Roadmap

[mronian]

@timholy What all functionality would be a good start for this package?

• show
• in
• length
• subset
• . or *, ∩ (intersection)
• +, ∪ (union)
• isequal

Currently doing ClosedSet. For this, if someone does ClosedSet(a, b) where a>b what should be the behaviour?

[timholy]

Looks good. A couple of comments/questions:

• what do you mean by "subset"?
• I would only define ∩ (intersect) and ∪ (union), and not ., *, or +. Those might mean something else to other people.

[mronian]

Subset as in if A belongs to B i.e. ⊆, ⊇, ⊃ et al. :)

[timholy]

Oh, gotcha. That's called issubset (I thought you were talking about making a subset.)

[ararslan]

Regarding ClosedSet... for base ranges, having an upper bound greater than the lower bound results in (the equivalent of) an empty set, but the empty set is both open and closed, so this is kind of a tricky case. Would you have ClosedSet(4, 3) == OpenSet(4, 3)? To me it seems like the best option would be an error.

[mronian]

Do we check for this every time a ClosedSet is created? One of the motivations behind this package was to avoid that. ClosedIntervals.jl does that.

[ararslan]

If you don't check for a > b at all, how would you be able to define any kind of behavior in that scenario?

[timholy]

I would say ClosedSet(a, b) for a>b just returns that literal object, without any checking at construction time. It should return true for isempty, and I agree it should compare equal to empty OpenSets when someone gets around to implementing that type.

I don't think it's a problem that the empty set is both closed and open; we also have the property that ClosedSet(4,3) == ClosedSet(2,-1) as well. This is no different from the following:

julia> isa((), NTuple{0, Int})
true

julia> isa((), NTuple{0, Float64})
true

[timholy]

You only check it when asked to do so, by calling isempty.

[ararslan]

Ah, gotcha. Thanks for the explanation, Tim. That sounds like the best course of action to me.

[timholy]

The fanciest thing the constructor should do is promotion,

ClosedSet(a, b) = ClosedSet(promote(a,b)...)

[simonbyrne]

@dpsanders might be interested in this as well.

[timholy]

I'd also add the .. and ± constructors to the list. Since only one package can productively use those as constructors without conflicts, I'd suggest that for the sake of people who want to implement autoswapping interval mathematics on top of this package, we should export

autoswap{T}(a::T, b::T) = ifelse(a < b, (a, b), (b, a))
autoswap(a, b) = autoswap(promote(a, b)...)

(but of course the constructor doesn't call this, it has to be called manually, ClosedInterval(autoswap(a, b))). It's a good idea to use an explicit promote here because comparison typically involves promotion, and there's no sense in doing it twice.

EDIT: or maybe ordered is a better name.

[dpsanders]

This looks good, but just for the record seems to be duplicating a lot of functionality in ValidatedNumerics.jl.

[simonbyrne]

On that note: what is the purpose of this package?

[timholy]

Background is here and here. The most important points are:

• for some uses you need the ability to create an empty interval in the same way that UnitRange does. Autoswapping is hot death.
• having nice interval constructor operators .. and ± will run into conflicts if multiple packages define them. This argues for a dirt-simple (nearly trivial) package that might serve as the foundation for other packages that add more functionality.
• we definitely don't need all the numerics.

So the idea is that this package just represents a connect set on an ordered domain, and nothing more.

But no objections if people add operations to these sets in other packages.