ReLoC Reloaded:A Mechanized Relational Logic for Fine-Grained Concurrency and Logical Atomicity

We present a new version of ReLoC: a relational separation logic for proving refinements of programs with higher-order state, fine-grained concurrency, polymorphism and recursive types. The core of ReLoC is its refinement judgment $e \precsim e' : \tau$, which states that a program $e$ refines a program $e'$ at type $\tau$. ReLoC provides type-directed structural rules and symbolic execution rules in separation-logic style for manipulating the judgment, whereas in prior work on refinements for languages with higher-order state and concurrency, such proofs were carried out by unfolding the judgment into its definition in the model. ReLoC's abstract proof rules make it simpler to carry out refinement proofs, and enable us to generalize the notion of logically atomic specifications to the relational case, which we call logically atomic relational specifications. We build ReLoC on top of the Iris framework for separation logic in Coq, allowing us to leverage features of Iris to prove soundness of ReLoC, and to carry out refinement proofs in ReLoC. We implement tactics for interactive proofs in ReLoC, allowing us to mechanize several case studies in Coq, and thereby demonstrate the practicality of ReLoC. ReLoC Reloaded extends ReLoC (LICS'18) with various technical improvements, a new Coq mechanization, and support for Iris's prophecy variables. The latter allows us to carry out refinement proofs that involve reasoning about the program's future. We also expand ReLoC's notion of logically atomic relational specifications with a new flavor based on the HOCAP pattern by Svendsen et al

Formal Analysis of Concurrent Programs

In this thesis, extensions of Kleene algebras are used to develop algebras for rely-guarantee style reasoning about concurrent programs. In addition to these algebras, detailed denotational models are implemented in the interactive theorem prover Isabelle/HOL. Formal soundness proofs link the algebras to their models. This follows a general algebraic approach for developing correct by construction verification tools within Isabelle. In this approach, algebras provide inference rules and abstract principles for reasoning about the control flow of programs, while the concrete models provide laws for reasoning about data flow. This yields a rapid, lightweight approach for the construction of verification and refinement tools. These tools are used to construct a popular example from the literature, via refinement, within the context of a general-purpose interactive theorem proving environment

Automated and foundational verification of low-level programs

Formal verification is a promising technique to ensure the reliability of low-level programs like operating systems and hypervisors, since it can show the absence of whole classes of bugs and prevent critical vulnerabilities. However, to realize the full potential of formal verification for real-world low-level programs one has to overcome several challenges, including: (1) dealing with the complexities of realistic models of real-world programming languages; (2) ensuring the trustworthiness of the verification, ideally by providing foundational proofs (i.e., proofs that can be checked by a general-purpose proof assistant); and (3) minimizing the manual effort required for verification by providing a high degree of automation. This dissertation presents multiple projects that advance formal verification along these three axes: RefinedC provides the first approach for verifying C code that combines foundational proofs with a high degree of automation via a novel refinement and ownership type system. Islaris shows how to scale verification of assembly code to realistic models of modern instruction set architectures-in particular, Armv8-A and RISC-V. DimSum develops a decentralized approach for reasoning about programs that consist of components written in multiple different languages (e.g., assembly and C), as is common for low-level programs. RefinedC and Islaris rest on Lithium, a novel proof engine for separation logic that combines automation with foundational proofs.Formale Verifikation ist eine vielversprechende Technik, um die Verlässlichkeit von grundlegenden Programmen wie Betriebssystemen sicherzustellen. Um das volle Potenzial formaler Verifikation zu realisieren, müssen jedoch mehrere Herausforderungen gemeistert werden: Erstens muss die Komplexität von realistischen Modellen von Programmiersprachen wie C oder Assembler gehandhabt werden. Zweitens muss die Vertrauenswürdigkeit der Verifikation sichergestellt werden, idealerweise durch maschinenüberprüfbare Beweise. Drittens muss die Verifikation automatisiert werden, um den manuellen Aufwand zu minimieren. Diese Dissertation präsentiert mehrere Projekte, die formale Verifikation entlang dieser Achsen weiterentwickeln: RefinedC ist der erste Ansatz für die Verifikation von C Code, der maschinenüberprüfbare Beweise mit einem hohen Grad an Automatisierung vereint. Islaris zeigt, wie die Verifikation von Assembler zu realistischen Modellen von modernen Befehlssatzarchitekturen wie Armv8-A oder RISC-V skaliert werden kann. DimSum entwickelt einen neuen Ansatz für die Verifizierung von Programmen, die aus Komponenten in mehreren Programmiersprachen bestehen (z.B., C und Assembler), wie es oft bei grundlegenden Programmen wie Betriebssystemen der Fall ist. RefinedC und Islaris basieren auf Lithium, eine neue Automatisierungstechnik für Separationslogik, die maschinenüberprüfbare Beweise und Automatisierung verbindet.This research was supported in part by a Google PhD Fellowship, in part by awards from Android Security's ASPIRE program and from Google Research, and in part by a European Research Council (ERC) Consolidator Grant for the project "RustBelt", funded under the European Union’s Horizon 2020 Framework Programme (grant agreement no. 683289)

Unifying Theories of Reactive Design Contracts

Design-by-contract is an important technique for model-based design in which a composite system is specified by a collection of contracts that specify the behavioural assumptions and guarantees of each component. In this paper, we describe a unifying theory for reactive design contracts that provides the basis for modelling and verification of reactive systems. We provide a language for expression and composition of contracts that is supported by a rich calculational theory. In contrast with other semantic models in the literature, our theory of contracts allow us to specify both the evolution of state variables and the permissible interactions with the environment. Moreover, our model of interaction is abstract, and supports, for instance, discrete time, continuous time, and hybrid computational models. Being based in Unifying Theories of Programming (UTP), our theory can be composed with further computational theories to support semantics for multi-paradigm languages. Practical reasoning support is provided via our proof framework, Isabelle/UTP, including a proof tactic that reduces a conjecture about a reactive program to three predicates, symbolically characterising its assumptions and guarantees about intermediate and final observations. This allows us to verify programs with a large or infinite state space. Our work advances the state-of-the-art in semantics for reactive languages, description of their contractual specifications, and compositional verification

Cogent: uniqueness types and certifying compilation

This paper presents a framework aimed at significantly reducing the cost of proving functional correctness for low-level operating systems components. The framework is designed around a new functional programming language, Cogent. A central aspect of the language is its uniqueness type system, which eliminates the need for a trusted runtime or garbage collector while still guaranteeing memory safety, a crucial property for safety and security. Moreover, it allows us to assign two semantics to the language: The first semantics is imperative, suitable for efficient C code generation, and the second is purely functional, providing a user-friendly interface for equational reasoning and verification of higher-level correctness properties. The refinement theorem connecting the two semantics allows the compiler to produce a proof via translation validation certifying the correctness of the generated C code with respect to the semantics of the Cogent source program. We have demonstrated the effectiveness of our framework for implementation and for verification through two file system implementations

Interaction Tree Specifications: A Framework for Specifying Recursive, Effectful Computations That Supports Auto-Active Verification

This paper presents a specification framework for monadic, recursive, interactive programs that supports auto-active verification, an approach that combines user-provided guidance with automatic verification techniques. This verification tool is designed to have the flexibility of a manual approach to verification along with the usability benefits of automatic approaches. We accomplish this by augmenting Interaction Trees, a Coq datastructure for representing effectful computations, with logical quantifier events. We show that this yields a language of specifications that are easy to understand, automatable, and are powerful enough to handle properties that involve non-termination. Our framework is implemented as a library in Coq. We demonstrate the effectiveness of this framework by verifying real, low-level code