Re: Idempotence and "Replication Insensitivity" are equivalent ?
Date: 20 Sep 2006 22:11:21 -0700
Message-ID: <1158815481.145783.232040_at_m7g2000cwm.googlegroups.com>
William Hughes wrote:
> Marshall wrote:
>
> The question posed by the title of this thread "are idempotence
> and replication insensitivity equivalent?". Since idempotence
> only applies to functions of the type A,A->A we get that
> idempotence only applies to a restricted set of functions
> on M(A). Since this restricted set does not include all
> the functions we would like to apply the term "replication
> insensitive" to, I would conclude that the terms
> "idempotent" and "replication insensitive" are not equivalent.
Well, they were never proposed to be *equivalent*, at least
not by me. The two kinds of functions have different types,
for one thing. They certainly look *related* though.
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? I went back over the
Anyway, do you have a counterexample? Please bear in mind that:
- I agree that "idempotence" only applies to functions of type A, A -> A
- I agree that an arbitrary function of type {|A|} -> B might be duplicate insensitive but not have an associated idempotent binary function. (For example, the function:
f:{|A|} -> nat
f(x) = 7
)
Marshall Received on Thu Sep 21 2006 - 07:11:21 CEST