# Re: Idempotence and "Replication Insensitivity" are equivalent ?

Date: Wed, 20 Sep 2006 23:20:55 -0600

Message-ID: <MPG.1f7bcf1ecd445123989725_at_news.altopia.net>

Marshall <marshall.spight_at_gmail.com> wrote:

> The proposal is that an aggregate function defined

*> by a fold of a function f will be "duplicate insensitive"
**> iff f is idempotent. Chris has pointed out the additional
**> requirement that the starting value for the fold has to
**> be an identity of f.
**>
**> Has there been a counterexample?
*

See my recent response for a counter-example as you stated the claim in the first sentence above. You don't seem to agree that the function is well-defined or that it is duplicate-insensitive, but I believe both are true. I'll try to prove them in a second.

If you add my additional condition that the starting value is an identity of f, then a proof has been given of the equivalence of idempotence of f and duplicate-insensitivity of the fold. The proof was given for an older definition, but it should still apply. I can try to write that to the most recent definition as well, if you like. Unless someone's made an error in the proof, of course there can't be a counterexample.

-- Chris SmithReceived on Thu Sep 21 2006 - 07:20:55 CEST