Asynchronous Probabilistic Couplings in Higher-Order Separation Logic

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 ret...

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Bibliographic Details
Published in:arXiv.org 2023-11
Main Authors: Simon Oddershede Gregersen, Aguirre, Alejandro, Haselwarter, Philipp G, Tassarotti, Joseph, Birkedal, Lars
Format: Article
Language:English
Subjects:
Clutches
Couplings
Logic
Polymorphism
Probability theory
Random sampling
Separation
Synchronism
Online Access:Get full text
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.2301.10061