Re: Idempotence and "Replication Insensitivity" are equivalent ?

Chris Smith <cdsmith_at_twu.net> wrote:
> There was another definition, which is essentially
>
> ff: M(A) -> B, f: A x B -> B
> ff({|a,b,...,z|}) = f(a,f(b,...f(y,f(z,initial)...)
>
> where initial is some arbitrary value. With that definition, the set of
> functions definable as aggregates becomes equivalent to the entire set
> of functions on multisets (though some can be defined "better" than
> others), and it becomes possible to find some non-associative and non-
> commutative binary functions that nevertheless yield well-defined
> aggregate functions.

I should add that Marshall and William Hughes both disagree with calling the function binary in this case. The terminology is irrelevant, but there are certainly distinctions worth making. For example, if A does not equal B, then f *cannot* be associative, commutative, or idempotent, for obvious reasons.

-- 
Chris Smith