State of play on Motion 61 (§7 revision)
P1788
Motion 61 on Clause 7 "Flavors" is paused, waiting for a revised text that I have been discussing with Vincent Lefevre, Michel Hack and others.
* What's at stake?
The issue has been that several of us agreed the old text is not precise enough about what a flavor should contain in its underlying theory, hence require of its implementations. A basic P1788 principle is the relation between Levels 1 and 2:
- Level 2 intervals are a subset of the Level 1 intervals (if one drops any type-tagging information).
- A Level 1 interval yy is mapped to a Level 2 interval zz, of a type T, by the T-hull operation of that type.
- The tightest type-T version of an interval library operation, say exp(xx), is the one that forms the T-hull of the Level 1 value of exp(xx).
zz=hull_T(yy) must "contain" yy, so one can hardly avoid concluding a flavor must have a "contains" relation at Level 1.
Also, a flavor must, for each of its intervals xx, specify what the "Level 1 value of yy=exp(xx)" is (or specify that this value doesn't exist)
Otherwise, an implementation cannot know what value yy to enclose by a zz at Level 2 -- something Bill Walster has reminded us of on occasion.
(Example in the usual Kaucher flavor: if, say, xx is an improper interval then exp(xx) always exists but defining it is quite a sophisticated business; on the other hand if xx is a proper interval containing 0 then recip(xx)=1/xx is undefined.)
* Why didn't we do this hardening up of the text before? This is partly my fault for not having brought the "Flavors Levels 1 and 2" issue into general discussion when I first saw it.
* Why is it tricky? Because it's about *meta-issues* of the form "What should 1788 require a flavor to require about XYZ?" Hear Vincent:
On 2014 Jan 14, at 17:39, Vincent Lefevre wrote:
> My point here is: we don't forbid bad flavors[*], but we allow flavors to forbid bad implementations.
>
> [*] Forbidding bad flavors has the risk to forbid some good ones.
> Designing a flavor is more or less reserved to specialists (more
> than implementations) for later standardization.
Good advice, I think.
* How much longer will Motion 61 be paused? On Jan 17th I sent a revised draft to the group of experts/co-editors, and have had one comment as of writing this, which I will act on today. I aim to have a text to circulate within two days, and restart general Motion 61 discussion then. But the imminent start of my teaching semester may slow things down.
Regards
John Pryce