Interactive Theorem Proving

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Interactive theorem proving develops proofs inside systems such as Lean, Isabelle, Coq/Rocq, Agda, and EasyCrypt, where a small trusted kernel checks each result. Common approaches include tactic search, SMT and automated theorem prover integration, and language-model agents that formalize problems, propose proof steps, and revise them using proof-state or compiler feedback. Benchmarks such as miniF2F, Putnam problems, and software-verification suites test these methods, while textbook formalizations and interactive tools also support mathematical understanding and teaching. Automation is becoming more capable, but reliable performance on unfamiliar, multi-step problems remains difficult, and proof acceptance alone does not guarantee faithful assumptions, authorized edits, or usable proof structure.

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34 papers3 papers in the last four weeks, down 40% on the four weeks before. 0.0% of all new papers.

Neuro-Symbolic Proof Generation for Scaling Systems Software Verification
Mar 20, 2026Baoding He, Zenan Li, Wei Sun +4Large Language Model-Guided Theorem Proving Automated Theorem Proving
State Key Laboratory of Novel Software Technology, Nanjing University, China · School of Computer Science, Nanjing University, China · Department of Computer Science, ETH Zurich, Switzerland +1
Agent Hunt: Bounty Based Collaborative Autoformalization With LLM Agents
Mar 6, 2026Chad E. Brown, Cezary Kaliszyk, Josef UrbanAutoformalization Multi-Agent Collaboration
AI4REASON · University of Melbourne · AI4REASON, University of Gothenburg and Chalmers University of Technology
Pipeline for Verifying LLM-Generated Mathematical Solutions
Feb 24, 2026Varvara Sazonova, Dmitri Shmelkin, Stanislav Kikot +1LLM Answer Verification LLM Evaluation
Moscow State University · Huawei Technologies Co., Ltd
When Agda met Vampire
Feb 21, 2026Artjoms Šinkarovs, Michael RawsonInteractive Theorem Proving Automated Theorem Proving
Electronics and Computer Science, University of Southampton, UK

Mar 20, 2026J/K move · Enter open · S save

Neuro-Symbolic Proof Generation for Scaling Systems Software Verification

Baoding He, Zenan Li, Wei Sun, Yuan Yao+3

State Key Laboratory of Novel Software Technology, Nanjing University, China · School of Computer Science, Nanjing University, China · Department of Computer Science, ETH Zurich, Switzerland+1

Large Language Model-Guided Theorem Proving Automated Theorem Proving Formal Verification Interactive Theorem Proving Neuro-Symbolic Reasoning

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Formal verification via interactive theorem proving is increasingly used to ensure the correctness of critical systems, yet constructing large proof scripts remains highly manual and limits scalability. Advances in large language models (LLMs), especially in mathematical reasoning, make their integration into software verification increasingly promising. This paper introduces a neuro-symbolic proof generation framework designed to automate proof search for system-level verification projects. The framework performs a best-first tree search over proof states, repeatedly querying an LLM for the next candidate proof step. On the neural side, we fine-tune LLMs using datasets of proof state-step pairs; on the symbolic side, we incorporate a range of ITP tools to repair rejected steps, filter and rank proof states, and automatically discharge subgoals when search progress stalls. This synergy enables data-efficient LLM adaptation and semantics-informed pruning of the search space. We implement the framework on a new Isabelle REPL that exposes fine-grained proof states and automation tools, and evaluate it on the FVEL seL4 benchmark and additional Isabelle developments. On seL4, the system proves up to 77.6% of the theorems, substantially surpassing previous LLM-based approaches and standalone Sledgehammer, while solving significantly more multi-step proofs. Results across further Isabelle benchmarks demonstrate strong generalization, indicating a viable path toward scalable automated software verification.

Latest papers

Neuro-Symbolic Proof Generation for Scaling Systems Software Verification

Agent Hunt: Bounty Based Collaborative Autoformalization With LLM Agents

Pipeline for Verifying LLM-Generated Mathematical Solutions

When Agda met Vampire