Hoare-style Specifications as Correctness Conditions for Non-linearizable Concurrent Objects

Designing scalable concurrent objects, which can be efficiently used on multicore processors, often requires one to abandon standard specification techniques, such as linearizability, in favor of more relaxed consistency requirements. However, the variety of alternative correctness conditions makes it difficult to choose which one to employ in a particular case, and to compose them when using objects whose behaviors are specified via different criteria. The lack of syntactic verification methods for most of these criteria poses challenges in their systematic adoption and application. In this paper, we argue for using Hoare-style program logics as an alternative and uniform approach for specification and compositional formal verification of safety properties for concurrent objects and their client programs. Through a series of case studies, we demonstrate how an existing program logic for concurrency can be employed off-the-shelf to capture important state and history invariants, allowing one to explicitly quantify over interference of environment threads and provide intuitive and expressive Hoare-style specifications for several non-linearizable concurrent objects that were previously specified only via dedicated correctness criteria. We illustrate the adequacy of our specifications by verifying a number of concurrent client scenarios, that make use of the previously specified concurrent objects, capturing the essence of such correctness conditions as concurrency-aware linearizability, quiescent, and quantitative quiescent consistency. All examples described in this paper are verified mechanically in Coq.Comment: 18 page

Concurrent Data Structures Linked in Time

Arguments about correctness of a concurrent data structure are typically carried out by using the notion of linearizability and specifying the linearization points of the data structure's procedures. Such arguments are often cumbersome as the linearization points' position in time can be dynamic (depend on the interference, run-time values and events from the past, or even future), non-local (appear in procedures other than the one considered), and whose position in the execution trace may only be determined after the considered procedure has already terminated. In this paper we propose a new method, based on a separation-style logic, for reasoning about concurrent objects with such linearization points. We embrace the dynamic nature of linearization points, and encode it as part of the data structure's auxiliary state, so that it can be dynamically modified in place by auxiliary code, as needed when some appropriate run-time event occurs. We name the idea linking-in-time, because it reduces temporal reasoning to spatial reasoning. For example, modifying a temporal position of a linearization point can be modeled similarly to a pointer update in separation logic. Furthermore, the auxiliary state provides a convenient way to concisely express the properties essential for reasoning about clients of such concurrent objects. We illustrate the method by verifying (mechanically in Coq) an intricate optimal snapshot algorithm due to Jayanti, as well as some clients

A framework for automated concurrency verification

Reasoning systems based on Concurrent Separation Logic make verifying complex concurrent algorithms readily possible. Such algorithms contain subtle protocols of permission and resource transfer between threads; to cope with these intricacies, modern concurrent separation logics contain many moving parts and integrate many bespoke logical components. Verifying concurrent algorithms by hand consumes much time, effort, and expertise. As a result, computer-assisted verification is a fertile research topic, and fully automated verification is a popular research goal. Unfortunately, the complexity of modern concurrent separation logics makes them hard to automate, and the proliferation and fast turnover of such logics causes a downward pressure against building tools for new logics. As a result, many such logics lack tooling. This dissertation proposes Starling: a scheme for creating concurrent program logics that are automatable by construction. Starling adapts the existing Concurrent Views Framework for sound concurrent reasoning systems, overlaying a framework for reducing concurrent proof outlines to verification conditions in existing theories (such as those accepted by off-the-shelf sequential solvers). This dissertation describes Starling in a bottom-up, modular manner. First, it shows the derivation of a series of general concurrency proof rules from the Views framework. Next, it shows how one such rule leads to the Starling framework itself. From there, it outlines a series of increasingly elaborate frontends: ways of decomposing individual Hoare triples over atomic actions into verification conditions suitable for encoding into backend theories. Each frontend leads to a concurrent program logic. Finally, the dissertation presents a tool for verifying C-style concurrent proof outlines, based on one of the above frontends. It gives examples of such outlines, covering a variety of algorithms, backend solvers, and proof techniques

Programming and Proving with Distributed Protocols

Distributed systems play a crucial role in modern infrastructure, but are notoriously difficult to implement correctly. This difficulty arises from two main challenges: (a) correctly implementing core system components (e.g., two-phase commit), so all their internal invariants hold, and (b) correctly composing standalone system components into functioning trustworthy applications (e.g., persistent storage built on top of a two-phase commit instance). Recent work has developed several approaches for addressing (a) by means of mechanically verifying implementations of core distributed components, but no methodology exists to address (b) by composing such verified components into larger verified applications. As a result, expensive verification efforts for key system components are not easily reusable, which hinders further verification efforts. In this paper, we present Disel, the first framework for implementation and compositional verification of distributed systems and their clients, all within the mechanized, foundational context of the Coq proof assistant. In Disel, users implement distributed systems using a domain specific language shallowly embedded in Coq and providing both high-level programming constructs as well as low-level communication primitives. Components of composite systems are specified in Disel as protocols, which capture system-specific logic and disentangle system definitions from implementation details. By virtue of Disel’s dependent type system, well-typed implementations always satisfy their protocols’ invariants and never go wrong, allowing users to verify system implementations interactively using Disel’s Hoare-style program logic, which extends state-of-the-art techniques for concurrency verification to the distributed setting. By virtue of the substitution principle and frame rule provided by Disel’s logic, system components can be composed leading to modular, reusable verified distributed systems. We describe Disel, illustrate its use with a series of examples, outline its logic and metatheory, and report on our experience using it as a framework for implementing, specifying, and verifying distributed systems

Fifty years of Hoare's Logic

We present a history of Hoare's logic.Comment: 79 pages. To appear in Formal Aspects of Computin