isempty_interval return false on empty ill intervals

[Kolaru]

While playing with Supposition.jl at JuliaCon hackathon (with somebody I would like to credit, but I don't know her GH handle x_x), we notice the following:

1. isempty_interval returns false on empty ill intervals
2. The docstring of the function (and of isentire_interval) point to the wrong (should be 10.5.10)
3. I cannot find a mention of the behavior in the standard
4. Yet, the itl1788 test suite includes a test for this case, with the current behavior

Does anyone know why this behavior is enforced in the itl1788 test suite ?

[OlivierHnt]

Going through the standard, I found in Section 12.12.9 (Boolean functions of intervals)

Each bare interval operation in this subclause shall have a decorated version, where each input of bare interval
type is replaced by an input having the corresponding decorated interval type. Following 11.7, if any input
is NaI, the result is false (in particular equal(NaI,NaI) is false). Otherwise the result is obtained by
discarding the decoration and applying the corresponding bare interval operation.

They refer to the functions described in 10.5.10, which includes the isEmpty function:

There is a function isEmpty(x), with value 1 if x is the empty set, 0 otherwise. There is a function
isEntire(x), with value 1 if x is the whole line, 0 otherwise.

[Kolaru]

Great catch! Then I'll just make an update to the docstrings and doc.

The only thing that I'm still wondering is: should we display ∅_ill as NaI instead? The only useful information is that the interval is ill.

[OlivierHnt]

Yes printing NaI seems better than ∅_ill.