Re: [boost] thinking algebraically (was Re: proto::or_ arity

From: Larry Evans (cppljevans_at_[hidden])
Date: 2007-04-22 06:31:44

On 04/21/2007 07:57 AM, Larry Evans wrote:
> On 04/17/2007 09:24 PM, Maurizio Vitale wrote:
[snip]
> and likewise for or_ and proto::not_<_>.  The zeros
> would be just the reverse.  IOW,
> 
>           zero     one
>           ____     ___
>    and_:  not_<_>  _
>    or_ :  _        not_<_>
> 

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).