From: Douglas Gregor (gregod_at_[hidden])
Date: 2002-09-04 07:43:10
On Wednesday 04 September 2002 06:50 am, Peter Dimov wrote:
> Natural equivalence for intervals? I don't see it.
> What I see as "natural" (regarding interval arithmetic, and not intervals
> as objects) is:
> I relop J :- foreach(x in I, y in J) x relop y.
This brings to mind a small question: how should I think of a variable 'x'
interval<T> x(a, b);
Is 'x' every value in the interval [a,b]? Or is 'x' some value that is bounded
by the interval [a,b] (but our information isn't exact enough to get the true
value of x)? I know that the latter is the more useful interpretation for
static analysis, but it also seems to be the interpretation used in interval
arithmetic as the library was intended for (the true result is some value
bounded by the interval, and the interval bounds assure that the true value
doesn't fall out of the interval because of rounding).
If we were to agree on the second interpretation, then Peter's semantics seem
to be the only semantics that make sense to us non-mathematicians :)
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