Re: Interval comparisons
Maarten van Emden schrieb:
According to Motion 2 on process structure we should settle issues
at level 1 of that motion before descending into the details of
the lower levels. An outstanding unresolved issue at level 1 is
the definition of relation operators.
What we have so far are the relational operators in the Vienna Proposal
section 5.4 (henceforth "Vienna 5.4"). Here == is the name given to
the interval extension of the equality relation among reals. Is this
satisfactory?
A consequence of Vienna 5.4:
if E computes f and if x in xx, then E(xx) == hull(f(x)) is false.
but xx and f(x) are usually different anyway, die to overestimation.
Remember, == is the interval extension of equality.
Vienna 5.4 has several interpretations of realtions; none of them
deserves the name interval extension.
The proper test for equality is areIdentical(xx,yy) defined in
Section 2.5.7. The strange properties of ==, as obtained by
uniformization of the natural rules for <= and >=,
are spelled out as a remark, though we forgot to refer to 2.5.7.
Arnold Neumaier