Re: about emp (was: Motion 42: NO)
Le jeudi 07 février 2013 à 14:50 +0100, Vincent Lefevre a écrit :
> On 2013-02-06 22:07:15 +0100, Guillaume Melquiond wrote:
> > - Finally, the emp decoration seems superfluous to me. There is no point
> > in decorating a nonempty interval with an emp decoration (except maybe
> > for wreaking havoc in an interval library), so the emp decoration could
> > just as well be removed. An empty interval would then be decorated with
> > trv when it does not designate a NaI.
>
> IIRC, there can be problems with that. For instance, take zz = g(yy)
> where yy is Empty. Since g is defined and continuous on the empty set
> yy, one can return zz = (Empty,dac). But now assume that yy wasn't
> actually an input, but yy = f(xx) for some non-empty xx, e.g.
> sqrt([-2,-1]). So, one would get:
>
> (g o f)(xx) = (Empty,dac)
>
> which is wrong.
As I understand it, decorations propagate from inputs to output and you
can never get an output with a stronger decoration than an input. So, on
your example, you would get:
f(xx) = (Empty,trv)
g(f(xx)) = (Empty,trv)
which is right.
Best regards,
Guillaume