Domain as an interface

[daanhb]

The discussion came up again whether or not to see domains as inheriting from Domain{T}, or whether it can be an interface instead: JuliaMath/IntervalSets.jl#117 and JuliaMath/IntervalSets.jl#115

Related to that is the question of what is the role of T in Domain{T}.

[daanhb]

As a random example, this is current behaviour in DomainSets:

julia> using IntervalSets, DomainSets

julia> using DomainSets: ×

julia> d = (0..1.0) × ComplexUnitCircle()
(0.0 + 0.0im..1.0 + 0.0im) × ComplexUnitCircle()

julia> eltype(d)
SVector{2, ComplexF64} (alias for StaticArraysCore.SArray{Tuple{2}, Complex{Float64}, 1, 2})

julia> numtype(d)
ComplexF64 (alias for Complex{Float64})

julia> prectype(d)
Float64

A type promotion happens when taking the cartesian product. Next, the T in this example is a static vector and conveys information about the numeric type (the elements of the vector, here ComplexF64) and the precision type (Float64).

[dlfivefifty]

One comment: we can still support eltype even if it is just an interface (that is, each domain would overload eltype)

[daanhb]

Related issue on moving the definition of a Domain into a new and very lightweight package: JuliaMath/IntervalSets.jl#136