On Tue, Apr 04, 2006 at 11:23:14AM -0700, Jonathan Lang wrote: : Larry Wall wrote: : > On Tue, Apr 04, 2006 at 11:02:55AM -0700, Jonathan Lang wrote: : > : Will perl6 Sets include set negation and/or a universal set? In : > : effect, an internal flag that says, "this set contains every possible : > : element _except_ the ones listed"? : > : > Arguably, that's what none() is. : : ...except that none() is a Junction, not a Set. As such, the same : arguments that say that any() and all() aren't suitable for use as : Sets apply to none(), don't they?
You're confusing the map with the territory. We're trying to decide *how* Junctions are like Sets, not defining them into two different universes. I'm saying that all() is the Junction tha is most like a Set. A none() Junction can be viewed as the specification for an infinite set of sets that do not intersect with the corresponding all() junction. Infinite sets are a bit hard to compute with directly. A one() junction is the spec for a number of sets corresponding to the values of the corresponding all() junction, each of which contains only one element from that set. An any() Junction is all possible subsets not counting the null set. So junctional logic could be defined in terms of set theory, but not in a necessarily computable way. Larry
