arXiv subjects

Jan Tušil

Publications and source records attributed to Jan Tušil.

3 recordsLinked to original sources

arXiv2024

Minuska: Towards a Formally Verified Programming Language Framework

Programming language frameworks allow us to generate language tools (e.g., interpreters) just from a formal description of the syntax and semantics of a programming language. As these frameworks tend to be quite complex, an issue arises whether we can trust the generated tools. To address this issue, we introduce a practical formal programming language framework called Minuska, which always generates a provably correct interpreter given a valid language definition. This is achieved by (1) defining a language MinusLang for expressing programming language definitions and giving it formal semantics and (2) using the Coq proof assistant to implement an interpreter parametric in a MinusLang definition and to prove it correct. Minuska provides strong correctness guarantees and can support nontrivial languages while performing well. This is the extended version of the SEFM24 paper of the same name.

cs.PL↗

arXiv2023

Validating Labelled State Transition and Message Production Systems: A Theory for Modelling Faulty Distributed Systems

Modeling and formally reasoning about distributed systems with faults is a challenging task. To address this problem, we propose the theory of Validating Labeled State transition and Message production systems (VLSMs). The theory of VLSMs provides a general approach to describing and verifying properties of distributed protocols whose executions are subject to faults, supporting a correct-by-construction system development methodology. The central focus of our investigation is equivocation, a mode of faulty behavior that we formally model, reason about, and then show how to detect from durable evidence that may be available locally to system components. Equivocating components exhibit behavior that is inconsistent with single-trace system executions, while also only interacting with other components by sending and receiving valid messages. Components of system are called validators for that system if their validity constraints validate that the messages they receive are producible by the system. Our main result shows that for systems of validators, the effect that Byzantine components can have on honest validators is precisely identical to the effect that equivocating components can have on non-equivocating validators. Therefore, for distributed systems of potentially faulty validators, replacing Byzantine components with equivocating components has no material analytical consequences, and forms the basis of a sound alternative foundation to Byzantine fault tolerance analysis. All of the results and examples in the paper have been formalised and checked in the Coq proof assistant.

cs.DC↗

arXiv2022

Mechanizing Matching Logic In Coq

Matching logic is a formalism for specifying, and reasoning about, mathematical structures, using patterns and pattern matching. Growing in popularity, it has been used to define many logical systems such as separation logic with recursive definitions and linear temporal logic. In addition, it serves as the logical foundation of the K semantic framework, which was used to build practical verifiers for a number of real-world languages. Despite being a fundamental formal system accommodating substantial theories, matching logic lacks a general-purpose, machine-checked formalization. Hence, we formalize matching logic using the Coq proof assistant. Specifically, we create a new representation of matching logic that uses a locally nameless encoding, and we formalize the syntax, semantics, and proof system of this representation in the Coq proof assistant. Crucially, we prove the soundness of the formalized proof system and provide a means to carry out interactive matching logic reasoning in Coq. We believe this work provides a previously unexplored avenue for reasoning about matching logic, its models, and the proof system.

cs.LO↗