Re: Motion 42: NO
On 2013-02-10 15:10:15 +0000, John Pryce wrote:
> The definition in 8.8.2 *does* match with 8.8.3 (which, I agree,
> gives a more intuitive meaning) in a respectable way. Despite
> Vincent (7 Feb 2013, at 14:44) saying
> > "Dom(f) is empty" was introduced by John on 13 Nov 2012
>
> this is NOT so. This idea of "ill" is Arnold Neumaier's invention
> (early 2011?) and has been discussed at various times.
I meant, it appeared in our new late-2012 disccusion at this date.
But indeed, it was already there in Motion 26 (which failed, BTW).
> I & Arnold (possibly others) have done a correctness check, which is necessary technical mumbo-jumbo on the border between math and computer science, summarised at the end of this email. Its conclusions:
> - Constants are zero-argument functions.
> - NaN is the unique zero-argument real function with empty domain.
> - NaN's natural (=tightest) bare interval extension is the interval constant (zero-argument interval function) whose value is Empty; the corresponding decorated interval extension is the decorated interval constant whose value is (Empty,ill). (This depends on the decoration scheme of course.) It is reasonable to give this the name NaI.
> - A bare or decorated interval constructor constructs a bare or decorated interval constant, i.e. one of these zero-argument functions.
But this doesn't take into account the case where ill is attached to
an input variable, when instantiated.
Or you need to say what happens at the leaves of the computation tree.
--
Vincent Lefèvre <vincent@xxxxxxxxxx> - Web: <http://www.vinc17.net/>
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