Re: Concurrency in an RDB - another question about recursive definitions
From: Bob Badour <bbadour_at_pei.sympatico.ca>
Date: Sat, 20 Jan 2007 19:27:24 GMT
Message-ID: <w2ush.3263$1x.55094_at_ursa-nb00s0.nbnet.nb.ca>
>> Bob Badour wrote:
>>
>>> paul c wrote:
>>>
>>>> Bob Badour wrote:
>>>>
>>>>> ...
>>>>> What I am saying is: When you project onto A, the data type of B is
>>>>> mostly** irrelevant. Likewise, when you project onto B, the data
>>>>> type of A is mostly irrelevant.
>>>>>
>>>>> The fact that you have a recursive data type definition has no
>>>>> effect on project or join or restrict or union or intersect or
>>>>> difference etc. The values identified as B are simply values.
>>>>>
>>>>> Assuming:
>>>>>
>>>>> A = { a1, a2, a3, a4, a5 }
>>>>> B = { {a,b} | a in A and b in B }
>>>>>
>>>>> Given relation R{a in A,b in B}: /* Using C-style comments */
>>>>>
>>>>> R = { { a1, { a2, { a3, {} } } } /* a=a1, b={ a2, { a3, {} } */
>>>>> , { a4, { a3, {} } } /* a=a4, b={ a3, {} } */
>>>>> , { a5, { a2, { a3, {} } } } /* a=a5, b={ a2, { a3, {} } */
>>>>> }
>>>>> ...
>>>>
>>>>
>>>>
>>>>
>>>>
>>>> Bob, now I remember a parallel question that struck me about your
>>>> subtle definition of B, B = { {a,b} | a in A and b in B }. I take
>>>> it that you meant B to be a type that is used by the R relation.
>>>> But is it somehow plausible to see B as a relation?
>>>
>>>
>>>
>>>
>>> B must be a relation type, in fact.
>>>
>>>
>>>> If so, I would think that a value for relation B that has one tuple:
>>>>
>>>> B = { { a1, {a2, {a3, {} } } } } /* a=a1, b={ a2, { a3, {} } */
>>>>
>>>> is not possible because by definition (B "referencing" itself),
>>>> there would need to be two additional tuples to make it stick to the
>>>> definition, namely
>>>>
>>>> { a2, { a3, {} }
>>>>
>>>> and
>>>>
>>>> { a3, {} }.
>>>>
>>>> Thanks for any comments,
>>>> p
>>>
>>>
>>>
>>>
>>> Relations are sets and {} is one of them. Thus {} is a valid B value;
>>> although, I omitted the headers for brevity. Joe Thurbon introduced a
>>> ...
>>
>>
>>
>> Thanks but if this is answering my question, it may be too terse for
>> me to see it!
>>
>> Are you saying that
>>
>> B = { { a1, {a2, {a3, {} } } } } /* a=a1, b={ a2, { a3, {} } */
>>
>> is possible, given the self-refencing definition?
Date: Sat, 20 Jan 2007 19:27:24 GMT
Message-ID: <w2ush.3263$1x.55094_at_ursa-nb00s0.nbnet.nb.ca>
paul c wrote:
> paul c wrote: >
>> Bob Badour wrote:
>>
>>> paul c wrote:
>>>
>>>> Bob Badour wrote:
>>>>
>>>>> ...
>>>>> What I am saying is: When you project onto A, the data type of B is
>>>>> mostly** irrelevant. Likewise, when you project onto B, the data
>>>>> type of A is mostly irrelevant.
>>>>>
>>>>> The fact that you have a recursive data type definition has no
>>>>> effect on project or join or restrict or union or intersect or
>>>>> difference etc. The values identified as B are simply values.
>>>>>
>>>>> Assuming:
>>>>>
>>>>> A = { a1, a2, a3, a4, a5 }
>>>>> B = { {a,b} | a in A and b in B }
>>>>>
>>>>> Given relation R{a in A,b in B}: /* Using C-style comments */
>>>>>
>>>>> R = { { a1, { a2, { a3, {} } } } /* a=a1, b={ a2, { a3, {} } */
>>>>> , { a4, { a3, {} } } /* a=a4, b={ a3, {} } */
>>>>> , { a5, { a2, { a3, {} } } } /* a=a5, b={ a2, { a3, {} } */
>>>>> }
>>>>> ...
>>>>
>>>>
>>>>
>>>>
>>>>
>>>> Bob, now I remember a parallel question that struck me about your
>>>> subtle definition of B, B = { {a,b} | a in A and b in B }. I take
>>>> it that you meant B to be a type that is used by the R relation.
>>>> But is it somehow plausible to see B as a relation?
>>>
>>>
>>>
>>>
>>> B must be a relation type, in fact.
>>>
>>>
>>>> If so, I would think that a value for relation B that has one tuple:
>>>>
>>>> B = { { a1, {a2, {a3, {} } } } } /* a=a1, b={ a2, { a3, {} } */
>>>>
>>>> is not possible because by definition (B "referencing" itself),
>>>> there would need to be two additional tuples to make it stick to the
>>>> definition, namely
>>>>
>>>> { a2, { a3, {} }
>>>>
>>>> and
>>>>
>>>> { a3, {} }.
>>>>
>>>> Thanks for any comments,
>>>> p
>>>
>>>
>>>
>>>
>>> Relations are sets and {} is one of them. Thus {} is a valid B value;
>>> although, I omitted the headers for brevity. Joe Thurbon introduced a
>>> ...
>>
>>
>>
>> Thanks but if this is answering my question, it may be too terse for
>> me to see it!
>>
>> Are you saying that
>>
>> B = { { a1, {a2, {a3, {} } } } } /* a=a1, b={ a2, { a3, {} } */
>>
>> is possible, given the self-refencing definition?
Yes, it is possible. In fact, the above describes it.
>> (Whereas I was thinking that it would be impossible for B to have only
>> one tuple.)
>>
>> p
> > > Let me change that last comment to: > > (Whereas I was thinking that it would be impossible for B to have only > one such tuple.)
How so? Received on Sat Jan 20 2007 - 20:27:24 CET