Gradual Parametricity, Revisited
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Bringing the benefits of gradual typing to a language with parametric polymorphism like System F, while preserving relational parametricity, has proven extremely challenging: first attempts were formulated a decade ago, and several recent developments have been published in the past year. In addition to leaving some properties as conjectures or future work, we observe that all prior work improperly handle type instantiations when imprecise types are involved. This observation further suggests that existing polymorphic cast calculi are not well suited for supporting a gradual counterpart of System F. Consequently, we revisit the challenge of designing a gradual language with explicit parametric polymorphism, exploring the extent to which the Abstracting Gradual Typing methodology helps us derive such a language, GSF. We present the design and metatheory of GSF. In addition to avoiding the uncovered semantic issues, GSF satisfies all the expected properties of a gradual parametric language, save for one property: the dynamic gradual guarantee, which was left as conjecture in all prior work, is here proven to be simply incompatible with parametricity. We nevertheless establish a weaker property that allows us to disprove several claims about gradual free theorems, clarifying the kind of reasoning supported by gradual parametricity.
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