Re: representation and replacement
- From: "george" <greeneg@xxxxxxxxxx>
- Date: 26 Apr 2005 17:53:36 -0700
> In article <M5fae.1559$pk5.1255@fed1read02>, "vsgdp" <spam@xxxxxxxx>
wrote:
>
> >Okay, suppose you have two objects, where one object A represents
the other
> >object B, and you can always obtain one object from the other.
> >
> >I would like to write A = B (to do replacements), but technically,
they are
> >not of the same type, so it doesn't seem like you can really say
they are
> >equal unless you accept the abuse of notation.
> >
> >I though of using the logical equivalence symbol, but these are
objects and
> >not truth statements.
Well, what are they?
In the semantics of C, they could be an lvalue
and an rvalue. Which are sort of of the same
type but not quite. I mean, a variable of
type t and a RESULT/constant of type t are both
of type t but they are NOT of the same type;
the variable is arguably rather of type pointer-to-t.
Nevertheless, you can assign the value to the variable,
and you can use the name of the variable in contexts
where the value is acceptable. That is not so much
an abuse as an overloading of the notation.
Barb Knox wrote:
> Maybe try axiomatizing the behaviour that you want "represents" to
have.
> For example, let rep(a,b) mean that a "represents" b. With only
that, it's
> an undefined notion; so then construct appropriate axioms to define
it. For
> example, you appear to want various axioms of replacement:
> Aa Ab (phi(b) ^ rep(a,b) -> phi(a))
> where phi(x) is any first-order formula with 1 free variable x.
The first likely objection to that is likely to be that
since a and b are not of the same type,
if phi(b) is well-formed
then phi(a) is likely not to be.
.
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