Re: Concurrency in an RDB - another question about recursive definitions
From: paul c <toledobythesea_at_oohay.ac>
Date: Sat, 13 Jan 2007 16:52:40 GMT
Message-ID: <s78qh.616524$1T2.362371_at_pd7urf2no>
>
>
> 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?
>
> 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, {} }.
Date: Sat, 13 Jan 2007 16:52:40 GMT
Message-ID: <s78qh.616524$1T2.362371_at_pd7urf2no>
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?
>
> 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, {} }.
Oops, maybe I should take that back, I just realized that that last tuple above, { a3, {} } is not possible given my assumption, unless {a, b} is an RVA and maybe not even then, I'm not sure!
thanks anyway,
p
Received on Sat Jan 13 2007 - 17:52:40 CET