Re: choice of character for relational division

From: Bob Badour <bbadour_at_pei.sympatico.ca>
Date: Sat, 31 Mar 2007 21:35:05 GMT
Message-ID: <duAPh.17832$PV3.184637@ursa-nb00s0.nbnet.nb.ca>

Marshall wrote:

> On Mar 31, 9:55 am, Bob Badour <bbad..._at_pei.sympatico.ca> wrote:
>

>>Bob Badour wrote:
>>
>>>Marshall wrote:
>>
>>>>Let us consider the choice of characters to use for
>>>>relational operators. It might be desirable to use
>>>>different characters for the relational operators from
>>>>the scalar ones, so we avoid using * for join, even
>>>>though it is in some sense a product operator.
>>
>>>>Set subtraction already has a standard character
>>>>in common usage: \
>>
>>>>But we also need a character for relational division.
>>>>The / character is often used, but that's the same
>>>>as numerical division. Bummer.
>>
>>>>So, if you had to choose an ascii character for
>>>>relational division, which one would you use
>>>>and why?
>>
>>>Does a unique relational "division" exist? If "product" has a completely
>>>different name "join", why should a "divide" use the same name?
>>
>>>If we have an equality operation for relations, does a "divide"
>>>operation give us all that much?
>>
>>Hmmmm... and division isn't really the inverse of join. It is the
>>inverse of cross product which is a special case of join. Is the divide
>>operation you contemplate the inverse of cross product or a more general
>>operation which is the inverse of join?

>
> More general. It encompasses the relation-relation operator that
> gets us "suppliers that supply all parts" as well as aggregation.
> Aggregate functions are a mapping from a collection type
> to a result type. Thus, integer sum() is a mapping from a
> bag of integers to an int. (It's the only application that seems
> to require bags that I've run into. I don't much like bags.)
> The operation of applying aggregate functions is the same
> operator as dividing two relations. Not that I would expect
> syntax to especially reflect that, since the mathematically
> cleanest way of thinking about it is for once not the most
> convenient way of doing it. I'd expect to have a group-by
> that behaved in a more convenient way, but that was
> defined in terms of relational division.
>
> So ... what character would you use? :-)

I am lost here. What does your divide do and how does it relate to aggregates? Received on Sat Mar 31 2007 - 16:35:05 CDT