Sum of ranges in a set-like context

[rapus95]

Right now we have

julia> r1=range(-2, 4, step=0.5)
-2.0:0.5:4.0

julia> r2 = range(3, 9, step=0.5)
3.0:0.5:9.0

julia> r1+r2
1.0:1.0:13.0

julia> r1.+r2
1.0:1.0:13.0

But I wonder whether it would be worthwhile to make + the set addition (aka r1+r2 = {a+b | a\in r1, b\in r2})
and thus the step wouldn't change.
Implementation:

julia> function newadd(a::AbstractRange, b::AbstractRange)
    step(a)==step(b) || error("have to have same step")
    return range(first(a)+first(b), last(a)+last(b), step=step(a))
end
newadd (generic function with 1 method)

julia> newadd(r1,r2)
1.0:0.5:13.0 #step ist now 0.5 instead of 1.0

[mbauman]

+ means addition. Full stop. This isn't going to change. Even more ranges are arrays. It would be very strange for + to mean one thing for some arrays, but another for other sorts of arrays.

Now, we could potentially try to do something clever with union/∪ — that's the operation you want. But you'd also have to be careful about non-overlapping ranges.

[rapus95]

+ means addition. Full stop. This isn't going to change. Even more ranges are arrays. It would be very strange for + to mean one thing for some arrays, but another for other sorts of arrays.

I meanwhile stumbled over AbstractRange<:AbstractVector aswell and from there I must say that I'd hate the inconsistency if addition wouldn't behave vector-like.

Now, we could potentially try to do something clever with union/∪ — that's the operation you want. But you'd also have to be careful about non-overlapping ranges.

Though for the other point you made I need to disagree. The range in the mathematical sense is just an intersection of a discrete set with an interval. (In case of AbstractUnitRange the discrete set is Z)
Thus the addition of two objects, each defined as an intersection of sets, can indeed be treated as the addition of sets, which in turn behaves different than a union.
The union would not necessarily produce a contiguous set as the intervals can be disjoint and length(r1\union r2)!= length(setadd(r1,r2))=length(r1)+length(r2)-1
Thus as a summary: AbstractRange has multiple abstractions, the one as a vector, which it is currently referring to, and the one as a set, which I was referring to.
As we cannot and do not want to implement context-sensitive addition I'd also stick with the non-breaking definition of +.
Remaining question is now, where to put such set-oriented addition and how to allow for elegant solutions in both contexts.

[mbauman]

Oh I see — I was misunderstanding the operation you were after. It looks like what you want is sometimes called the Minkowski sum.

Ranges (and arrays in general) are totally capable set-like objects — they support union, intersect, setdiff, and more.

[tkf]

FYI, there are discussions about using broadcasting to implement this kind of "product-based" arithmetics: #33282, JuliaMath/IntervalSets.jl#55