2 research outputs found
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 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
Trillium: Unifying Refinement and Higher-Order Distributed Separation Logic
We present a unification of refinement and Hoare-style reasoning in a foundational mechanized higher-order distributed separation logic. This unification enables us to prove formally in the Coq proof assistant that concrete implementations of challenging distributed systems refine more abstract models and to combine refinement-style reasoning with Hoare-style program verification. We use our logic to prove correctness of concrete implementations of two-phase commit and single-decree Paxos by showing that they refine their abstract TLA+ specifications. We further use our notion of refinement to transfer fairness assumptions on program executions to model traces and then transfer liveness properties of fair model traces back to program executions, which enables us to prove liveness properties such as strong eventual consistency of a concrete implementation of a Conflict-Free Replicated Data Type and fair termination of a concurrent program