Re: Motion M0062: YES
Michel
On 2014 Jun 17, at 18:52, Michel Hack wrote:
> After several hours of reading the June 10 version of the document, I
> spotted a couple of editorial nits and typos -- and one unanticipated
> change that may need more serious consideration.
>
> First, the nits:
>
> Page viii, there appear to be two unnumbered sub-bullets of 11.7
> (decoration of non-arithmetic operations).
Fixed
> Page 10, 2nd para of 4.2.57 tightest:
> denotes ones -> denotes one
done
> Page 59, 3rd line of 12.13.5 Exact reduction operations:
> capable to represent -> capable of representing
done
> Page 63, middle of paragraph just above 14.3:
> there is an unique NaN -> there is a unique NaN
done
> Page 64, middle (see also below):
> is the least significant bits -> is the least significant bit
done
> Page 72, C2.2 Intervals, where "the whole real line" is mentioned,
> say that this is also denoted by Entire.
> (This is to make Chapter C self-contained; it is
> needed in C2.5.1, Interval constants, on page 75.)
done
> Page 79, 1st bullet in C3.3 The ill-formed interval:
> can not -> cannot
done
> Page 79, Note at the end of C3.5.2: I *think* we want FTIA -> FTDIA
This shows a bit of confusion in the document. I had been trying to eliminate "FTDIA" and use only "FTIA". But there *is* a difference between them; e.g. the theorem in Annex B is definitely FTDIA, not FTIA.
FTIA/FTDIA is a small but significant matter -- like the current discussion on interchange representation. The latter will affect how one programs; the former, how one explains.
IMO a suitable distinction is:
- The FTIA states conditions under which, for a function f defined by an expression, one can conclude definedness, continuity, etc. -- without saying how these conditions may be verified.
- The FTDIA says that when a calculation with decorated intervals gives a particular outcome, the corresponding FTIA condition holds and the corresponding conclusion follows.
Both FTIA and FTDIA are about Level 2 calculations, Level 1 being the special case where arithmetic is exact.
Does that seem sensible? I aim to make the relevant changes now; they may affect "The Fundamental Theorem" p.iv; 4.2.29 & maybe 4.2.24; 6.2 & 6.4; not 7.6 I think; 11.5 & 11.6 where FTIA should become FTDIA I think.
Query: does Note 2 in 11.6 (p.39) need to be so wordy?
If anyone has objections or improvements to the distinction I'm making here, please say so ASAP.
John Pryce