Re: Lucid statement of the MV vs RM position?

From: Bob Badour <bbadour_at_pei.sympatico.ca>
Date: Sat, 06 May 2006 18:05:38 GMT
Message-ID: <Sz57g.4039$A26.107108@ursa-nb00s0.nbnet.nb.ca>

Jon Heggland wrote:

> Bob Badour wrote:
>

>>Jon Heggland wrote:
>>
>>>That said, I guess GROUP could also be defined as a SUMMARIZE with an
>>>aggregate operator (or "summary"; TTM distinguishes between them) that
>>>computes the RVA value based on a set of attributes. That aggop/summary
>>>would be a bit non-standard, though, since it would need take a variable
>>>number of arguments, not just one. That still wouldn't make GROUP an
>>>aggregate operator, though.
>>
>>What would make it an aggregate? It has an identity element and one can
>>define it as a repeated union operation. Of course, one must first
>>perform a type conversion to change each tuple to a relation with
>>cardinality 1 before one can perform the union operation.

>
>
> Maybe I was unclear. TTM has such an aggregate operator; it is called
> UNION. You could define GROUP as SUMMARIZE ... ADD (UNION(...) AS
> RVA)---provided you have this mechanism for "converting" a set of
> attributes to a singleton relation---but GROUP is still not an aggregate
> operator. UNION is. In other words, UNION is to (eh...) UNION as SUM is
> to +.

Actually, GROUP is to UNION as SUM is to +

>>I don't see this as any different than performing a type conversion
>>before performing the addition for SUM.

>
> I think we are just quibbling over Tutorial D syntax, or over which
> operators should be defined in terms of which others.
> R GROUP ({X} AS Y) is a valid expression;
> R SUM (X AS Y) is not.
> SUMMARIZE R BY { ALL BUT X } ADD (SUM(X) AS Y) is a valid expression;
> SUMMARIZE R BY { ALL BUT X } ADD (GROUP(X) AS Y) is not.

Is your complaint that Tutorial D is not orthogonal? Or that it uses a different syntax for GROUP ?

>>Aggregate operations are defined using an identity element and a
>>repeated operation or as an expression on other aggregate operations.

>
> Thanks! Source?

Sorry. I still haven't unpacked since I moved last summer. I suspect you will find the definition in _Concrete Mathematics_ by Graham, Knuth, Patashnik. I further suspect you will find it in TTM.

However, I cannot easily verify this at the moment. Received on Sat May 06 2006 - 13:05:38 CDT