Related papers: Reconstructing veriT Proofs in Isabelle/HOL

SMT solvers have been used successfully as reasoning engines for automated verification and other applications based on automated reasoning. Current techniques for dealing with quantified formulas in SMT are generally incomplete, forcing…

We describe a method for building composable and extensible verification procedures within the Coq proof assistant. Unlike traditional methods that rely on run-time generation and checking of proofs, we use verified-correct procedures with…

Language models (LMs) can solve tasks such as answering questions about tables or images by writing programs. However, using primitive functions often leads to verbose and error-prone programs, and higher-level functions require expert…

Formal verification of cyber-physical and robotic systems requires that we can accurately model physical quantities that exist in the real-world. The use of explicit units in such quantities can allow a higher degree of rigour, since we can…

Mathematical theorem proving is an important testbed for large language models' deep and abstract reasoning capability. This paper focuses on improving LLMs' ability to write proofs in formal languages that permit automated proof…

The present dissertation introduces the research project on HOLMS (\textbf{HOL} Light Library for \textbf{M}odal \textbf{S}ystems), a growing modular framework for modal reasoning within the HOL Light proof assistant. To provide an…

Automated theorem proving is essential for the formal verification of safety-critical systems. As the corpus of formal proofs grows, a natural paradigm is to learn from existing proofs. However, current learning-based approaches…

Real-world fact verification task aims to verify the factuality of a claim by retrieving evidence from the source document. The quality of the retrieved evidence plays an important role in claim verification. Ideally, the retrieved evidence…

Training language models to solve complex mathematical problems benefits from curriculum learning progressively training on simpler subproblems. However, existing decomposition methods are often heuristic, offering no guarantees that…

Aiming to offer a framework for blended learning to the teaching of proof theory, the present paper describes an interactive tutorial, called \textsc{TryLogic}, teaching how to solve logical conjectures either by proofs or refutations. The…

Computer-supported learning is an increasingly important form of study since it allows for independent learning and individualized instruction. In this paper, we discuss a novel approach to developing an intelligent tutoring system for…

This work discusses an approach to teach to mathematicians the importance and effectiveness of the application of Interactive Theorem Proving tools in their specific fields of interest. The approach aims to motivate the use of such tools…

The first iteration of the proof format used by the SMT solver veriT was presented ten years ago at the first PxTP workshop. Since then the format has matured. veriT proofs are used within multiple applications, and other solvers generate…

Proof assistants offer tactics to apply proof by induction, but these tactics rely on inputs given by human engineers. To automate this laborious process, we developed SeLFiE, a boolean query language to represent experienced users'…

We present an SMT-based symbolic model checking algorithm for safety verification of recursive programs. The algorithm is modular and analyzes procedures individually. Unlike other SMT-based approaches, it maintains both "over-" and…

For recursive functions general principles of induction needs to be applied. Instead of verifying them directly using the Vienna Development Method Specification Language (VDM-SL), we suggest a translation to Isabelle/HOL. In this paper,…

We present SilVer (Silq Verification), an automated tool for verifying behaviors of quantum programs written in Silq, which is a high-level programming language for quantum computing. The goal of the verification is to ensure correctness of…

Our objective is to formally verify the correctness of the hundreds of expression optimization rules used within the GraalVM compiler. When defining the semantics of a programming language, expressions naturally form abstract syntax trees,…

We introduce Meta-F*, a tactics and metaprogramming framework for the F* program verifier. The main novelty of Meta-F* is allowing the use of tactics and metaprogramming to discharge assertions not solvable by SMT, or to just simplify them…

LLMs can solve complex tasks by generating long, multi-step reasoning chains. Test-time scaling (TTS) can further improve performance by sampling multiple variants of intermediate reasoning steps, verifying their correctness, and selecting…