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

From: Maurizio Vitale (maurizio.vitale_at_[hidden])
Date: 2007-04-21 13:21:13

On Apr 21, 2007, at 8:57 AM, Larry Evans wrote:

>
> So, to summarize, what you want is:
>
>    proto::and_<> == proto::_
>    proto::or_<>  == proto::not_<_>
>
> where == means, "matches the same expressions".
> IOW, _ and not_<_> would be the "ones"
> of the and_ and or_ operators since:
>
>     proto::and_<proto::and_<X0,X1,...,Xn>, proto::_ >
> == proto::and_<X0,X1,...,Xn>
>
> and likewise for or_ and proto::not_<_>.  The zeros
> would be just the reverse.  IOW,
>
>           zero     one
>           ____     ___
>    and_:  not_<_>  _
>    or_ :  _        not_<_>
>

This would seem (to me) to be the logical extension, but I leave
to people who have design/used the mpl longer than me to decide
whether it is a good idea.

I'm not sure I understand zeros and ones:
the value which is interesting is the identity. In the case of additions
(and ORs) the identity is a 'zero'. In the case of multiplications  
(and ANDs)
the identity is a 'one'.
The 'other' value (zero for multiplications and one for additions)  
seems to
only be of interest for simplifying expressions, rather than being  
logically
important, but I might miss something here.

Best regards,

        Maurizio