Re: more algebra

From: paul c <toledobythesea_at_oohay.ac>
Date: Thu, 08 Apr 2010 17:35:28 GMT
Message-ID: <Atovn.1120$z%6.85_at_edtnps83>


Sampo Syreeni wrote:
> On Apr 7, 3:05 am, paul c <toledobythe..._at_oohay.ac> wrote:
>

>> ( r GROUP  ( { N } AS n ) )  =  ( EXTEND  r  ADD  ( RELATION { TUPLE { N
>>   }  AS  n )  { K, n }

>
> How about A join project_K(A)=A? ...

I believe it's always true, so not much use as a constraint. Suspect it's just a variation on Heath's theorem with the "third" attribute set empty. All you can conclude from Heath is NOT("K is key") OR ("A = A{K} JOIN A"). You can't conclude NOT("A = A{K} JOIN A") OR ("K is key"). Ie., if K->N is true, the equation is true, but if K->N is not true, I think the equation is still true when only two attribute sets are mentioned, at least it is for the values I gave, which is enough to make it useless as a constraint.

> ... No counts, nesting or aggregates
> there, ...

No counts or aggregates in either. By 'nesting' I presume you mean what D&D call 'GROUP'-ing - I believe they use the term to avoid confusion with so-called NFNF relations. Such a GROUP always implies a key and vice-versa. Keys being so fundamental from a practical point of view (the basic addressing mechanism), makes me wonder if there is a possible algebra where such a GROUP is fundamental. If possible, I guess it would have to be a binary operator (as Vadim's projection operator is).   But maybe it's the case that there is a proof that such an algebra would require NFNF relations. Received on Thu Apr 08 2010 - 19:35:28 CEST

Original text of this message