I don't think they're that separable. I could take a program that called Java APIs and, through a bytecode decompiler, reconstruct a header file for that API.
In fact, I've done this very thing through reverse engineering C code. I've produced header files that allow interoperability with proprietary code. In this case, the function names and parameter orderings were copied, but the type names, parameter names, and overall organization were my original creation. I never looked at the original header file. Is that copyright infringement?
Personally, I think any attempt to find hard and fast rules is going to fail, and the intent should be the most important criterion. (NB: this is not what I'm saying the law is, as I'm not a lawyer: rather, I think this is what the law should be.)
If you're saying that the API reference itself can be copyrighted, yes, I agree. My typesetting of it, my method ordering, etc. All protectable. But not the facts on which it's based.
> If you wrote out a prose description of [...]
Of course that would be fine, but you don't have to go that far.
And I could take your prose description and strip the prose from it and turn it back into an API description. In that scenario, whose copyright do you think is being violated? The original work which I've never seen, or yours?