Relational Reasoning via Probabilistic Coupling

International audienceProbabilistic coupling is a powerful tool for analyzing prob-abilistic processes. Roughly, coupling two processes requires finding an appropriate witness process that characterizes both processes in the same probability space. Applications of coupling include reasoning about convergence of distributions, and stochastic dominance—a probabilistic version of a monotonicity property. While the mathematical definition of coupling looks rather complex and difficult to manipulate, we show that the relational program logic pRHL—the logic underlying the EasyCrypt cryptographic proof assistant— internalizes a generalization of probabilistic coupling. We demonstrate how to express and verify classic examples of couplings in pRHL, and we mechanically verifying several couplings in EasyCrypt