Compositional Verification of a Lock-Free Stack with RGITL

Expressive state-of-the-art separation logics rely on step-indexing to model semantically complex features and to support modular reasoning about imperative higher-order concurrent and distributed programs. Stepindexing comes, however, with an inherent cost: it restricts the adequacy theorem of program logics to a fairly simple class of safety properties. In this paper, we explore if and how intensional refinement is a viable methodology for strengthening higher-order concurrent (and distributed) separation logic to prove non-trivial safety and liveness properties. Specifically, we introduce Trillium, a language-agnostic separation logic framework for showing intensional refinement relations between traces of a program and a model. We instantiate Trillium with a concurrent language and develop Fairis, a concurrent separation logic, that we use to show liveness properties of concurrent programs under fair scheduling assumptions through a fair liveness-preserving refinement of a model. We also instantiate Trillium with a distributed language and obtain an extension of Aneris, a distributed separation logic, which we use to show refinement relations between distributed systems and TLA + models.

Formal verification is an effective method to address the challenge of designing correct and efficient concurrent data structures. But verification efforts often ignore memory reclamation , which involves nontrivial synchronization between concurrent accesses and reclamation. When incorrectly implemented, it may lead to critical safety errors such as use-after-free and the ABA problem. Semi-automatic safe memory reclamation schemes such as hazard pointers and RCU encapsulate the complexity of manual memory management in modular interfaces. However, this modularity has not been carried over to formal verification. We propose modular specifications of hazard pointers and RCU, and formally verify realistic implementations of them in concurrent separation logic. Specifically, we design abstract predicates for hazard pointers that capture the meaning of validating the protection of nodes, and those for RCU that support optimistic traversal to possibly retired nodes. We demonstrate that the specifications indeed facilitate modular verification in three criteria: compositional verification, general applicability, and easy integration. In doing so, we present the first formal verification of Harris’s list, the Harris-Michael list, the Chase-Lev deque, and RDCSS with reclamation. We report the Coq mechanization of all our results in the Iris separation logic framework.

This paper presents CELL, a comprehensive and extensible framework for compositional verification of concurrent and real-time systems based on commonly used semantic models. For each semantic model, CELL offers three libraries, i.e., compositional verification paradigms, learning algorithms and model checking methods to support various state-of-the-art compositional verification approaches. With well-defined APIs, the framework could be applied to build customized model checkers. In addition, each library could be used independently for verification and program analysis purposes. We have built three model checkers with CELL. The experimental results show that the performance of these model checkers can offer similar or often better performance compared to the state-of-the-art verification tools.

<p>This thesis explores two kinds of program logics that have become important for modern program verification - separation logic, for reasoning about programs that use pointers to build mutable data structures, and rely guarantee reasoning, for reasoning about shared variable concurrent programs. We look more closely into the motivations for merging these two kinds of logics into a single formalism that exploits the benefits of both approaches - local, modular, and explicit reasoning about interference between threads in a shared memory concurrent program. We discuss in detail two such formalisms - RGSep and Local Rely Guarantee (LRG), in particular we analyse how each formalism models program state and treats the distinction between global state (shared by all threads) and local state (private to a given thread) and how each logic models actions performed by threads on shared state, and look into the proof rules specifically for reasoning about atomic blocks of code. We present full examples of proofs in each logic and discuss their differences. This thesis also illustrates how a weakest precondition semantics for separation logic can be used to carry out calculational proofs. We also note how in essence these proofs are data abstraction proofs showing that a data structure implements some abstract data type, and relate this idea to a classic data abstraction technique by Hoare. Finally, as part of the thesis we also present a survey of tools that are currently available for doing manual or semi-automated proofs as well as program analyses with separation logic and rely guarantee.</p>

<p>This thesis explores two kinds of program logics that have become important for modern program verification - separation logic, for reasoning about programs that use pointers to build mutable data structures, and rely guarantee reasoning, for reasoning about shared variable concurrent programs. We look more closely into the motivations for merging these two kinds of logics into a single formalism that exploits the benefits of both approaches - local, modular, and explicit reasoning about interference between threads in a shared memory concurrent program. We discuss in detail two such formalisms - RGSep and Local Rely Guarantee (LRG), in particular we analyse how each formalism models program state and treats the distinction between global state (shared by all threads) and local state (private to a given thread) and how each logic models actions performed by threads on shared state, and look into the proof rules specifically for reasoning about atomic blocks of code. We present full examples of proofs in each logic and discuss their differences. This thesis also illustrates how a weakest precondition semantics for separation logic can be used to carry out calculational proofs. We also note how in essence these proofs are data abstraction proofs showing that a data structure implements some abstract data type, and relate this idea to a classic data abstraction technique by Hoare. Finally, as part of the thesis we also present a survey of tools that are currently available for doing manual or semi-automated proofs as well as program analyses with separation logic and rely guarantee.</p>

In this paper we detail our effort to formalize and prove requirements for the Quad-redundant Flight Control System (QFCS) within NASA’s Transport Class Model (TCM). We use a compositional approach with assume-guarantee contracts that correspond to the requirements for software components embedded in an AADL system architecture model. This approach is designed to exploit the verification effort and artifacts that are already part of typical software verification processes in the avionics domain. Our approach is supported by an AADL annex that allows specification of contracts along with a tool, called AGREE, for performing compositional verification. The goal of this paper is to show the benefits of a compositional verification approach applied to a realistic avionics system and to demonstrate the effectiveness of the AGREE tool in performing this analysis.

We present a comprehensive set of tactics that make it practical to use separation logic in a proof assistant. These tactics enable the verification of partial correctness properties of complex pointer-intensive programs. Our goal is to make separation logic as easy to use as the standard logic of a proof assistant. We have developed tactics for the simplification, rearranging, splitting, matching and rewriting of separation logic assertions as well as the discharging of a program verification condition using a separation logic description of the machine state. We have implemented our tactics in the Coq proof assistant, applying them to a deep embedding of Cminor, a C-like intermediate language used by Leroy's verified CompCert compiler. We have used our tactics to verify the safety and completeness of a Cheney copying garbage collector written in Cminor. Our ideas should be applicable to other substructural logics and imperative languages.

United Nations have declared the current decade (2021-2030) as the ”UN Decade on Ecosystem Restoration” to join R&D forces to fight against the ongoing environmental crisis. Given the ongoing degradation of earth ecosystems and the related crucial services that they offer to the human society, ecosystem restoration has become a major society-critical issue. It is required to develop rigorously software applications managing ecosystem restoration. Reliable models of ecosystems and restoration goals are necessary. This paper proposes a rigorous approach for ecosystem requirements modeling using formal methods from a model-driven software engineering point of view. The authors describe the main concepts at stake with a metamodel in UML and introduce a formalization of this metamodel in Alloy. The formal model is executed with Alloy Analyzer, and safety and liveness properties are checked against it. This approach helps ensuring that ecosystem specifications are reliable and that the specified ecosystem meetsthe desired restoration goals, seen in our approach as liveness and safety properties. The concepts and activities of the approach are illustrated with CRESTO, a real-world running example of a restored Costa Rican ecosystem

Many concurrent systems are required to maintain certain safety and liveness properties. One emerging method of achieving confidence in such systems is to statically verify them using model checking. In this approach an abstract, finite-state model of the system is constructed; then an automatic check is made to ensure that the requirements are satisfied by the model. In practice, however, this method is limited by the state space explosion problem. We have developed a compositional method that directly addresses this problem in the context of multi-tasking programs. Our solution depends on three key space-saving ingredients: (1) checking for counter-examples, which leads to simpler search algorithms; (2) automatic extraction of interfaces, which allows a refinement of the finite model --- even before its communicating partners have been compiled; and (3) using propositional "strengthening assertions" for the sole purpose of reducing state space.In this paper we present our compositional approach, and describe the software tools that support it.

Many concurrent systems are required to maintain certain safety and liveness properties. One emerging method of achieving confidence in such systems is to statically verify them using model checking. In this approach an abstract, finite-state model of the system is constructed; then an automatic check is made to ensure that the requirements are satisfied by the model. In practice, however, this method is limited by the state space explosion problem.We have developed a compositional method that directly addresses this problem in the context of multi-tasking programs. Our solution depends on three key space-saving ingredients: (1) checking for counter-examples, which leads to simpler search algorithms; (2) automatic extraction of interfaces, which allows a refinement of the finite model --- even before its communicating partners have been compiled; and (3) using propositional "strengthening assertions" for the sole purpose of reducing state space.In this paper we present our compositional approach, and describe the software tools that support it.

Over the past two decades, there has been a great deal of progress on verification of full functional correctness of programs using separation logic, sometimes even producing “foundational” proofs in proof assistants like Coq. Unfortunately, even though existing approaches to this problem provide significant support for automated verification, they still incur a significant specification overhead : the user must supply the specification against which the program is verified, and the specification may be long, complex, or tedious to formulate. In this paper, we introduce Quiver, the first technique for inferring functional correctness specifications in separation logic while simultaneously verifying foundationally that they are correct. To guide Quiver towards the final specification, we take hints from the user in the form of a specification sketch , and then complete the sketch using inference. To do so, Quiver introduces a new abductive deductive verification technique, which integrates ideas from abductive inference (for specification inference) together with deductive separation logic automation (for foundational verification). The result is that users have to provide some guidance, but significantly less than with traditional deductive verification techniques based on separation logic. We have evaluated Quiver on a range of case studies, including code from popular open-source libraries.

A compositional Petri net based semantics is given to a simple pointer-manipulating language. The model is then applied to give a notion of validity to the judgements made by concurrent separation logic that emphasizes the process-environment duality inherent in such rely-guarantee reasoning. Soundness of the rules of concurrent separation logic with respect to this definition of validity is shown. The independence information retained by the Petri net model is then exploited to characterize the independence of parallel processes enforced by the logic. This is shown to permit a refinement operation capable of changing the granularity of atomic actions

Multiple successful compositional symbolic execution (CSE) tools and platforms exploit separation logic (SL) for compositional verification and/or incorrectness separation logic (ISL) for compositional bug-finding, including VeriFast, Viper, Gillian, CN, and Infer-Pulse. Previous work on the Gillian platform, the only CSE platform that is parametric on the memory model, meaning that it can be instantiated to different memory models, suggests that the ability to use custom memory models allows for more flexibility in supporting analysis of a wide range of programming languages, for implementing custom automation, and for improving performance. However, the literature lacks a satisfactory formal foundation for memory-model-parametric CSE platforms. In this paper, inspired by Gillian, we provide a new formal foundation for memory-model-parametric CSE platforms. Our foundation advances the state of the art in four ways. First, we mechanise our foundation (in the interactive theorem prover Rocq). Second, we validate our foundation by instantiating it to a broad range of memory models, including models for C and CHERI. Third, whereas previous memory-model-parametric work has only covered SL analyses, we cover both SL and ISL analyses. Fourth, our foundation is based on standard definitions of SL and ISL (including definitions of function specification validity, to ensure sound interoperation with other tools and platforms also based on standard definitions).

A number of tools have been developed for carrying out separation-logic proofs mechanically using an interactive proof assistant. One of the most advanced such tools is the Iris Proof Mode (IPM) for Coq, which offers a rich set of tactics for making separation-logic proofs look and feel like ordinary Coq proofs. However, IPM is tied to a particular separation logic (namely, Iris), thus limiting its applicability.In this paper, we propose MoSeL, a general and extensible Coq framework that brings the benefits of IPM to a much larger class of separation logics. Unlike IPM, MoSeL is applicable to both affine and linear separation logics (and combinations thereof), and provides generic tactics that can be easily extended to account for the bespoke connectives of the logics with which it is instantiated. To demonstrate the effectiveness of MoSeL, we have instantiated it to provide effective tactical support for interactive and semi-automated proofs in six very different separation logics.

Separation logic (SL) has recently evolved at an exciting pace, opening the way to more complex goals, notably soundness proof of Rust's ownership type system and functional verification of Rust programs. In this paper, we address verification of termination in the presence of advanced features, especially Rust's ownership types. Perhaps surprisingly, this goal cannot be achieved by a simple application of existing studies that dealt only with safety properties. For high-level reasoning about advanced shared mutable state as used in Rust, they used higher-order ghost state (i.e., logical state that depends on SL assertions), but in a way that depends on the later modality, a fundamental obstacle to verifying termination. To solve this situation, we propose a novel general framework, Nola, which achieves later-free higher-order ghost state. Even in the presence of advanced features such as invariants and borrows, Nola enables natural termination verification, allowing arbitrary induction in the meta-logic. Its key idea is to parameterize higher-order ghost state, generalizing and subsuming the existing approach. Nola is fully mechanized in Rocq as a library of Iris. Moreover, to demonstrate the power of Nola, we develop a prototype of RustHalt, the first semantic and mechanized foundation for total correctness verification of Rust programs.