Override * and ^ in a way that different packages can interpret the result differently

[dlfivefifty]

In ApproxFun.jl, I'd like to do function approximation on a square via:

Fun((x,y) -> exp(x*y), (0..1)^2)

Of course, (0..1)^2 has a completely different interpretation in the setting of ValidatedNumerics.jl. Overriding ^ in either package would be type piracy.

My proposal is to add a placeholder type to this package that can be interpreted by other packages however they please:

# in IntervalSets.jl
struct IntervalProduct{NT<:Tuple}
   intervals::NT
end

*(a::AbstractInterval, b::AbstractInterval, c::AbstractInterval...) = IntervalProduct(a,b,c...)

Then ApproxFun can override Fun(::Function, d::IntervalProduct) to interpret d as a rectangle, while ValidedNumerics.jl can override ValidatedNumerics.Interval(::IntervalProduct) to interpret it as an interval arithmetic operation.