[Agda] Re: Classical Mathematics for a Constructive World
Ramana Kumar
ramana at xrchz.net
Sun Dec 2 11:13:42 CET 2012
On Sun, Dec 2, 2012 at 10:10 AM, Jan Burse <janburse at fastmail.fm> wrote:
> wren ng thornton schrieb:
>
> You run into similar issues in separation logic. When using Hoare
>> separation logic we get this nice frame rule:
>>
>> {P} C {Q}
>> -------------
>> {P*R} C {Q*R}
>>
> >
> > (subject to some mild side conditions about R). People often focus on >
> the fact that the addition of R is preserved from precondition to
> > postcondition
>
> Correctness wise I guess the above inference
> rule is in most cases invalid. Take the following
> example:
>
> { x = 0 v x = 1 }
> x = x + 1
> { x = 1 v x = 2 }
>
> Now add the condition x = 0:
>
> { x = 0 }
> x = x + 1
> { false }
>
> What it needs is x = a & x = b -> false
> for a <> b. Should be possible in minimal
> logic without any choice principle. Its
> would be for example part of CET (Clark
> Equational Theory). So I guess it is not
> related. But I might be wrong.
>
> Or what would be the mild condition on R
> to make the inference rule meaningful?
>
The condition is that R does not mention any variables assigned in C.
>
> Bye
>
>
>
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