Re: Idempotence and "Replication Insensitivity" are equivalent ?

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Date: 22 Sep 2006 08:29:13 -0700
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Jan Hidders ha scritto:

> wrote:
> >
> > But the real world objection to this is that, sometimes,
> > the user ORDERs the record and would like to compute aggregate
> > functions that depends on such order. So does not really make sense
> > to restrict to ass/comm functions.
> Actually, also in that case it does.
> Let's say we use the "free monoid" formalism to define aggregates. That
> means we define our aggregation function over collections with elements
> of type T1 and resulting in a aggregate of type T2 by giving (E, S, A):
> - E ; a value of type T1 for the result of the empty collection
> - S : T1 -> T2 ; a function for the result of the singleton collection
> - A : T2 x T2 -> T2 ; the aggregation / combination function
> such that the function A is associative and E the unit of A.
> If the collections are bags (or sets) then we require A also to be
> commutative (and idempotent).
> Now supose we are talking about sets (and require A to be associative,
> commutative and idempotent), the it is clear

Sounds fashinating :)

...but not really clear to me.

Could you make an example to make us understand ? Let's assume a Datetime field and this aggregate function:

Central date = minDate + Half length of total time interval

what would (E, S, A) be?

that you can still give a
> triple (E,S,A) such that it computes for example the top 5 of the set
> according to some ordering.
> Figuring out the exact trio is left to the reader as an exercise. :-)
> -- Jan Hidders
Received on Fri Sep 22 2006 - 17:29:13 CEST

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