Relational Parametricity for Control Considered as a Computational Effect

AbstractThis paper investigates parametric polymorphism in the presence of control operators. Our approach is to specialise a general type theory combining polymorphism and computational effects, by extending it with additional constants expressing control. By defining relationally parametric models of this extended calculus, we capture the interaction between parametricity and control. As a worked example, we show that recent results of M. Hasegawa on type definability in the second-order (call-by-name) λμ-calculus arise as special cases of general results valid for arbitrary computational effects

Relational Parametricity for Computational Effects

According to Strachey, a polymorphic program is parametric if it applies a uniform algorithm independently of the type instantiations at which it is applied. The notion of relational parametricity, introduced by Reynolds, is one possible mathematical formulation of this idea. Relational parametricity provides a powerful tool for establishing data abstraction properties, proving equivalences of datatypes, and establishing equalities of programs. Such properties have been well studied in a pure functional setting. Many programs, however, exhibit computational effects, and are not accounted for by the standard theory of relational parametricity. In this paper, we develop a foundational framework for extending the notion of relational parametricity to programming languages with effects.Comment: 31 pages, appears in Logical Methods in Computer Scienc