Meaning of the ill decoration (was: Motion 42: NO)
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).
> 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).
--
Vincent Lefèvre <vincent@xxxxxxxxxx> - Web: <http://www.vinc17.net/>
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Work: CR INRIA - computer arithmetic / AriC project (LIP, ENS-Lyon)