RE: Comments on decoration ill, intersection and union
It is my understanding (and it may need clarifying the text) that emp does not literally mean that Dom(f) is empty, it means that we have proven that Dom(f) is empty. Yes, of course, sometimes it is actually empty bit since we cannot prove it, we do not use this decoration.
This is similar to using the enclosure instead of the original range: if the computed interval is [0,1], it only means that all possible values are within this interval, but it may be that some values from this interval are not actually in the range.
Similarly here: if the decoration emp is obtained, this means that Dom(f) is empty, but it may be that this decoration was not obtained but Dom(f) is actually empty.
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From: stds-1788@xxxxxxxx [stds-1788@xxxxxxxx] On Behalf Of Nathan T. Hayes [nh@xxxxxxxxxxxxxxxxx]
Sent: Saturday, December 01, 2012 10:19 AM
To: 'John Pryce'; 'stds-1788'
Subject: Comments on decoration ill, intersection and union
John, P1788,
It appears that knowing Dom(f) is empty requires global knowledge of the
function f. For example, some Computer Algebra System (CAS) or a user's
comprehensive run-time knowledge of an entire program may be required. But
complicated functions may be composed from collections of smaller functions
or subroutines that are part of pre-compiled libraries, for instance, so
even a CAS may not be able to prove the ill decoration. This leads me to
think it should be dropped.