Learning to prove theorems via interacting with proof assistants

Kaiyu Yang, Jia Deng

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Scopus citations

Abstract

Humans prove theorems by relying on substantial high-level reasoning and problem-specific insights. Proof assistants offer a formalism that resembles human mathematical reasoning, representing theorems in higher-order logic and proofs as high-level tactics. However, human experts have to construct proofs manually by entering tactics into the proof assistant. In this paper, we study the problem of using machine learning to automate the interaction with proof assistants. We construct CoqGym, a large-scale dataset and learning environment containing 71K human-written proofs from 123 projects developed with the Coq proof assistant. We develop ASTactic, a deep learning-based model that generates tactics as programs in the form of abstract syntax trees (ASTs). Experiments show that ASTactic trained on CoqGym can generate effective tactics and can be used to prove new theorems not previously provable by automated methods. Code is available at h t t p s: / / g i t h u b. com/ p r i n c e t o n - v l / C o q G y m.

Original languageEnglish (US)
Title of host publication36th International Conference on Machine Learning, ICML 2019
PublisherInternational Machine Learning Society (IMLS)
Pages12079-12094
Number of pages16
ISBN (Electronic)9781510886988
StatePublished - Jan 1 2019
Event36th International Conference on Machine Learning, ICML 2019 - Long Beach, United States
Duration: Jun 9 2019Jun 15 2019

Publication series

Name36th International Conference on Machine Learning, ICML 2019
Volume2019-June

Conference

Conference36th International Conference on Machine Learning, ICML 2019
CountryUnited States
CityLong Beach
Period6/9/196/15/19

All Science Journal Classification (ASJC) codes

  • Education
  • Computer Science Applications
  • Human-Computer Interaction

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  • Cite this

    Yang, K., & Deng, J. (2019). Learning to prove theorems via interacting with proof assistants. In 36th International Conference on Machine Learning, ICML 2019 (pp. 12079-12094). (36th International Conference on Machine Learning, ICML 2019; Vol. 2019-June). International Machine Learning Society (IMLS).