Re: Idempotence and "Replication Insensitivity" are equivalent ?

Chris Smith ha scritto:
An idempotent function can certainly be
> evaluated with unequal arguments.

of course, my meaning for the first part of the argument was different. I was trying to suggest some intuition. Did not expand fully. I try to explain the intuitive part:

  for an idempotent / assoc / comm function we have

  f( 4 3 3 3 3) = f( 4 f(3 3 3 3) ) = f(4 3)

 but adding another 4 and using the above result

  f( 4 4 3 3 3 3) = f( 4 f( 4 3 3 3 3) ) = f ( 4 f(4 3) )

 In general, f(4 3) and f ( 4 f(4 3) ) can be different.

 For a duplication insensitive function this cannot happen.

 Therefore I meant

f( 4 3 3 3 3) = f( 4 4 3 3 3 3) holds for duplication insensitive f( 4 3 3 3 3) = f( 4 4 3 3 3 3) may not hold for idempotence

 Therefore

  duplication insensitivity does not imply idempotent (n>3)

Make sense?

-P
> Chris Smith
Received on Thu Sep 21 2006 - 17:36:34 CEST