Related papers: Towards Smart Proof Search for Isabelle
Metis is an ordered paramodulation prover built into the Isabelle/HOL proof assistant. It attempts to close the current goal using a given list of lemmas. Typically these lemmas are found by Sledgehammer, a tool that integrates external…
We introduce Prove-It, a Python-based general-purpose interactive theorem-proving assistant designed with the goal of making formal theorem proving as easy and natural as informal theorem proving (with moderate training). Prove-It uses a…
Debate has been widely adopted as a strategy to enhance critical thinking skills in English Language Arts (ELA). One important skill in debate is forming effective argumentation, which requires debaters to select supportive evidence from…
In this paper, we compare different existing approaches employed in data mining of big proof libraries in automated and interactive theorem proving.
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…
System assurance is confronted by significant challenges. Some of these are new, for example, autonomous systems with major functions driven by machine learning and AI, and ultra-rapid system development, while others are the familiar,…
The use of autonomous vehicles in real-world applications is often precluded by the difficulty of providing safety guarantees for their complex controllers. The simulation-based testing of these controllers cannot deliver sufficient safety…
With the growing popularity of Large Reasoning Models and their results in solving mathematical problems, it becomes crucial to measure their capabilities. We introduce a pipeline for both automatic and interactive verification as a more…
The Abella interactive theorem prover has proven to be an effective vehicle for reasoning about relational specifications. However, the system has a limitation that arises from the fact that it is based on a simply typed logic:…
We investigate how large language models can be used as research tools in scientific computing while preserving mathematical rigor. We propose a human-in-the-loop workflow for interactive theorem proving and discovery with LLMs. Human…
In this paper we report the experience of using AutoProof to statically verify a small object oriented program. We identified the problems that emerged by this activity and we classified them according to their nature. In particular, we…
Considerable progress has been made in the recent literature studies to tackle the Algorithms Selection and Parametrization (ASP) problem, which is diversified in multiple meta-learning setups. Yet there is a lack of surveys and comparative…
We present the Theorem Prover Museum, and initiative to conserve -- and make publicly available -- the sources and source-related artefacts of automated reasoning systems. Theorem provers have been at the forefront of Artificial…
The proof of the relative consistency of the axiom of choice has been mechanized using Isabelle/ZF. The proof builds upon a previous mechanization of the reflection theorem. The heavy reliance on metatheory in the original proof makes the…
How difficult are interactive theorem provers to use? We respond by reviewing the formalization of Hilbert's tenth problem in Isabelle/HOL carried out by an undergraduate research group at Jacobs University Bremen. We argue that, as…
This paper develops an algorithmic-based approach for proving inductive properties of propositional sequent systems such as admissibility, invertibility, cut-elimination, and identity expansion. Although undecidable in general, these…
There has been considerable growth and interest in industrial applications of machine learning (ML) in recent years. ML engineers, as a consequence, are in high demand across the industry, yet improving the efficiency of ML engineers…
An interactive theorem prover, Isabelle, is under development. In LCF, each inference rule is represented by one function for forwards proof and another (a tactic) for backwards proof. In Isabelle, each inference rule is represented by a…
We present StepFun-Prover Preview, a large language model designed for formal theorem proving through tool-integrated reasoning. Using a reinforcement learning pipeline that incorporates tool-based interactions, StepFun-Prover can achieve…
In the recent years, we have linked a large corpus of formal mathematics with automated theorem proving (ATP) tools, and started to develop combined AI/ATP systems working in this setting. In this paper we first relate this project to the…