Re: Requirements for update languages?

Mikito,

thanks for your answer

>
> Cartesian Product on bags is easily defined if we allow "unproject"
> operations. In your example we need to add a sequence columns C01 to
> T1 and C02 to T2 so that both T1(C01,C1) and T2(C02,C2) are sets.
> Then, calculate the cartesian product of the sets and project away C01
> and C02 from the result.
>
> Proposition. The Cartesian Product as defined above is a well defined
> operation; it doesn't depend on the details of the "unproject"
> operation.
>

This definition seems to validate Date's following comment:

"If you do try this exercise, I believe you'll find you're inevitably led into using the language of sets, not bags, in order to get around the errors and ambiguities."  

> The other way to legitimate bags is a theory of distributions: each
> distribution is a generalization of a bag. Cartesian Product is just
> a product of 2 distributions. Given
>
> T1: {0->2} and T2: {1->1, 2->1}
>
> then
>
> T1*T2 = {<0,1> -> 2, <0,2> -> 2}
>
>
> Note, that aggregation fits naturally into distribution theory, and
> not
> into logic or set theory.

Unfortunately I can't understand this definition - my fault - have to educate myself on this.

regards,
Lauri Pietarinen Received on Wed Nov 13 2002 - 00:04:39 CET