Re: thinking about UPDATE
From: Jan Hidders <jan.hidders_at_REMOVETHIS.pandora.be>
Date: Mon, 26 Jul 2004 17:40:30 GMT
Message-Id: <pan.2004.07.26.17.41.23.393221_at_REMOVETHIS.pandora.be>
>> > prove or disprove the above?
>> Yep, normalization theory. You can translate the candidate keys to
>> functional dependencies and these always also hold for the projection, and
>> those that hold for the projection also hold for the original relation. So
>> the proof of completeness goes something like this.
>> Suppose that in the projection we have a candidate key A that is not in
>> K'. Then the FD A->P holds in the projection, but also in the original
>> relation. However, the only FDs that hold in the original relation are
>> those that are implied by its CKs so A must have already been a CK in the
>> original relation. But then A is by definition in K' which leads to a
>> contradiction. So the original assumption that the projection has a CK
>> that is not in K' must be false. QED
Date: Mon, 26 Jul 2004 17:40:30 GMT
Message-Id: <pan.2004.07.26.17.41.23.393221_at_REMOVETHIS.pandora.be>
On Mon, 26 Jul 2004 16:07:11 +0300, x wrote:
> **** Post for FREE via your newsreader at post.usenet.com ****
> "Jan Hidders" <jan.hidders_at_REMOVETHIS.pandora.be> wrote in message
> news:pan.2004.07.22.18.06.23.604113_at_REMOVETHIS.pandora.be...
>
>> If K is the set of original candidate keys and P is the set of attribute
>> on which we project then:
>> - Let K' = { k in K | k subset P }
>> - If K' is not empty then return K' otherwise { P }
>>> > have any suggestions as to a formalism to apply to either
>> > Also I note that my post here is simply thinking out the
>> > cases, and I have no formalism to back this up. Does anyone
>> > prove or disprove the above?
>
>> Yep, normalization theory. You can translate the candidate keys to
>> functional dependencies and these always also hold for the projection, and
>> those that hold for the projection also hold for the original relation. So
>> the proof of completeness goes something like this.
>
>> Suppose that in the projection we have a candidate key A that is not in
>> K'. Then the FD A->P holds in the projection, but also in the original
>> relation. However, the only FDs that hold in the original relation are
>> those that are implied by its CKs so A must have already been a CK in the
>> original relation. But then A is by definition in K' which leads to a
>> contradiction. So the original assumption that the projection has a CK
>> that is not in K' must be false. QED
> > What made you think this: > "However, the only FDs that hold in the original relation are those that are > implied by its CKs"
- Jan Hidders