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

From: Larry Evans (cppljevans_at_[hidden])
Date: 2007-04-21 08:57:24

On 04/17/2007 09:24 PM, Maurizio Vitale wrote:
>>  (and maybe 0 arguments as
>>
>>>well).
>>
>>
>>Ick, no. It's not obvious what it should mean.
> 
> 
> A way to define it would be similar to what scheme/lisp do for
> operators applied to no arguments: they return the identity
> for the operation.
> For logical and and or, the identities would be #t and #f.
> 
> For grammars, and_ would be something that always matches
> and or_ would be something that never matches,
> 
> Maybe not particularly useful here, because probably nobody
> recurses on grammars this way, but very useful to have
> in scheme and lisp.
> 
> But I think having the same behaviour as mpl::and_ and mpl::or_
> is very important, so if one is changed the other probably should
> as well. The nice thing about this change is that it shouldn't
> make any code that was valid invalid (unless there's a way
> to have SFINAE effects visible).

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_<_>