Re: about emp (was: Motion 42: NO)
First, the subject line should be changed. The discussion veered into
dependent vs independent intervals, which matters when an interval
represents the range of ONE real number, or whether it represents a
set of numbers. This is an interpretation issue which I have raised
repeatedly, but have come to see as being very difficult to formalize.
In the set-based flavor it is easy to stick to the strict set-based
interpretation, where an interval is precisely the entire set of reals
represented by it, and in that model, x**2, and x*y where y happens to
have the same value (as an interval) as x, lead to the same result.
The question then becomes: do we want to have a mechanism to allow a
programmer to state that a single-value-in-a-range interpretation is
desired?
(1) The single-scalar interpretation never gives a wider result than the
set interpretation, so the latter is ALWAYS valid (if not tightest).
(2) The single-scalar interpretation requires tagging, implicit or explicit,
to denote that multiple instances (necessary to write an expression in
a given syntactic environment) refer to the same entity.
(3) Implicit tagging is nearly impossible in some languages, and still
difficult in others. Fortran, which passes arguments by reference
instead of by value, has an easier job than C, for example. But it
is still tricky: Assignment creates a new reference; one would have
to use EQUIVALENCE instead -- and there is no general agreement on
how common subexpressions are to be interpreted in this context.
So, do we want to introduce an explicit tagging mechanism? (This would
immediately "solve" the 17-byte problem!)
Michel.
---Sent: 2013-02-19 16:38:12 UTC