Re: Meaning of the ill decoration (was: Motion 42: NO)
Le jeudi 07 février 2013 à 14:07 +0100, Vincent Lefevre a écrit :
> On 2013-02-06 22:07:15 +0100, Guillaume Melquiond wrote:
> > - I miss the point of the ill decoration as defined in Section 8.8.2,
> > since it is undecidable whether Dom(f) is empty for an arbitrary
> > real-valued function f. (And it does not even have to be that arbitrary:
> > you just need addition, multiplication, floor, conditional, and a
> > function that is not defined on the whole real line, say square root.)
>
> The fact that it is undecidable whether Dom(f) is empty is not a
> problem, since an implementation can return emp instead (the best
> decoration is not required).
That is right: as an implementer, I would always return emp, because I
would have no way to decide whether the function has an empty domain.
This defeats the point of such a definition of ill.
> > The note at the end of that section does not say otherwise. Section
> > 8.8.3 later gives a different meaning to ill, which makes much more
> > sense to me, but its relation to the definition of 8.8.2 eludes me.
>
> I agree, there seems to be a problem with the definition.
> For instance, take f(x) = x^2 and xx = (Empty,ill). One would
> get f(xx) = (Empty,ill), even though Dom(f) is not empty.
>
> I think the definition should be replaced by: Dom(f) is empty and/or
> at least one of the inputs has the ill decoration (i.e. is a NaI).
Do people really care about functions that are defined nowhere?
My point was that defining the output decoration as "one of the inputs
has the ill decoration" seems like the only meaningful definition to me.
Trying to relate that decoration to functions with empty domains does
not bring anything, neither to the user nor to the implementer.
Best regards,
Guillaume