I realise this comes a bit late, but somehow this document had slipped
to the bottom of my pile of 1788-related stuff. Sorry.
Now, perhaps I'm simply way out-of-date, and there is a newer version
available. If so, where?
I am aware of the fact that this document is an early attempt to use
a P754 draft as a starting point, and turn it into a P1788 proposal.
(This is especially obvious to me, as I was part of the P754 process.)
There are a few things that did not translate easily from P754 to P1788
however, most notably some subtleties of DFP (Decimal FP).
2.1.2 and 2.1.3: In the case of improper intervals the description in
terms of value order is incompatible with the description in
terms of first element and second element in Clause 3.
Since this document explicitly defines Division to be capable
of returning an improper interval as an encoding of a gap, this
matters. (3) States "The first element is the lower bound..."
Perhaps section 2.1 needs to introduce Proper and Improper
intervals, and then restrict 2.1.2 and 2.1.3 to proper intervals.
All interval functions in 4.3 need to define how improper
intervals are handled. Arnold Neumaier steps around this by
defining Division to return two intervals, the containment
and the gap, neither of which is improper. The gap may be
Empty; if not, the containment would be Entire.
Perhaps there should be a Gap() function that turns an improper
interval into a proper interval by exchanging the bounds (it
should transform Empty and proper intervals to Empty however).