Why does Dual inherit from Real but not Number?

[xukai92]

I thinks the definition should be Dual{N,T<:Real} <: Number.

[jrevels]

There was a long discussion about this in a previous issue. It's tempting to think that Dual <: Number in order to mirror the dual number set's mathematical relationship to the set of reals, but the Julia type hierarchy needn't reflect the relationship between these sets. We ultimately decided it would be most practical for Dual <: Real because Dual should programmatically support all Real operations, and be insertable wherever a Real is allowed.

[xukai92]

Actually I came up with this issue when I was trying to use Dual with Distributions.jl package, where they import functions from Rmath.jl, which replies on external R library. As these functions supports floats and ints, so the define the type with Real in their wrapper. This lead to the fact that I can pass them to the wrapper but it will give error.

[jrevels]

Yeah, unfortunately ForwardDiff's Dual cannot be used where generic Real types are not allowed (such as in calls to external libraries). It's an inherent limitation of language-specific AD - the code that's getting differentiated has to be Julia code "all the way down."