Logical Relations for Monadic Types

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Logical relations and their generalizations are a fundamental tool in proving properties of lambda-calculi, e.g., yielding sound principles for observational equivalence. We propose a natural notion of logical relations able to deal with the monadic types of Moggi’s computational lambda-calculus. The treatment is categorical, and is based on notions of subsconing and distributivity laws for monads. Our approach has a number of interesting applications, including cases for lambda-calculi with non-determinism (where being in logical relation means being bisimilar), dynamic name creation, and probabilistic systems.