> Hello, > > Do junctions have a direct representation as predicate logic statements?
Yes. Damian and I have already worked them out in a link I have already posted today: http://groups.google.com/groups?hl=en&lr=&ie=UTF-8&oe=UTF-8&safe=off&selm=3DF2FE76.6050602%40conway.org&rnum=2 > In particular, do the following logic statements correspond directly > to the following perl6 junctions: > > LOGIC PERL6 JUNCTION (DESCRIP) > ===== ======================== > (forall x)(x is true) all (conjunction) > (exists x)(x is true) any (disjunction) > (forall x)(x is false) none (injunction) > (exists x)(x is false) one (abjunction) > > I don't have a really clear understanding of junctions (which is why I'm > posting this message, to try to clarify junctions in relation to a topic > I'm more familiar with), but it seems that the fourth type of junction, > "one" is inconsistent with the logic definition. > > Maybe "one" should be named "one_isnt", or the logic statement should > become (exists a single x)(x is true). Yeah, the latter. The thing about one_isnt is that it is exactly the same as all() except for its behavior when given no arguments. I don't see that as particularly useful... > Either way, maybe another junction is needed! Don't think so. I think it's important to make it easy to add new junctive types, however. So perhaps Junction is an abstract class which requires the definition of the two methods prefix:? () and states(). Then, to make one_isnt: class Indisjunction is Junction { method prefix:? () { ? grep { !$_ } self.args } method states () { die "Not smart enough to write this one" } } sub one_isnt([EMAIL PROTECTED]) { new Nondisjunction: @args } Luke > > Derek Ross.
