Marco wrote:
On Sun, 22 Apr 2007 12:31:44 +0200, Larry Evans <cppljevans@cox-internet.com> wrote:
Actually, I think and_ and or_ are the meet and join of a lattice:
http://en.wikipedia.org/wiki/Lattice_%28order%29
where:
proto::_ is the top element proto::not_<proto::_> is the bottom element
However, I'm not sure about this since I don't know if the and_ and or_ operations are associative and commutative, which is one of the requirements for a lattic (I think).
Well, the last word is up to the author's library, however I'd be surprised if the following relations were not valid:
associativity: or_< T1, or_<T2, T3> > == or_< T1, T2, T3 > == or_< or_<T1, T2,>, T3 > and_< T1, and_<T2, T3> > == and_< T1, T2, T3 > == and_< and_<T1, T2,>, T3 >
Excuse my mathematical pedantry and going off topic. The operations or_ and and_ are binary, not ternary. Each of the middle expressions is, by definition (that is, mathematical consensus), equal to at least one of the corresponding outer terms. One or both of the equalities in each of the above relations is therefore tautologous (that is, always true). The only requirement for associativity is: or_< T1, or_<T2, T3> > == or_< or_<T1, T2,>, T3 > and_< T1, and_<T2, T3> > == and_< and_<T1, T2,>, T3 >