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On Feb 24, 7:55 am, Bob Badour <bbad..._at_pei.sympatico.ca> wrote:
> Marshall wrote:
> > [...]
>
> Those look good to me. Domain constraints are very easy:
>
> forall R(a1,...an): a1 in d1 and ... an in dn
Does the term "domain constraint" mean anything different than "type constraint?"
It is mind bendingly whacky to me to think of merging type constraints into the general constraint system. This is very different from the usual programming languages way of thinking about them, at least for me. But I have to say I am very intrigued by the idea.
> I don't know why you think one cannot express unboundedness--not that
> the constraint is meaningful for finite computers.
>
> forall R(a): exists R(a'): a' = a + 1
>
> or
>
> forall R(a): exists R(a'): a' > a
One can express unboundedness, but since I was proposing limiting what one can quantify over to named relations, and since the natural numbers are something other than that, (an infinite set) my expressiveness restrictions make it impossible to express the unboundedness *of the natural numbers* specifically.
Although as I mentioned in another post, there do exist systems that can prove (static) properties of the natural numbers, using algebraic manipulations, not exhaustive computation. (Clearly, as you mentioned, the technique of exhaustive computation is inapplicable to infinite sets.)
Marshall Received on Sat Feb 24 2007 - 10:53:14 CST