# Re: How is this collection called?

Date: Wed, 31 Mar 2004 12:30:58 +0200

Message-ID: <406A9DE2.D88C80CC_at_michael.mendelsohn.de>

Paul schrieb:

> I think the problem is you've not defined exactly what you mean by

*> "binary aggregation operator".
*

I'd define aggregation to fulfil the axioms that

x is-in A => x is-in A*B

x is-in B => x is-in A*B

and that rules your approach out, because with

> Define a*b as "a U {b}" (where U is set union)

x is-in b => x is-in A*B breaks.

> There's no reason why a "union" of bags or lists has to be defined in

*> the usual way, it's just an arbitrary choice that fits in with our
**> vague conceptual ideas about what a union is.
*

With my aggregation constraint, I believe the collections defined by Mikito's set and bag axioms can only be set and bag, and that you cannot choose an aggregation operation that breaks these definitions.

I think that the list is not so useful because you can define
aggregators to keep or break the third axiom; and you can (with ease)
define the aggregator to always keep a*b=b*a if there's an ordering on
the collections.

Now wait, I think I just contradicted half of what I wrote above! :-P

So could I have a collection and aggregation with

a*a!=a a*b=b*a a*(b*c)!=(a*b)*c

?

Michael

-- Feel the stare of my burning hamster and stop smoking!Received on Wed Mar 31 2004 - 12:30:58 CEST