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Re: An error-catching question

Nate Hayes wrote:

Who would want a standard to require that?


Not me!

Please keep in mind that Clause 2.3 of Motion 8 specifically requires that
any arithmetic operation on bare decorations must return a bare decoration. 
This is consistent with the "Uber NaI" concept mentioned above. In other
words, once a forgetful operator is used to strip away the interval portion 
of a decorated interval, no arithmetic operation will ever be allowed to
propagate anything other than a bare decoration for such an operand. This is consistent with how IEEE 754 propagates NaNs in floating-point computations 
and, I believe, addresses the conerns you've raised.
In this discussion, we should also be very careful not to confuse Level 2 definitions and semantics with Level 3 representations.
For exmaple, at Level 3 it may be possible to represent a bare decoration as: 
   [-NaN,-NaN]
with decoration bits encoded in the NaN payloads.

At the same time, a Level 3 representation of empty set could be:
   [+NaN,+NaN].
In this case, the payload of the NaNs are irrelavent, since "empty set" is a bare interval, not a bare decoration.
Just because Level 3 might use NaNs to encode both bare decorations (NaIs) and empty set (a bare interval), be careful not to conclude that both are necissarily NaI. For example, empty set might be "absorbed" by in a lengthy computation by a union operation, but this will never happen to a bare decoration.
In other words, its possible that distinct Level 2 objects (such as a bare decoration and the empty set, which is a bare interval) could both map to Level 3 objects represented in some way by NaNs. 

Nate