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d :: Num a => (forall b. (Num b) => (a -> b) -> b -> b) -> a -> a d f x = let (Bundle y y') = f lift (Bundle x 1) in y'

The key change is in the type of d, which now accepts a polymorphic function on numbers, but passes in a "lift" function, which allows us to pass in higher-level variables. In one sense this function is ugly. In another sense, it's prettier, as you can now hide *all* of the Bundle data in a "differentiation" module.

To summarize: In my original version it is necessary to export 'd' and 'lift', which both expose 'Bundle' through their type signatures (and 'lift' even returns a 'Bundle', though how one could (ab)use it outside the intended context of a 'd' escapes me). In constrast, with your variation only 'd' need be exported and everything else in the module (including 'Bundle) is completely hidden. The cost is that functions must be "conditioned" before they can be differentiated. Thanks for your input! -Bjorn