Fine-grained concurrent programs are difficult to get right, yet play an important role in modern-day computers. We want to prove strong specifications of such programs, with minimal user effort, in a trustworthy way. In this paper, we present DiaframeÐan automated and foundational verification tool for fine-grained concurrent programs.Diaframe is built on top of the Iris framework for higherorder concurrent separation logic in Coq, which already has a foundational soundness proof and the ability to give strong specifications, but lacks automation. Diaframe equips Iris with strong automation using a novel, extendable, goaldirected proof search strategy, using ideas from linear logic programming and bi-abduction. A benchmark of 24 examples from the literature shows that the proof burden of Diaframe is competitive with existing non-foundational tools, while its expressivity and soundness guarantees are stronger.

Recent advances in concurrent separation logic enabled the formal verification of increasingly sophisticated fine-grained ( i.e. , lock-free) concurrent programs. For such programs, the golden standard of correctness is linearizability , which expresses that concurrent executions always behave as some valid sequence of sequential executions. Compositional approaches to linearizability (such as contextual refinement and logical atomicity) make it possible to prove linearizability of whole programs or compound data structures ( e.g. , a ticket lock) using proofs of linearizability of their individual components ( e.g. , a counter). While powerful, these approaches are also laborious—state-of-the-art tools such as Iris, FCSL, and Voila all require a form of interactive proof. This paper develops proof automation for contextual refinement and logical atomicity in Iris. The key ingredient of our proof automation is a collection of proof rules whose application is directed by both the program and the logical state. This gives rise to effective proof search strategies that can prove linearizability of simple examples fully automatically. For more complex examples, we ensure the proof automation cooperates well with interactive proof tactics by minimizing the use of backtracking. We implement our proof automation in Coq by extending and generalizing Diaframe, a proof automation extension for Iris. While the old version (Diaframe 1.0) was limited to ordinary Hoare triples, the new version (Diaframe 2.0) is extensible in its support for program verification styles: our proof search strategies for contextual refinement and logical atomicity are implemented as modules for Diaframe 2.0. We evaluate our proof automation on a set of existing benchmarks and novel proofs, showing that it provides significant reduction of proof work for both approaches to linearizability.

Concurrent separation logic has been responsible for major advances in the formal verification of fine-grained concurrent algorithms and data structures such as locks, barriers, queues, and reference counters. The key ingredient of the verification of a fine-grained program is an invariant, which relates the physical data representation (on the heap) to a logical representation (in mathematics) and to the state of the threads (using a form of ghost state). An invariant is typically represented as a disjunction of logical states, but this disjunctive nature makes invariants a difficult target for automated verification. Current approaches roughly suffer from two problems. They use backtracking to introduce disjunctions in an uninformed manner, which can lead to unprovable goals if an appropriate case analysis has not been made before choosing the disjunct. Moreover, they eliminate disjunctions too eagerly, which can cause poor efficiency. While disjunctions are no problem for automated provers based on classical (i.e., non-separating) logic, the challenges with disjunctions are prominent in the study of proof automation for intuitionistic logic. We take inspiration from that area—specifically, based on ideas from connection calculus , we design a simple multi-succedent calculus for separation logic with disjunctions featuring a novel concept of a connection . While our calculus is not complete, it has the advantage that it can be extended with features of the state-of-the-art concurrent separation logic Iris (such as modalities, higher-order quantification, ghost state, and invariants), and can be implemented effectively in the Coq proof assistant with little need for backtracking. We evaluate the practicality on 24 challenging benchmarks, 14 of which we can verify fully automatically.