Re: boolean datatype ... wtf?

On 29/09/2010 8:45 AM, Bob Badour wrote:
> paul c wrote:
>
>> On 29/09/2010 7:45 AM, Bob Badour wrote:
>>
>>> Paul Mansour wrote:
>>>
>>>> On Sep 29, 9:46 am, paul c <toledobythe..._at_oohay.ac> wrote:
>>>>
>> ...
>>
>>>>> Aren't A=B and A>B relations?
>>>>
>>>>
>>>> I was under the impression that they are not, even if A and B are
>>>> relations. But I may have misintepreted C.J. Date on this.
>>>>
>>>> In "Database in Depth" he writes:
>>>>
>>>> "In Chapter 2, I mentioned the fact that the equality comparison
>>>> operator "=" applies to every type. In partitular, therefore it
>>>> applies to relation types.... Now I must immediatly explain that these
>>>> opeartors are not relational operators as such -- that is they are not
>>>> part of the relational algebra-- because their result is a truth
>>>> value, not a relation."
>>>
>>>
>>> An algebra is a set of values and a set of operations closed on that set
>>> of values.
>>>
>>> Date is saying that comparisons are not part of the relational algebra
>>> in the same way that division is not part of the integer algebra because
>>> dividing any two arbitrary integers is not necessarily closed on
>>> integers.
>>>
>>> Consider an expression of the form:
>>>
>>> R = f(A,B)
>>>
>>> where both A and B are relations and f is some binary operation. If f is
>>> natural join, then R is a relation. If f is a comparison, then R is not
>>> a relation; it is a boolean.
>>> ...
>>
>> Thanks for the precise example. It seems to me that Date means your
>> last sentence as his starting point. Nothing 'wrong' with that, but my
>> question might be 'why does that have to be so'? Isn't it just as
>> valid to say that R can be one of DEE or DUM for certain f?
>
> Sure, but that's a different f. The first f is part of a closed boolean
> algebra, and the second f is not.

Okay, then my next question is why couldn't any operation on relations return a relation? eg., subsetof(r1,r2).

Is it because language designers want to use the same 'type' for ops that don't operate on relations? If so, I'd say that's their right, just as it's Erwin S's right to call "whether A=B should be treated as a relation" hairsplitting. I don't see a logical requirement for either attitude, although I'm sure there are lots of practical ones.

Regarding division by zero, as impractical as it might be, I also might have a mental block about that. If there were an op called 'integer division', is there a theoretical reason why its operands couldn't be relations and the result an empty relation? Received on Wed Sep 29 2010 - 18:47:29 CEST