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Parametricity And Local Variables, Peter W. O'Hearn, R. D. Tennent

Electrical Engineering and Computer Science - Technical Reports

We propose that the phenomenon of local state may be understood in terms of Strachey's concept of parametric (i.e., uniform) polymorphism. The intuitive basis for our proposal is the following analogy: a non-local procedure is independent of locally-declared variables in the same way that a parametrically polymorphic function is independent of types to which it is instantiated. A connection between parametricity and representational abstraction was first suggested by J. C. Reynolds. Reynolds used logical relations to formalize this connection in languages with type variables and user-defined types. We use relational parametricity to construct a model for an Algol-like language in …