Is the presumption that these parameters are floats, or at least numeric? It seems like if I took the functions from some random program (e.g., GNU diff), most would not be meaningfully differentiable. Or perhaps I'm missing something?
Yes, the parameters you're differentiating with respect to need to be floats.
Though there might be potential for extending the frameworks to e.g. differential cryptanalysis - I'm not knowledgeable enough about it to say how much differential cryptanalysis can be done programmatically.
