Re: grouping in tuple relational calculus

From: Jan Hidders <jan.hidders_at_REMOVETHIS.pandora.be>
Date: Thu, 17 Feb 2005 22:27:40 GMT
Message-ID: <wT8Rd.14220$hD4.1177660@phobos.telenet-ops.be>

Vadim Tropashko wrote:

> Mikito Harakiri wrote:
> 

>> "Paul" <paul_at_test.com> wrote in message
>> news:4213e7b7$0$53482$ed2619ec_at_ptn-nntp-reader03.plus.net...
>>

>>> Mikito Harakiri wrote:
>>> 
>>>> Speaking of aggregates, I always wondered why some aggregates
>>>> are expressable by standard means (min, max can be expressed as
>>>> antijoins), while the others aren't (sum).
>>> 
>>> I guess that min and max only require an ordering, which is a
>>> more fundamental concept than addition, which is required for
>>> sum.

>>
>> That's right, on one hand, aggregate min and max are based upon
>> lattice join and meet binary operators, similar to sum based upon
>> binary addition. This makes all of them to fit into aggregate
>> framework. On the other hand, lattice implies order, and with order
>> one can leverage antijoin.

>  
> Not quite. In a lattice that is not a total order, we can have both 
> max(a,b)!=a and max(a,b)!=b. Therefore, no antijoin can help
> producing those new values. Thus, it is essential for the order to be
> total. Why?

If you allow infinite relations that's actually not true. You can then take the whole domain, select those that are upperbounds of all the elements in the set you aggregate over, and finally select from those the unique one that is minimal.

But, of course, the premisse that aggregation is based upon lattices is false because in essence they are operations over bags and so the idempotency laws don't always apply.

• Jan Hidders

Received on Thu Feb 17 2005 - 16:27:40 CST