axiom-developer
[Top][All Lists]
Advanced

[Date Prev][Date Next][Thread Prev][Thread Next][Date Index][Thread Index]

[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





reply via email to

[Prev in Thread] Current Thread [Next in Thread]