Missed simplification opportunity for `productmeasure`

[cscherrer]

In this measure

julia> d = productmeasure(fill(Lebesgue(), 5))
ProductMeasure([Lebesgue(ℝ), Lebesgue(ℝ), Lebesgue(ℝ), Lebesgue(ℝ), Lebesgue(ℝ)])

we have

julia> Base.issingletontype(eltype(marginals(d)))
true

But this guarantees we could instead have written it as a power measure. Let's update the powermeasure to account for this.

[oschulz]

Oh, nice!

[theogf]

But you would lose type stability no? Can you infer the type just from the input arguments?

Unless you want to make PowerMeasure a special case of ProductMeasure?

[cscherrer]

I think it will still be type-stable. When we call

productmeasure(::AbstractArray{T,N})

the rule can fire or not depending on issingletontype(T). I think it's enough for it to be a function of the type like this. Am I missing something?

[cscherrer]

Currently (in #120) we have

_generic_productmeasure_impl(mar::AbstractArray) = ProductMeasure(asmeasure.(mar))

We could change this to

function _generic_productmeasure_impl(mar::AbstractArray{T}) where {T}
    if Base.issingletontype(T)
        first(mar) ^ size(mar)
    else
        ProductMeasure(asmeasure.(mar))
    end
end

[cscherrer]

I guess we could even make it

if Base.issingletontype(T) || allequal(mar)

This requires walking through mar, and the fallback asmeasure.(mar) will require another traversal. It'd be better if we could fuse those. Shouldn't be too hard...

[cscherrer]

Keeping it simple for now. Added this as a test:

julia> productmeasure(fill(Lebesgue(), 5)) isa PowerMeasure
true

[oschulz]

Maybe add @inferred to the test?

[cscherrer]

Good idea! Done.