Interactive Theorem Proving

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Overview

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.

Latest papers

CardsList

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

  1. Theorem prover Arend

    Oct 19, 2026Fedor Part, Valery Isaev, Sergey SinchukInteractive Theorem Proving

    JetBrains Research

  2. Mathematical Proof Assistants for Teaching Logic: The LogiKEy Methodology

    Oct 6, 2026Christoph Benzmüller, David Fuenmayor, Luca PasettoLogical ReasoningInteractive Theorem Proving

    Otto-Friedrich-Universität Bamberg, Germany · Freie Universität Berlin, Germany · University of Luxembourg, Luxembourg

  3. Growing an Agent/Prover Interface: Evolutionary Tool Design for Cost-Efficient Theorem Proving in Rocq and Lean

    Sep 30, 2026Jules Viennot, Guillaume Baudart, Marc LelargeAutomated Theorem ProvingEvolutionary Optimization

    IRIF, Universit´e Paris Cit´e, Inria, CNRS · DI ENS, PSL University, Inria

  4. Choir: An Open Protocol for Distributed Multi-Agent Autoformalization

    Sep 25, 2026Yidi Qi, Melanie WeberMulti-Agent CollaborationLLM Agent Orchestration

    Harvard University

  5. Lean Pool: An AI-Maintained Archive of Formalized Mathematics

    Sep 21, 2026Vasily IlinAI Coding AgentsInteractive Theorem Proving

    University of Washington

  6. Autoformalizing Argumentative Material Inferences

    Sep 15, 2026Xin Quan, Reto Gubelmann, André FreitasLogical ReasoningInteractive Theorem Proving

    1Idiap Research Institute, Switzerland · University of Zurich, Switzerland · Department of Computer Science, University of Manchester, UK

  7. Monadic Second-Order Logic in HOL: Deep and Shallow with Automated Faithfulness (Extended Preprint)

    Sep 7, 2026Christoph Benzmueller, Daniel KirchnerInteractive Theorem Proving

    University of Bamberg, Bamberg, Germany · Freie Universität Berlin, Berlin, Germany

  8. Scratchy: Visual-Scratchpad Multimodal Reasoning for Cryptographic Proof Generation in EasyCrypt

    Sep 5, 2026Yupeng Ren, Zhaoxuan Li, Rui ZhangInteractive Theorem ProvingMultimodal Large Language Models

    State Key Laboratory of Cyberspace Security Defense, Institute of Information Engineering, Chinese Academy of Sciences, Beijing 100085, China · School of Cyber Security, University of Chinese Academy of Sciences, Beijing 100049, China

  9. CAPRI: Contract-Aware Proof Repair for Isabelle

    Aug 13, 2026Jim Woodcock, Gabriel Leite, Augusto Sampaio +1LLM AuditingInteractive Theorem Proving

    Southwest University, China · Aarhus University, Denmark · University of York, UK +2

  10. Can Open-Weight LLMs Produce Kernel-Verified Coq Proofs? A Pilot Study

    Aug 5, 2026Ahmed Ryan, Md Erfan, Akond Ashfaque Ur Rahman +1LLM EvaluationAutomated Theorem Proving

    University of Alabama, Tuscaloosa, Alabama, USA · Auburn University, Auburn, Alabama, USA

  11. BlueprintRepair: Typed Local Edits for Failed Lean Proof Blueprints

    Jul 30, 2026Ruslan KhrulevAutomated Theorem ProvingInteractive Theorem Proving

    Lomonosov Moscow State University

  12. Encoding Event-B Proof Rules in Prolog: An Interactive Sequent Prover for ProB

    Jul 23, 2026Katharina Engels, Jan Gruteser, Michael LeuschelAutomated Theorem ProvingInteractive Theorem Proving

    Heinrich Heine University Düsseldorf · Faculty of Mathematics and Natural Science, Institute of Computer Science, Heinrich Heine University Düsseldorf, Universitätsstr. 1, D-40225 Düsseldorf

  13. AoA: Theorem Proving Agent over Abstract Syntax Tree of Redesigned Language

    Jul 17, 2026Qiyuan Xu, Joshua Ong Jun Leang, Renxi Wang +4Large Language Model-Guided Theorem ProvingAutomated Theorem Proving

    Nanyang Technological University · Singapore · Imperial College London +5

  14. MathCoPilot: An Interactive System for Human-AI Symbiotic Paradigm of Mathematical Research

    Jul 16, 2026Junjie Zhang, Jiayu Liu, Wenbin Liu +11Multi-Agent LLM SystemsAutomated Theorem Proving

    1State Key Laboratory of Cognitive Intelligence, University of Science and Technology of China · School of Mathematical Sciences, University of Science and Technology of China

  15. TreeThink: A Modular Tree Search Library for Mathematical Reasoning with LLMs

    Jul 13, 2026Burak S. Akbudak, Zeynel A. Uluşan, Can S. Erer +1Automated Theorem ProvingTree Search

    Computer Engineering Department, Bogazici University, Istanbul, Turkey · Computer Engineering Department, Koç University, Istanbul, Turkey · Codeway Studios, Istanbul, Turkey +2

  16. First-Order Modal Logic in HOL: Deep and Shallow Embeddings with Automated Faithfulness (Extended Preprint)

    Jul 12, 2026Christoph Benzmüller, Daniel KirchnerAutomated Theorem ProvingInteractive Theorem Proving

    University of Bamberg, Bamberg, Germany · Freie Universität Berlin, Berlin, Germany

  17. OpenProver: Agentic and Interactive Theorem Proving with Lean 4

    Jul 10, 2026Matěj Kripner, Milan StrakaMulti-Agent LLM SystemsAutomated Theorem Proving

    Charles University, Faculty of Mathematics and Physics, Prague, Czech Republic

  18. From Solvers to Research: Large Language Model-Driven Formal Mathematics at the Research Frontier

    Jul 8, 2026Eric Jiang, Xiao Liang, Yingjia Wan +17Automated Theorem ProvingInteractive Theorem Proving

    University of California, Los Angeles · Lawrence Livermore National Laboratory

  19. Reformalization of the Jordan Curve Theorem

    Jul 2, 2026Simon Guilloud, Sankalp Gambhir, Samuel ChassotInteractive Theorem ProvingAutoformalization

    Ecole Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland.

  20. AXLE: A Cloud Infrastructure for Lean 4 Theorem Proving Utilities

    Jun 24, 2026Jimmy Xin, Alex Schneidman, Chris Cummins +3Interactive Theorem ProvingFormal Verification

    Axiom Math · Thinking Machines Lab · Recursive Superintelligence, Inc.

  21. Abduction Prover in Isabelle/HOL

    Jun 3, 2026Yutaka Nagashima, Daniel Sebastian GocAutomated Theorem ProvingAbductive Reasoning

    Institute of Computer Science, the Czech Academy of Sciences, Czechia

  22. Proof-Refactor: Refactoring Generated Formal Proofs into Modular Artifacts

    Jun 2, 2026Yiming Fu, Peixuan Liu, Zichen Wang +1Interactive Theorem ProvingLean Theorem Proving

    Department of Mathematics Southern University of Science and Technology · School of Mathematical Sciences Peking University · Center for Machine Learning Research Peking University

  23. LEAP: Supercharging LLMs for Formal Mathematics with Agentic Frameworks

    Jun 2, 2026Po-Nien Kung, Linfeng Song, Dawsen Hwang +10Mathematical Reasoning BenchmarksLarge Language Model-Guided Theorem Proving

    Google Cloud AI Research · Google Cloud · Google DeepMind

  24. Many Logics, One Methodology: A Plea for Logical Pluralism in Formalised Reasoning (preprint)

    May 26, 2026Christoph Benzmüller, Daniel Kirchner, Luca PasettoLogical ReasoningInteractive Theorem Proving

    Otto-Friedrich-Universität Bamberg, Kapuzinerstraße 16, 96047 Bamberg, Germany · Freie Universität Berlin, Kaiserswerther Str. 16-18, 14195 Berlin, Germany · University of Luxembourg, P. de l’Université 2, 4365 Esch-sur-Alzette, Luxembourg

  25. Keep the Proof State Live: Snapshotting for Efficient Tactic Search in Lean 4

    May 25, 2026Austin Shen, Yunong ShiInference-Time SearchAutomated Theorem Proving

    University of Michigan · Amazon Web Services

  26. Just Type It in Isabelle! AI Agents Drafting, Mechanizing, and Generalizing from Human Hints

    Apr 17, 2026Kevin Kappelmann, Maximilian Schäffeler, Lukas Stevens +3Interactive Theorem ProvingAutoformalization

    Department of Computer Science, University of Sheffield, United Kingdom · Department of Informatics, King’s College London, United Kingdom · Department of Computer Science, University of Copenhagen, Denmark

  27. Munkres' General Topology Autoformalized in Isabelle/HOL

    Apr 8, 2026Dustin Bryant, Jonathan Julián Huerta y Munive, Cezary Kaliszyk +1AutoformalizationInteractive Theorem Proving

    Independent · Aalborg University · University of Melbourne +1

  28. Explorable Proofs: Making Written Proofs Explorable by Grounding Them in Formal Representations

    Apr 3, 2026Hita Kambhamettu, Will Crichton, Sean Welleck +2LLM GroundingInteractive Theorem Proving

    University of Pennsylvania Philadelphia, PA, USA · Brown University Providence, RI, USA · Carnegie Mellon University Pittsburgh, PA, USA +1

  29. WybeCoder: Verified Imperative Code Generation

    Mar 31, 2026Fabian Gloeckle, Mantas Baksys, Darius Feher +5Verified Code GenerationFormal Verification

    FAIR, Meta · CERMICS, ENPC, Institut Polytechnique de Paris, CNRS · Computer Lab, University of Cambridge +3

  30. Putnam 2025 Problems in Rocq using Opus 4.6 and Rocq-MCP

    Mar 20, 2026Guillaume Baudart, Marc Lelarge, Tristan Stérin +1Large Language Model-Guided Theorem ProvingAutomated Theorem Proving

    IRIF, Université Paris Cité, Inria, CNRS · DI ENS, PSL University, Inria · PRGM DEV