Re: Concurrency in an RDB
From: Bob Badour <bbadour_at_pei.sympatico.ca>
Date: Sat, 23 Dec 2006 16:29:18 GMT
Message-ID: <yPcjh.36680$cz.539494_at_ursa-nb00s0.nbnet.nb.ca>
>> 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, {} } */
>>>> }
>>>>
>>>>
>>>> Project R onto R1=R{A}:
>>>>
>>>> R1 = { { a1 }, { a4 }, { a5 } }
>>>>
>>>> Project R onto R2=R{B}:
>>>>
>>>> R2 = { { a2, { a3, {} } }, { a3, {} } }
>>>>
>>>>
>>>> ** I say "mostly" irrelevant because the predicate for the projected
>>>> relation still makes reference to B in the sense of "A where exists
>>>> some B".
>>>
>>>
>>>
>>>
>>> Suppose (as in the example):
>>>
>>> R = { { a1, { a2, { a3, {} } } } /* a=a1, b={ a2, { a3, {} } */
>>> , { a4, { a3, {} } } /* a=a4, b={ a3, {} } */
>>> , { a5, { a2, { a3, {} } } } /* a=a5, b={ a2, { a3, {} } */
>>> }
>>>
>>> and that we are able to insert { a3, {} } (somehow) giving:
>>>
>>> R = { { a1, { a2, { a3, {} } } } /* a=a1, b={ a2, { a3, {} } */
>>> , { a4, { a3, {} } } /* a=a4, b={ a3, {} } */
>>> , { a5, { a2, { a3, {} } } } /* a=a5, b={ a2, { a3, {} } */
>>> , { a3, { } }
>>> }
>>>
>>> Does this state anything useful?
>>
>>
>>
>> It states something different. Whether it is useful depends on the
>> predicate of the relation. I had not noticed when I created the
>> example that I associate a3 with {} in each tuple. Nothing says that
>> is necessary. I could just as easily created the example as:
>>
>> R = { { a1, { a2, { a3, {} } } } /* a=a1, b={ a2, { a3, {} } */
>> , { a4, { a3, {} } } /* a=a4, b={ a3, {} } */
>> , { a5, { a3, { a2, {} } } } /* a=a5, b={ a3, { a2, {} } */
>> }
>>
>> R1 = R{a} = { { a1 }, { a4 }, { a5 } }
>> R2 = R{b} = { { a2, { a3, {} } }, { a3, {} }, { a3, { a2 {} } } }
>>
>>
>> Or is it redundant?
>>
>> It is not redundant.
>>
>>
>> One way I look at
>>
>>> this is to imagine that the value a3 stands in the same relation to
>>> {} as a2 stands to { a3, {} } or put another way a3 has the same
>>> relation to {} as a2 has to { a3, {} }. But in the tuple
>>>
>>> { { a1, { a2, { a3, {} } } } /* a=a1, b={ a2, { a3, {} } */
>>>
>>> is it not already implicit that a3 stands in that same relation to {}?
>>
>> As I clarified above, nothing says a3 always stands in the same
>> relation to {}. That was merely incidental in my example.
>>
>>
>>> Eg., why bother with the fourth tuple? If I go without the inserted
>>> (fourth) tuple, then by itself, it must be false, ie., it must be
>>> true in the logical complement of R. So the first tuple implies that
>>> a3 has relation R to {} but the complement or R says it doesn't,
>>> which looks like a contradiction to me!
>>
>> Why bother? Only bother if it is or becomes true.
>>
>>
>>> Maybe this is nonsense, but I'd to know why!
>>
>> I think my original example misled you.
Date: Sat, 23 Dec 2006 16:29:18 GMT
Message-ID: <yPcjh.36680$cz.539494_at_ursa-nb00s0.nbnet.nb.ca>
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, {} } */
>>>> }
>>>>
>>>>
>>>> Project R onto R1=R{A}:
>>>>
>>>> R1 = { { a1 }, { a4 }, { a5 } }
>>>>
>>>> Project R onto R2=R{B}:
>>>>
>>>> R2 = { { a2, { a3, {} } }, { a3, {} } }
>>>>
>>>>
>>>> ** I say "mostly" irrelevant because the predicate for the projected
>>>> relation still makes reference to B in the sense of "A where exists
>>>> some B".
>>>
>>>
>>>
>>>
>>> Suppose (as in the example):
>>>
>>> R = { { a1, { a2, { a3, {} } } } /* a=a1, b={ a2, { a3, {} } */
>>> , { a4, { a3, {} } } /* a=a4, b={ a3, {} } */
>>> , { a5, { a2, { a3, {} } } } /* a=a5, b={ a2, { a3, {} } */
>>> }
>>>
>>> and that we are able to insert { a3, {} } (somehow) giving:
>>>
>>> R = { { a1, { a2, { a3, {} } } } /* a=a1, b={ a2, { a3, {} } */
>>> , { a4, { a3, {} } } /* a=a4, b={ a3, {} } */
>>> , { a5, { a2, { a3, {} } } } /* a=a5, b={ a2, { a3, {} } */
>>> , { a3, { } }
>>> }
>>>
>>> Does this state anything useful?
>>
>>
>>
>> It states something different. Whether it is useful depends on the
>> predicate of the relation. I had not noticed when I created the
>> example that I associate a3 with {} in each tuple. Nothing says that
>> is necessary. I could just as easily created the example as:
>>
>> R = { { a1, { a2, { a3, {} } } } /* a=a1, b={ a2, { a3, {} } */
>> , { a4, { a3, {} } } /* a=a4, b={ a3, {} } */
>> , { a5, { a3, { a2, {} } } } /* a=a5, b={ a3, { a2, {} } */
>> }
>>
>> R1 = R{a} = { { a1 }, { a4 }, { a5 } }
>> R2 = R{b} = { { a2, { a3, {} } }, { a3, {} }, { a3, { a2 {} } } }
>>
>>
>> Or is it redundant?
>>
>> It is not redundant.
>>
>>
>> One way I look at
>>
>>> this is to imagine that the value a3 stands in the same relation to
>>> {} as a2 stands to { a3, {} } or put another way a3 has the same
>>> relation to {} as a2 has to { a3, {} }. But in the tuple
>>>
>>> { { a1, { a2, { a3, {} } } } /* a=a1, b={ a2, { a3, {} } */
>>>
>>> is it not already implicit that a3 stands in that same relation to {}?
>>
>> As I clarified above, nothing says a3 always stands in the same
>> relation to {}. That was merely incidental in my example.
>>
>>
>>> Eg., why bother with the fourth tuple? If I go without the inserted
>>> (fourth) tuple, then by itself, it must be false, ie., it must be
>>> true in the logical complement of R. So the first tuple implies that
>>> a3 has relation R to {} but the complement or R says it doesn't,
>>> which looks like a contradiction to me!
>>
>> Why bother? Only bother if it is or becomes true.
>>
>>
>>> Maybe this is nonsense, but I'd to know why!
>>
>> I think my original example misled you.
>
> Yes, can't argue with any of that. I suppose whether a predicate is
> nonsensical depends on the application. In a genealogical app, say,
> maybe one could choose to say the parent relation allows a2 to be a
> parent of a parent a3 of an empty family
> {a3, {} }
> at the same time as a5 could be the parent of the parent a3 of a
> non-empty family
> { a3, { a2, {} } } !
For genealogy, it might not make sense. But consider the chains of commands in various committees. a2 could be the committee chair over a3 in one committee, and a5 could be the committee chair over the secretary a3 over committee member a2 in another comittee. Received on Sat Dec 23 2006 - 17:29:18 CET