Asynchronous Probabilistic Couplings in Higher-Order Separation Logic

TL;DR

Clutch is a higher-order probabilistic relational separation logic that enables reasoning about asynchronous couplings, expanding the capabilities of probabilistic program verification beyond synchronized sampling.

Contribution

It introduces Clutch, a novel logic supporting asynchronous probabilistic couplings for higher-order programs with complex features.

Findings

Formalized in Coq using Iris and Coquelicot

Applied to case studies demonstrating effectiveness

Enables reasoning about contextual refinement and equivalence

Abstract

Probabilistic couplings are the foundation for many probabilistic relational program logics and arise when relating random sampling statements across two programs. In relational program logics, this manifests as dedicated coupling rules that, e.g., say we may reason as if two sampling statements return the same value. However, this approach fundamentally requires aligning or "synchronizing" the sampling statements of the two programs which is not always possible. In this paper, we develop Clutch, a higher-order probabilistic relational separation logic that addresses this issue by supporting asynchronous probabilistic couplings. We use Clutch to develop a logical step-indexed logical relational to reason about contextual refinement and equivalence of higher-order programs written in a rich language with higher-order local state and impredicative polymorphism. Finally, we demonstrate the usefulness of our approach on a number of case studies. All the results that appear in the paper have been formalized in the Coq proof assistant using the Coquelicot library and the Iris separation logic framework.