axiom-developer] Unions in Spad, Gabriel Dos Reis, 2007/07/13
- [Axiom-developer] Re: rep, per, Rep in SPAD/Aldor, Ralf Hemmecke, 2007/07/13
- [Axiom-developer] Re: rep, per, Rep in SPAD/Aldor, Gabriel Dos Reis, 2007/07/14
- [Axiom-developer] Re: rep, per, Rep in SPAD/Aldor,
Ralf Hemmecke <=
- Re: [Axiom-developer] Re: rep, per, Rep in SPAD/Aldor, Gabriel Dos Reis, 2007/07/14
- [Axiom-developer] Re: [Aldor-l] rep, per, Rep in SPAD/Aldor, Christian Aistleitner, 2007/07/14
- Re: [Axiom-developer] Unions in Spad, Ralf Hemmecke, 2007/07/13
- Re: [Axiom-developer] Unions in Spad, Stephen Wilson, 2007/07/13
Re: [Axiom-developer] Unions in Spad, Bill Page, 2007/07/08
Re: [Axiom-developer] Unions in Spad, Waldek Hebisch, 2007/07/09