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Large Language Models (LLMs) present an intriguing avenue for exploration in the field of formal theorem proving.
Learning to reason in large theories without imitation
Kshitij Bansal, Christian Szegedy, Markus N Rabe, Sarah M Loos, and Viktor Toman · 1905
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Lawrence C Paulson · 1994
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The Coq proof assistant reference manual: Version 6.1
Bruno Barras, Samuel Boutin, Cristina Cornes, Judicaël Courant, Jean-Christophe Filliatre, Eduardo Gimenez, Hugo Herbelin, Gerard Huet, Cesar Munoz, Chetan Murthy, et al · 1997
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Formal proof sketches. types for proofs and programs, proceedings of types 2003. lncs 3085, 2003
F Wiedijk · 2003
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Formal proof–getting started
Freek Wiedijk · 2008
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Imagenet: A large-scale hierarchical image database
Jia Deng, Wei Dong, Richard Socher, Li-Jia Li, Kai Li, and Li Fei-Fei · 2009
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Three years of experience with sledgehammer, a practical link between automatic and interactive theorem provers
Lawrence C. Paulson · 2010
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Sequence to sequence learning with neural networks
Ilya Sutskever, Oriol Vinyals, and Quoc V Le · 2014
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The lean theorem prover (system description)
Leonardo de Moura, Soonho Kong, Jeremy Avigad, Floris Van Doorn, and Jakob von Raumer · 2015
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On calibration of modern neural networks
Chuan Guo, Geoff Pleiss, Yu Sun, and Kilian Q Weinberger · 2017
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A general reinforcement learning algorithm that masters chess, shogi, and go through self-play
David Silver, Thomas Hubert, Julian Schrittwieser, Ioannis Antonoglou, Matthew Lai, Arthur Guez, Marc Lanctot, Laurent Sifre, Dharshan Kumaran, Thore Graepel, et al · 2018
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Deep learning for symbolic mathematics
Guillaume Lample and François Charton · 2019
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A computer language for mathematical proofs
Norman Megill and David A Wheeler · 2019
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Learning to prove theorems via interacting with proof assistants
Kaiyu Yang and Jia Deng · 2019
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Language models are few-shot learners
Tom Brown, Benjamin Mann, Nick Ryder, Melanie Subbiah, Jared D Kaplan, Prafulla Dhariwal, Arvind Neelakantan, Pranav Shyam, Girish Sastry, Amanda Askell, et al · 2020
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How can we know what language models know?
Zhengbao Jiang, Frank F Xu, Jun Araki, and Graham Neubig · 2020
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Generative language modeling for automated theorem proving
Stanislas Polu and Ilya Sutskever · 2020
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A promising path towards autoformalization and general artificial intelligence
Christian Szegedy · 2020
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Exploration of neural machine translation in autoformalization of mathematics in mizar
Qingxiang Wang, Chad Brown, Cezary Kaliszyk, and Josef Urban · 2020
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Int: An inequality benchmark for evaluating generalization in theorem proving
Yuhuai Wu, Albert Qiaochu Jiang, Jimmy Ba, and Roger Grosse · 2020
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Evaluating large language models trained on code
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Tactictoe: learning to prove with tactics
Thibault Gauthier, Cezary Kaliszyk, Josef Urban, Ramana Kumar, and Michael Norrish · 2021
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Naturalprover: Grounded mathematical proof generation with language models
Sean Welleck, Jiacheng Liu, Ximing Lu, Hannaneh Hajishirzi, and Yejin Choi · 2022
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Autoformalization with large language models
Yuhuai Wu, Albert Qiaochu Jiang, Wenda Li, Markus Rabe, Charles Staats, Mateja Jamnik, and Christian Szegedy · 2022
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Proofnet: Autoformalizing and formally proving undergraduate-level mathematics
Zhangir Azerbayev, Bartosz Piotrowski, Hailey Schoelkopf, Edward W Ayers, Dragomir Radev, and Jeremy Avigad · 2023
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Sébastien Bubeck, Varun Chandrasekaran, Ronen Eldan, Johannes Gehrke, Eric Horvitz, Ece Kamar, Peter Lee, Yin Tat Lee, Yuanzhi Li, Scott Lundberg, Harsha Nori, Hamid Palangi, Marco Tulio Ribeiro, and Yi Zhang · 2023
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Proof artifact co-training for theorem proving with language models
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A neural network solves, explains, and generates university math problems by program synthesis and few-shot learning at human level
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