Re: Concurrency in an RDB - another question about recursive definitions

From: paul c <toledobythesea_at_oohay.ac>
Date: Sat, 20 Jan 2007 19:04:07 GMT
Message-ID: <HItsh.724648$1T2.60035@pd7urf2no>

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?
>
> (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.)

p Received on Sat Jan 20 2007 - 13:04:07 CST