Re: "Disjoint" relation

["Nate Hayes" <nh@xxxxxxxxxxxxxxxxx>]

Arnold Neumaier wrote:
> Nate Hayes wrote:
> > Michel Hack wrote:
> > > I agree with Arnold that the "Disjoint" relation deserves to be a
> > > primitive.  Interestingly, Motion 21 also requires synthesizing it
> > > out of two of the "overlapping" states.
> >
> > Arnolds "observation" that
> >    disjoint(A,B) = ( A \prec B ) or ( B \prec A )    (*)
> > requires twice as much computational effort than a "primitive" disjoint 
> > operation is pure misinformation.
>
> Please provide the pure information that substantiaties your
> present claim.
>
> How are you going to evaluate your expression as efficiently as evaluating 
> directly
>     disjoint(A,B) = (A.sup<B.inf) or (B.sup<A.inf)
> ?

Because by Motion 13.04, A.sup < B.inf is the definition (and 
implementation) of A \prec B and B.sup < A.inf is the definition (and 
implementation) of B \prec A. An optimizing compiler will therefore 
automatically generate the inlined code:
   disjoint(A,B) = (A.sup<B.inf) or (B.sup<A.inf)
There is no need for a special "primitive" disjoint operation... or if there 
is, it should be defined in terms of the "preceeding" relation as given in 
Motion 13.04, anyways.

Nate