JL writes, A formal treatment of parametricity in the presence of overloading has not been written up (Eric Meijer has talked of doing so). The problem with writing it up is that it's too simple: it reduces to a single observation, namely that the parametricity theorem coming from an overloaded type is the regular parametricity theorem that arises after performing the dictionary expansion. You can find this observation in Section 3.4 of the original `Theorems for Free'. So it is written up! -- P
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