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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 relation to reason about contextual refinement and equivalence of higher-order programs written in a rich language with a probabilistic choice operator, higher-order local state, and impredicative polymorphism. Finally, we demonstrate 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. 

This paper presents ProbCompCert, a compiler for a subset of the Stan probabilistic programming language (PPL), in which several key compiler passes have been formally verified using the Coq proof assistant. Because of the probabilistic nature of PPLs, bugs in their compilers can be difficult to detect and fix, making verification an interesting possibility. However, proving correctness of PPL compilation requires new techniques because certain transformations performed by compilers for PPLs are quite different from other kinds of languages. This paper describes techniques for verifying such transformations and their application in ProbCompCert. In the course of verifying ProbCompCert, we found an error in the Stan language reference manual related to the semantics and implementation of a key language construct. 

Multi-version concurrency control (MVCC) is a widely used, sophisticated approach for handling concurrent transactions. vMVCC is the first MVCC-based transaction library that comes with a machine-checked proof of correctness, providing clients with a guarantee that it will correctly handle all transactions despite a complicated design and implementation that might otherwise be error-prone. vMVCC is implemented in Go, stores data in memory, and uses several optimizations, such as RDTSC-based timestamps, to achieve high performance (25–96% the throughput of Silo, a state-of-the-art in-memory database, for YCSB and TPC-C workloads). Formally specifying and verifying vMVCC required adopting advanced proof techniques, such as logical atomicity and prophecy variables, owing to the fact that MVCC transactions can linearize at timestamp generation prior to transaction execution. 

This paper develops a new approach to verifying a performant file system that isolates crash safety and concurrency reasoning to a transaction system that gives atomic access to the disk, so that the rest of the file system can be verified with sequential reasoning. We demonstrate this approach in DaisyNFS, a Network File System (NFS) server written in Go that runs on top of a disk. DaisyNFS uses GoTxn, a new verified, concurrent transaction system that extends GoJournal with two-phase locking and an allocator. The transaction system's specification formalizes under what conditions transactions can be verified with only sequential reasoning, and comes with a mechanized proof in Coq that connects the specification to the implementation. As evidence that proofs enjoy sequential reasoning, DaisyNFS uses Dafny, a sequential verification language, to implement and verify all the NFS operations on top of GoTxn. The sequential proofs helped achieve a number of good properties in DaisyNFS: easy incremental development (for example, adding support for large files), a relatively short proof (only 2x as many lines of proof as code), and a performant implementation (at least 60% the throughput of the Linux NFS server exporting ext4 across a variety of benchmarks). 

Formal reasoning about hashing-based probabilistic data structures often requires reasoning about random variables where when one variable gets larger (such as the number of elements hashed into one bucket), the others tend to be smaller (like the number of elements hashed into the other buckets). This is an example of negative dependence , a generalization of probabilistic independence that has recently found interesting applications in algorithm design and machine learning. Despite the usefulness of negative dependence for the analyses of probabilistic data structures, existing verification methods cannot establish this property for randomized programs. To fill this gap, we design LINA, a probabilistic separation logic for reasoning about negative dependence. Following recent works on probabilistic separation logic using separating conjunction to reason about the probabilistic independence of random variables, we use separating conjunction to reason about negative dependence. Our assertion logic features two separating conjunctions, one for independence and one for negative dependence. We generalize the logic of bunched implications (BI) to support multiple separating conjunctions, and provide a sound and complete proof system. Notably, the semantics for separating conjunction relies on a non-deterministic , rather than partial, operation for combining resources. By drawing on closure properties for negative dependence, our program logic supports a Frame-like rule for negative dependence and monotone operations. We demonstrate how LINA can verify probabilistic properties of hash-based data structures and balls-into-bins processes. 

The main contribution of this paper is GoJournal, a verified, concurrent journaling system that provides atomicity for storage applications, together with Perennial 2.0, a framework for formally specifying and verifying concurrent crash-safe systems. GoJournal’s goal is to bring the advantages of journaling for code to specs and proofs. Perennial 2.0 makes this possible by introducing several techniques to formalize GoJournal’s specification and to manage the complexity in the proof of GoJournal’s implementation. Lifting predicates and crash framing make the specification easy to use for developers, and logically atomic crash specifications allow for modular reasoning in GoJournal, making the proof tractable despite complex concurrency and crash interleavings. GoJournal is implemented in Go, and Perennial is implemented in the Coq proof assistant. While verifying GoJournal, we found one serious concurrency bug, even though GoJournal has many unit tests. We built a functional NFSv3 server, called GoNFS, to use GoJournal. Performance experiments show that GoNFS provides similar performance (e.g., at least 90% throughput across several benchmarks on an NVMe disk) to Linux’s NFS server exporting an ext4 file system, suggesting that GoJournal is a competitive journaling system. We also verified a simple NFS server using GoJournal’s specs, which confirms that they are helpful for application verification: a significant part of the proof doesn’t have to consider concurrency and crashes. 

This paper introduces MEDS, a modular and elastic framework that simplifies the development of high-performance concurrent data structures that support linearizable primitive (i.e., add, remove, contains) and bulk (e.g., range query) operations.