Re: Reasons (not) to vote Motion 27: NO
Arnold Neumaier wrote:
I mean, what is the purpose
of having all the formalism for a FTDIA if a user's program can no
longer be
validated by it as soon as they include a single intersection or union
operation?
Intersection and union are very common operations in interval programs
and
algorithms...
Motion 26 has a concept of intersection and union, hence supports all such
calculations. But for safety reasons it requires that the result is always
a bare interval -- since the decoration it should get (if any) must depend
on the context.
Can you please give several real-world (Level 1) examples demonstrating each
different context?
I'm very skeptical of this statement.
so perhaps the majority of programs will be beyond the reach
of FTDIA to verify.
Traditional interval arithmetic without decorations has no FTIA for
computations with intersection. Nevertheless, many verifying interval
algorithms using intersection are in use.
IMO, this will be true for decorated intervals, as well, and is why
decoration semantics for these operations need to be standardized (not left
to chance).
Note: the bare semantics of intersection and union are pretty much
standardized even in such existing cases.
Second note: most existing semantics that I'm aware of have intersection and
union operating on sets (as in Motion 27), not real numbers.
Interval techniques usually validate things without decorations -
otherwise they couldn't have thrived in the past.
For verification, decorations are only needed for checking the hypotheses
of fixed point theorems.
Hmmm. I've already seen/given examples for other purposes, e.g., finding the
common domain where two functions are both defined but not necessarily
equal.
Nate