Draft decoration system for discussion

[John Pryce <prycejd1@xxxxxxxxxxxxx>]

P1788

I attach a reasonably complete draft of the proposed decoration system to be used by the set-based interval standard. I submit a motion that this be accepted in outline. Specifically

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.
3. There shall be five decoration values, or six for a multi-flavor 
   implementation. They represent properties of a function over a box,
   such as continuity, etc.
4. Interval arithmetic operations propagate decorations. Most other
   interval operations do not. A user can implement a customized
   arithmetic operation that propagates decorations.
5. Compressed decorated interval arithmetic is to be described in an
   informative sub-clause, but is not required.

This text draws heavily on the work done in 2010-2011 by Nate Hayes, Arnold Neumaier, myself and others, to devise and exploit the idea of decoration values lying in a linear order from "best" to "worst" in some sense. In the last few weeks Vincent Lefevre and Jürgen Wolff von Gudenberg have helped me with removing inessentials, so the text now concentrates on specification, and most theory is relegated to an Annex (to be rewritten).

However any defects of the text are my responsibility. I am sure a fair number will be found during the discussion period. There are a few defects, gaps or questions in red text marked by an "alert" sign, waiting to be fixed or debated.

One thing that I think Jürgen noted, is that an implementation should have ways of turning a particular decoration value into a "hard" exception, similar to the way, e.g., one can set a switch that says "terminate execution on division by zero". A suitable form of words for this will be welcome.

Regards

John Pryce

Attachment: 20121130DecoSystemCirculated.pdf
Description: Adobe PDF document