相关论文: Automated verification of termination certificates
We describe an embedding of the QWIRE quantum circuit language in the Coq proof assistant. This allows programmers to write quantum circuits using high-level abstractions and to prove properties of those circuits using Coq's theorem proving…
We introduce COREQQA, a tool for assisting requirements engineers in acquiring a better understanding of compliance requirements by means of automated Question Answering. Extracting compliance-related requirements by manually navigating…
We present three projects concerned with applications of proof assistants in the area of programming language theory and mathematics. The first project is about a certified compilation technique for a domain-specific programming language…
Largely adopted by proof assistants, the conventional induction methods based on explicit induction schemas are non-reductive and local, at schema level. On the other hand, the implicit induction methods used by automated theorem provers…
Software certification aims at proving the correctness of programs but in many cases, the use of external libraries allows only a conditional proof: it depends on the assumption that the libraries meet their specifications. In particular, a…
A compiler consists of a sequence of phases going from lexical analysis to code generation. Ideally, the formal verification of a compiler should include the formal verification of each component of the tool-chain. An example is the…
This article examines the use of the Prolog language for writing verification, analysis and transformation tools. Guided by experience in teaching and the development of verification tools like ProB or specialisation tools like ECCE and…
Formal reasoning and automated theorem proving constitute a challenging subfield of machine learning, in which machines are tasked with proving mathematical theorems using formal languages like Lean. A formal verification system can check…
This paper describes a formalization of discrete real closed fields in the Coq proof assistant. This abstract structure captures for instance the theory of real algebraic numbers, a decidable subset of real numbers with good algorithmic…
We consider temporal logic verification of (possibly nonlinear) dynamical systems evolving over continuous state spaces. Our approach combines automata-based verification and the use of so-called barrier certificates. Automata-based…
Chain-of-thought (CoT) prompting enables large language models (LLMs) to solve complex reasoning tasks by generating an explanation before the final prediction. Despite it's promising ability, a critical downside of CoT prompting is that…
This paper presents the deductive formal verification of high-level properties of control systems with theorem proving, using the Why3 tool. Properties that can be verified with this approach include stability, feedback gain, and…
Current approaches for formal verification of algorithms face important limitations. For specification, they cannot express algorithms naturally and concisely, especially for algorithms with states and flexible control flow. For…
We present crest, a tool for automatically proving (non-)confluence and termination of logically constrained rewrite systems. We compare crest to other tools for logically constrained rewriting. Extensive experiments demonstrate the promise…
We propose an automated method for proving termination of $\pi$-calculus processes, based on a reduction to termination of sequential programs: we translate a $\pi$-calculus process to a sequential program, so that the termination of the…
Interactive theorem provers such as Coq are powerful tools to formally guarantee the correctness of software. However, using these tools requires significant manual effort and expertise. While Large Language Models (LLMs) have shown promise…
One of the main issues in proof certification is that different theorem provers, even when designed for the same logic, tend to use different proof formalisms and produce outputs in different formats. The project ProofCert promotes the…
This article introduces Globular, an online proof assistant for the formalization and verification of proofs in higher-dimensional category theory. The tool produces graphical visualizations of higher-dimensional proofs, assists in their…
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…
We describe several views of the semantics of a simple programming language as formal documents in the calculus of inductive constructions that can be verified by the Coq proof system. Covered aspects are natural semantics, denotational…