Hmm... I guess that this may be a non-issue. I tried the following:

    type Foo
      a::Float64
    end

    function Foo(a::Int64)
      a
    end

    Foo(1.0) #Foo(1.0)
    Foo(1) #1

...and it seems there's no syntactic issues with having a function named 
the same as a type which returns values of a different type. So I could 
just create a new function Normal(DualNumber,DualNumber) which returns a 
DifferentiableNormal object, and everything would work.

So this question reduces to: is that a stylistic no-no?

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