LIPIcs.ITP.2024.27.pdf
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Teaching Mathematics Using Lean and Controlled Natural Language
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Patrick Massot 
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15th International Conference on Interactive Theorem Proving (ITP 2024)
Series: Leibniz International Proceedings in Informatics (LIPIcs)
Conference: International Conference on Interactive Theorem Proving (ITP) - License:
Creative Commons Attribution 4.0 International license
- Publication Date: 2024-09-02
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Acknowledgements
The library described here is the result of work spread over five years and benefited from many interactions. Marie-Anne Poursat made it possible by trusting me to teach using a proof assistant. Frédéric Bourgeois and Christine Paulin-Mohring later joined me in teaching this course and discussing how to make it more useful. Our students also participated with their patience, questions and enthusiasm. Very recently, Julien Narboux, Pierre Boutry and Evmorfia-Iro Bartzia started using this library with students and made valuable comments. Simon Hudon started my Lean meta-programming education. It was then continued by Mario Carneiro and Kyle Miller who both also directly contributed crucial code that I would have been incapable of writing. Wojciech Nawrocki helped me a lot with widgets, adding several features to his ProofWidgets library for the needs of this project. More generally many people from the Mathlib community contributed indirectly by formalizing basic mathematics and creating tactics that we built on. I also benefited from conversations about teaching using a proof assistant, particularly with Heather Macbeth, Jim Portegies and Jelle Wemmenhove. Most of the work on the Lean 4 version was made possible by Jeremy Avigad’s invitation to benefit from some of Charles Hoskinson’s generous donation to CMU. And of course none of this would exist without the amazing work of Leonardo de Moura and Sebastian Ullrich on Lean 4.
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Patrick Massot. Teaching Mathematics Using Lean and Controlled Natural Language. In 15th International Conference on Interactive Theorem Proving (ITP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 309, pp. 27:1-27:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.ITP.2024.27
Abstract
We present Verbose Lean, a library using the flexibility of the Lean programming language and proof assistant to teach undergrad mathematics students how to read and write traditional paper proofs. After explaining our main pedagogical goals, we explain how students use the library with varying levels of assistance to write proofs that are easy to transfer to paper because they look like natural language. We then describe how teachers can customize the student experience based on their specific pedagogical goals and constraints. Finally we describe some aspects of the implementation of the library, emphasizing how new aspects of the very recently released version 4 of Lean allow a lot of flexibility that could benefit many new creative uses of a proof assistant.
Subject Classification
ACM Subject Classification
- Human-centered computing → Natural language interfaces
- Applied computing → Interactive learning environments
- Theory of computation → Logic and verification
Keywords
- mathematics teaching
- proof assistant
- controlled natural language
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References
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