Revised Motion 26 decoration scheme

[John Pryce <j.d.pryce@xxxxxxxxxxxx>]

Dear P1788

Arnold and I submit a revised version of our Motion 26 decoration scheme, as a position paper extracted from the draft Level 1 standard text. 

I have _included_ the definitions of functions, expressions, interval evaluation etc. for completeness, but _omitted_ the required/recommended operations material. Also omitted the Annex with proof of FTDIA. If anyone wants a fuller version I'll send it.

Here are the main changes from previous version.
- Simpler (but equivalent) statement of FTDIA, eliminating "decorated
  interval enclosure" machinery.
- It is phrased for a 7-decoration scheme, but could use
  any of the simpler schemes that have been proposed.
- I hope we are close to converging with the combined motion 25/27.
  We adopt the same propagation rule. 
  However does the "static vs. tracking" difference of basic
  philosophy remain?
- We have a simplified, conceptual proof of the FTDIA - hardly any 
  case analysis needed - that works for all the schemes.
  I am now convinced it stands up, though it would be nice to
  make things even simpler.
- Arnold now agrees that union and intersection should produce 
  bare output, because of semantic problems that require expert 
  knowledge to be made correct in any given context.

Note also that our text continues to include Nate's "bare object arithmetic", whose importance for efficiency I accept.

Best wishes

John Pryce

Attachment: 20110718Decorations.pdf
Description: Adobe PDF document

PS. I'm not keen on the document class I'm using, which is an AMS-LaTeX one. Section headers don't stand out well. I changed to this to make the Annex mechanism work, but will look for a way to go back to what I used before.