P1788
I made a one-word change today. In §6.4 I changed SHOULD to SHALL in the second sentence below.
In each flavor the decoration system, Clause 8, shall make it possible, while evaluating an arithmetic expression, to determine that some sub-case of the FTIA holds. It shall be supported by a Fundamental Theorem of Decorated Interval Arithmetic (FTDIA) stating that if evaluating an expression using decorated intervals returns a certain decoration d on the result, then the conditions for a corresponding FTIA sub-case are verified, hence the corresponding FTIA conclusion follows.
My reasons:
(1) Yesterday, agreeing with a comment from Christian that requirements for the FTIA/FTDIA should be mentioned in Clause 8, I changed the start of §8.2 from
8.2. Decoration definition and propagation. Each flavor shall document its set of provided decorations and their mathematical definitions.
to
8.2. Decoration definition and propagation. Each flavor shall document its set of provided decorations, their mathematical definitions, and their associated Fundamental Theorems, the FTIA and the FTDIA, as described in §6.4.
(2) Then I saw this contradicted §6.4, which had SHALL for FTIA and only SHOULD for FTDIA.
(3) When I added that §6.4 text on 21 June, I asked the group if it should be SHALL+SHALL, SHALL+SHOULD or SHOULD+SHOULD, saying I thought SHOULD+SHOULD is pointless.
No one gave an opinion, so it seems the decision is left to me.
(4) If the §8.2 text above is changed to say SHALL for the FTIA and SHOULD for the FTDIA, it looks really lame (as well as verbose). If someone asks "why the difference?", I haven't a good reason.
In fact why have a decoration system at all if you can't back it up with theory that says "If the output has decoration X, that means Y"?
Hence the change to SHALL+SHALL in §6.4.
The result is revision 381 on the SVN.
Baker: Please circulate this version under your authority. It is the FINAL FINAL version as far as I'm concerned. Even if I find other inconsistencies.
Christian: Please make a latexdiff version.
John Pryce