Re: Motion 41, Draft decoration system
P1788
Here are some responses, and other points, about draft decoration system, Motion 41.
A.
I've seen two errors in 8.8.3 "Permitted combinations". First, I think the "Unbounded dac intervals" item is nonsense as it stands. It applied, not to dac "defined and continuous", but to the decoration bdc "bounded, defined and continuous" that I was using earlier, and abolished in favour of dac as a result of discussions with Jürgen & Vincent. Of course "An unbounded interval may be decorated dac"! What is said here applies, roughly, to intervals decorated com "common", but care in rephrasing is needed.
Second, "Decorations of Empty" is either incomplete or wrong depending on one's view. Vincent and I are currently discussing this, details shortly.
B.
I apologise for not making clear in the text of Motion 41 and/or the PDF that this is a draft for the *set-based* standard. I'm currently separating the flavor-independent material, which will go in Chapter 1, from the set-based. But I thought it important to get this out in public quickly.
Items 3 to 5 are for the *set-based* standard. Items 1 & 2:
> 1. The standard shall have a decoration system.
> 2. It shall be based on attaching information called a decoration to an
> interval, and some simple, easily implemented rules for propagating
> these through arithmetic expressions.
are flavor-independent. (Except it is not for the group as a whole to require that a particular flavor's propagation rules shall be "simple and easily implemented".)
There is one other, to my mind crucial, flavor-independent requirement, §8.8.7: "A multi-flavor implementation shall, and other implementations may, provide the sixth decoration com". This enables one to recognise when an evaluation was common.
My proposal implies that the Kaucher flavor can have a different decoration system from this one, as long as it includes com defined exactly as in 8.8.7. "Let a hundred flowers bloom."
Nate, I considered including the "ein" decoration as in the autumn 2011 scheme, but felt the complications of making it self-consistent outweighed the advantages. (E.g., was a "dac" interval required to be nonempty, or not?) Your priorities may lead to a different tradeoff. I look forward to the result.
C.
I agree with the response of Vladik and others to Nate's (1 Dec 2012, at 17:19) criticism of the "ill" decoration. The true decoration may be ill, but in practice you may only be able to find a looser decoration (one that encloses it, in the interpretation of decorations as sets). Just as, you may not be able to find the true smallest enclosure of a function's range, but you can find a looser enclosure.
John Pryce