can this handle 3 arguments?

[denizyuret]

I ran into the following problem using JuliaLang/julia#22060 (comment) which I think may also apply to your code: Consider a .* (b ./ c) where a and b are regular numbers/arrays and c is the container type we want to protect from broadcast. This turns into broadcast(f, a, b, c), i.e. the special argument is in the fourth position. In both @ylxdzsw's hack and yours I think only second and third arguments are checked, but the "special" argument can occur anywhere in the argument list.

I had run into this problem before in AutoGrad and someone had suggested a workaround for defining a method signature which would apply "if at least one of the variable number of arguments is of the special type". Trying to find that hack now...

[denizyuret]

OK, the trick mentioned in the first msg was this: JuliaArrays/StaticArrays.jl#136 (comment)

So we declare a variable number of arguments with type Union{SpecialType,RegularTypes...}. But in generic code like AutoGrad or the broadcasting trick RegularTypes can be anything -- number, array, KnetArray, other yet uninvented types! I guess Union{SpecialType,Any} would be meaningless...

[denizyuret]

To answer my own question, the following seems to work ok (at least for regular types):

function broadcast(f, x::Union{Number,AbstractArray,Rec}...)
    bx = ntuple(i->(isa(x[i],Rec) ? Broadcasted(x[i]) : x[i]), length(x))
    f(bx...).value
end

However, by itself it matches regular broadcast operations (without Rec) because Base uses the less specific method broadcast(f, A, Bs...). To prevent this we need to declare a more specific method that has the same body as the Base method:

using Base.Broadcast: broadcast_c, containertype
broadcast(f, x::Union{Number,AbstractArray}...)=broadcast_c(f, containertype(x...), x...)