The Next 700 Relational Program Logics
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We propose the first framework for defining relational program logics for arbitrary monadic effects. The framework is embedded within a relational dependent type theory and is highly expressive. At the semantic level, we provide an algebraic characterization for relational specifications as a class of relative monads, and link computations and specifications by introducing relational effect observations, which map pairs of monadic computations to relational specifications in a way that respects the algebraic structure. For an arbitrary relational effect observation, we generically define the core of a sound relational program logic, and explain how to complete it to a full-fledged logic for the monadic effect at hand. We show that by instantiating our framework with state and unbounded iteration we can embed a variant of Benton's Relational Hoare Logic, and also sketch how to reconstruct Relational Hoare Type Theory. Finally, we identify and overcome conceptual challenges that prevented previous relational program logics from properly dealing with effects such as exceptions, and are the first to provide a proper semantic foundation and a relational program logic for exceptions.
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