Re: Constraints and Functional Dependencies

mAsterdam wrote:
> paul c wrote:

>> mAsterdam wrote:
>>> paul c wrote:
>>>> mAsterdam wrote:
>>>>> paul c wrote:
>>>>>> Marshall wrote:
>>>>>>> With such a system, a relation R with attribute a (which I will
>>>>>>> write as R(a)) having a as a foreign key into S(b) is expressed
>>>>>>> as follows:
>>> (i)
>>>>>>>   forall R(a): exists S(b): a = b
>>>>>>>
>>>>>>> So we can express foreign keys this way.
>>>>>>> ...
>>>>>>
>>>>>> I presume that if S had other attributes besides b, this 
>>>>>> definition would mean that b doesn't need to be a so-called 
>>>>>> primary key?  (That would be okay with me.)

>>>>> ...b should be a (candidate) key of S, ...
>>>>
>>>> My question is why?  Why should b be a key of S? You could answer 
>>>> "why not?" and I don't have a theoretical answer for that, other 
>>>> than the possibility, as Marshall hinted at, that requiring it to be 
>>>> a key isn't possible except on a relation-by-relation basis unless 
>>>> we just arbitrarily state it is always so, in which case my question 
>>>> remains "why?".
>>>
>>> Because (i) should, as Marshall stated, express
>>> the notion of foreign key, specifically a foreign key to S.
>>> I b is not a key of S, I don't see how it can.
>>>
>>> Cimode even gave a proof that it can't.
>>> Don't you agree?
>>> Is the proof flawed?
>>> ...
>>
>> I don't know where to look for Cimode's proof 

>> but I think what Marshall defined is what I call a "reference", which 
>> seems more general than Codd's original foreign key, ie., doesn't 
>> exclude the possibility of the reference being a key in the referenced 
>> table, if the person who declares the reference so desires. 

Please see:
http://groups.google.nl/group/comp.databases.theory/msg/1a23965d0bbf3362

> It is not what Marshall said he intended it to define.

[snip] Received on Sun Feb 25 2007 - 13:27:50 CET