Re: is pivoted phones view updateable?

"Aloha Kakuikanu" <aloha.kakuikanu_at_yahoo.com> wrote in news:1163439024.641672.37650_at_h54g2000cwb.googlegroups.com:

>
> This view can be inverted, therefore it's updateable. Here is how to
> formally invert it.
>
> Join each side with A:
>
> X /\ A = A /\ [ (Y /\ A) \/ (Z /\ B) ]
>
> (different kind of brackets are used only to make the expression more
> readable).
>
> Apply Spight distributivity criteria to the right side:
>
> X /\ A = (Y /\ A) \/ (Z /\ A /\ B)
>
> Union each side with (Z /\ 00):
>
> (Z /\ 00) \/ (X /\ A) = [(Y /\ A) \/ (Z /\ A /\ B)] \/ (Z /\ 00)
>
> Here we temporarily stuck, as we can no longer simplify the equation
> without leveraging some additional algebraic information, such as
> noticing that A and B have the same attributes, likewise Y and Z.
> Formally:
>
> A /\ B = A /\ 00 = B /\ 00
> Y /\ Z = Y /\ 00 = Z /\ 00
>
> Therefore we have:
>
> Z /\ A /\ B = Z /\ A /\ 00 = Z /\ 00 /\ A = Y /\ 00 /\ A
>
> and the equality can be rewritten as
>
> (Z /\ 00) \/ (X /\ A) = (Y /\ A) \/ (Y /\ 00 /\ A) \/ (Y /\ 00)
>
> Since Y /\ 00 /\ A > Y /\ 00 we have
>
> (Z /\ 00) \/ (X /\ A) = (Y /\ A) \/ (Y /\ 00)
>
> Spight distributivity again:
>
> (Z /\ 00) \/ (X /\ A) = Y /\ (A \/ 00)
>
> A is not empty, therefore
>
> (Z /\ 00) \/ (X /\ A) = Y /\ (01)
>
> And finally:
>
> (Z /\ 00) \/ (X /\ A) = Y
>
> which is meant to be written as
>
> Y = (X /\ A) \/ (Z /\ 00)
>
> Now, it seems like we didn't accomplish our goal of inverting the
> original equation, as Y formally depends on Z. This is a non issue,
> however: joining Z /\ 00 produces the empty relation with the same
> attributes as Z. It is simply that we need an extra symbol for such a
> relation, which would add confusion. In classic RA what we have is
> join and projection.
>
> Next the equation for Z can be derived symmetrically:
>
> Z = (X /\ B) \/ (Y /\ 00)
>
> Therefore, we have 2 views, Y and Z expressed in terms of X. How do we
> change Y and Z when X in updated? That is view maintenance problem!
>

What is "Spight distributivity criteria" and what is "00" ?

Please give the rules of transformation of your algebra.

--
Tegi