A Verified Packrat Parser Interpreter for Parsing Expression Grammars

Parsing expression grammars (PEGs) offer a natural opportunity for building verified parser interpreters based on higher-order parsing combinators. PEGs are expressive, unambiguous, and efficient to parse in a top-down recursive descent style. We use the rich type system of the PVS specification language and verification system to formalize the metatheory of PEGs and define a reference implementation of a recursive parser interpreter for PEGs. In order to ensure termination of parsing, we define a notion of a well-formed grammar. Rather than relying on an inductive definition of parsing, we use abstract syntax trees that represent the computational trace of the parser to provide an effective proof certificate for correct parsing and ensure that parsing properties including soundness and completeness are maintained. The correctness properties are embedded in the types of the operations so that the proofs can be easily constructed from local proof obligations. Building on the reference parser interpreter, we define a packrat parser interpreter as well as an extension that is capable of semantic interpretation. Both these parser interpreters are proved equivalent to the reference one. All of the parsers are executable. The proofs are formalized in mathematical terms so that similar parser interpreters can be defined in any specification language with a type system similar to PVS.Comment: 15 pages, 15 figures, Certified Proofs and Program

Towards A Practical High-Assurance Systems Programming Language

Writing correct and performant low-level systems code is a notoriously demanding job, even for experienced developers. To make the matter worse, formally reasoning about their correctness properties introduces yet another level of complexity to the task. It requires considerable expertise in both systems programming and formal verification. The development can be extremely costly due to the sheer complexity of the systems and the nuances in them, if not assisted with appropriate tools that provide abstraction and automation. Cogent is designed to alleviate the burden on developers when writing and verifying systems code. It is a high-level functional language with a certifying compiler, which automatically proves the correctness of the compiled code and also provides a purely functional abstraction of the low-level program to the developer. Equational reasoning techniques can then be used to prove functional correctness properties of the program on top of this abstract semantics, which is notably less laborious than directly verifying the C code. To make Cogent a more approachable and effective tool for developing real-world systems, we further strengthen the framework by extending the core language and its ecosystem. Specifically, we enrich the language to allow users to control the memory representation of algebraic data types, while retaining the automatic proof with a data layout refinement calculus. We repurpose existing tools in a novel way and develop an intuitive foreign function interface, which provides users a seamless experience when using Cogent in conjunction with native C. We augment the Cogent ecosystem with a property-based testing framework, which helps developers better understand the impact formal verification has on their programs and enables a progressive approach to producing high-assurance systems. Finally we explore refinement type systems, which we plan to incorporate into Cogent for more expressiveness and better integration of systems programmers with the verification process

Runners in action

Runners of algebraic effects, also known as comodels, provide a mathematical model of resource management. We show that they also give rise to a programming concept that models top-level external resources, as well as allows programmers to modularly define their own intermediate "virtual machines". We capture the core ideas of programming with runners in an equational calculus $\lambda_{\mathsf{coop}}$, which we equip with a sound and coherent denotational semantics that guarantees the linear use of resources and execution of finalisation code. We accompany $\lambda_{\mathsf{coop}}$ with examples of runners in action, provide a prototype language implementation in OCaml, as well as a Haskell library based on $\lambda_{\mathsf{coop}}$.Comment: ESOP 2020 final version + online appendi

Programming Languages and Systems

This open access book constitutes the proceedings of the 31st European Symposium on Programming, ESOP 2022, which was held during April 5-7, 2022, in Munich, Germany, as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2022. The 21 regular papers presented in this volume were carefully reviewed and selected from 64 submissions. They deal with fundamental issues in the specification, design, analysis, and implementation of programming languages and systems

Programming Languages and Systems

This open access book constitutes the proceedings of the 31st European Symposium on Programming, ESOP 2022, which was held during April 5-7, 2022, in Munich, Germany, as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2022. The 21 regular papers presented in this volume were carefully reviewed and selected from 64 submissions. They deal with fundamental issues in the specification, design, analysis, and implementation of programming languages and systems

Programming Languages and Systems

This open access book constitutes the proceedings of the 29th European Symposium on Programming, ESOP 2020, which was planned to take place in Dublin, Ireland, in April 2020, as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2020. The actual ETAPS 2020 meeting was postponed due to the Corona pandemic. The papers deal with fundamental issues in the specification, design, analysis, and implementation of programming languages and systems

Integration of the Process Algebra CSP in Dependent Type Theory - Formalisation and Verification

We introduce a library called CSP-Agda for representing processes in the dependently typed theorem prover and interactive programming language Agda. We will enhance processes by a monad structure. The monad struc-ture facilitates combining processes in a modular way, and allows to define recursion as a direct operation on processes. Processes are defined coinduc-tively as non-well-founded trees. The nodes of the tree are formed by a an atomic one step relation, which determines for a process the external, internal choices, and termination events it can choose, and whether the process has terminated. The data type of processes is inspired by Setzer and Hancock’s notion of interactive programs in dependent type theory. The operators of CSP will be defined rather than atomic operations, and compute new ele-ments of the data type of processes from existing ones.The approach will make use of advanced type theoretic features: the use of inductive-recursively defined universes; the definition of coinductive types by their observations, which has similarities to the notion of an object in object-oriented programming; the use of sized types for coinductive types, which allow coinductive definitions in a modular way; the handling of fini-tary information (names of processes) in a coinductive settings; the use of named types for automatic inference of arguments similar to its use in tem-plate Meta-programming in C++; and the use of interactive programs in dependent type theory.We introduce a simulator as an interactive program in Agda. The simula-tor allows to observe the evolving of processes following external or internal choices. Our aim is to use this in order to simulate railway interlocking system and write programs in Agda which directly use CSP processes.Then we extend the trace semantics of CSP to the monadic setting. We implement this semantics, together with the corresponding refinement and equality relation, formally in CSP-Agda. In order to demonstrate the proof capabilities of CSP-Agda, we prove in CSP-Agda selected algebraic laws of CSP based on the trace semantics. Because of the monadic settings, some adjustments need to be made to these laws.Next we implement the more advanced semantics of CSP, the stable fail-ures semantics and the failures divergences infinite traces semantics (FDI), in CSP-Agda, and define the corresponding refinement and equality relations. Direct proofs in these semantics are cumbersome, and we develop a tech-nique of showing algebraic laws in those semantics in an indirect way, which is much easier. We introduce divergence-respecting weak bisimilarity and strong bisimilarity in CSP-Agda, and show that both imply equivalence with respect to stable failures and FDI semantics. Now we show certain algebraic laws with respect to one of these two bisimilarity relations. As a case study, we model and verify a possible scenario for railways in CSP-Agda and in standard CSP tools