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Logical Relations for Monadic Types

Jean Goubault-Larrecq·Slawomir Lasota·David Nowak
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Abstract

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, mono factorization systems, and monad morphisms. 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.

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Jean Goubault-Larrecq, Slawomir Lasota, David Nowak. 2008-03-04. Logical Relations for Monadic Types. https://doi.org/10.1017/s0960129508007172

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