RE: Promotion of bare decorations & comparisons
Michel Hack wrote:
> In reply to my example (assuming a threshold of "dac" for compressed
intervals)
> [1,2] \subseteq floor([0,6])
> = [1,2] \subseteq ([0,6],def) // decorated result, below
threshold
> = [1,2] \subseteq def // compress decorated result
> = [1,2] \subseteq Empty
> = false
> Nate Hayes wrote:
> > So returning false in this example is exactly what the user expects,
> > since [1,2] cannot be a subset of any defined and continuous interval
> > range of floor([0,6]).
>
> Ok, so let's turn it around:
> floor([0,6] \subseteq [8,9]
> ...
> = Empty \subseteq [8,9]
> = true
>
> What is this supposed to mean?
If Empty is not an interval, i. e., if Empty is not an element of the
universal set of overline-IR, then all comparisons on Empty are unordered,
similar to how all comparisons on NaN in IEEE 754 are unordered. In this
case
= Empty \subseteq [8,9]
= false
matches user expectations.
Nate
P.S. Similar to this idea is the Interval Overlapping Relation of Motion
21.2, for example, which is defined for two nonempty intervals and may
detect if one or more operands is empty as an exceptional condition.