Re: Constraints and Functional Dependencies

Marshall wrote:

> 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

>>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

Suppose one has an extent function that returns a relation representing the extent of a type. Then "extent(natural)" is the name for a relation representing the set of all natural numbers.

However, in a real computer, the natural type will be finite not infinite and the unbounded constraint above would always fail (except for empty relations ironically).

How does one express that R has at least one tuple? Or that a specific instance exists?

Would the following do?

exists R(a): true

exists R(a): a = literal

If that works, I suppose one could describe the extent of the natural numbers as:

(exists extent(natural)(value): value = 1) and
(forall extent(natural)(value'):

     exists extent(natural)(value''):
         value'' = value' + 1

Of course, a finite computer would have to amend the above as follows:

(exists extent(natural)(value): value = 1) and
(forall extent(natural)(value'):

     value' = max(natural)
     or exists extent(natural)(value''):
         value'' = value' + 1

Assuming a max function that returns the largest value in an ordered type.

> 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 - 19:08:27 CET