Re: Principle of Orthogonal Design
From: Bob Badour <bbadour_at_pei.sympatico.ca>
Date: Fri, 08 Feb 2008 13:45:49 -0400
Message-ID: <47ac954e$0$4058$9a566e8b_at_news.aliant.net>
>
>
> Okay. I haven't run in to that before.
>
>
>
>
>
> If we substitute "lexical scope" for "sub-expression" in the above
> then I agree. I recoil from the idea of names that are local
> just to a specific sub-expression.
>
>
>
>
>
> Absolutely!
>
>
>
>
>
> Yes yes!
>
>
>
>
>
> Hmmm. That strikes me as weird--using existential quantification
> as projection. Is that your idea or is that more widely used?
Date: Fri, 08 Feb 2008 13:45:49 -0400
Message-ID: <47ac954e$0$4058$9a566e8b_at_news.aliant.net>
Marshall wrote:
> On Feb 7, 3:19 pm, David BL <davi..._at_iinet.net.au> wrote:
>
>>On Feb 8, 4:43 am, Marshall <marshall.spi..._at_gmail.com> wrote: >> >>>On Feb 7, 3:46 am, David BL <davi..._at_iinet.net.au> wrote: >>> >>>>On Feb 7, 6:44 pm, JOG <j..._at_cs.nott.ac.uk> wrote: >> >>>>A minor comment: when I see '⇔' I assume it means all apparently free >>>>variables are in fact bound and are implicitly universally >>>>quantified. >> >>>As I understand it, this is conventional for all theorems and axioms, >>>whether there is an <=> in them or not. >> >>Perhaps. I've seen some people only drop explicit universal >>quantifiers when they use =>. >> >>I had thought the reason for introducing '→' was to avoid this >>implicit universal quantification that was customary with '=>'.
>
>
> Okay. I haven't run in to that before.
>
>
>
>>>Well, at the very least we have to be careful to distinguish >>>the use of the equals sign between its use as the equality >>>relation and its use as name-binding. >> >>In a way I don't really see a fundamental distinction. I think the >>special syntax is needed to deal with variable names that are local to >>a sub-expression, because with implicit variable names on predicates >>we can get name clashes. These would be impossible to deal with if >>all variables had global scope.
>
>
> If we substitute "lexical scope" for "sub-expression" in the above
> then I agree. I recoil from the idea of names that are local
> just to a specific sub-expression.
>
>
>
>>>But yeah, there is a close relationship between variable names >>>and attribute names. >> >>As an example, we could think of >> >> x > y >> >>as a relation with attributes named x,y
>
>
> Absolutely!
>
>
>
>>If relation P has attributes y,z then the expression >> >> P & (x > y) >> >>could be regarded as shorthand for >> >> P(y,z) & (x > y) >> >>which can be regarded as join between two relations using common >>attribute y.
>
>
> Yes yes!
>
>
>
>>Suppose we want to project away y so only x,z are left in the result >>set. Then we use existential quantification on y: >> >> (Ey) (P(y,z) & (x > y))
>
>
> Hmmm. That strikes me as weird--using existential quantification
> as projection. Is that your idea or is that more widely used?
The existential quantifier is not all that surprising. After all, more than 1 such y could exist too, and we do not know how many. Received on Fri Feb 08 2008 - 18:45:49 CET