### 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 language | English (US) |
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Title of host publication | 36th International Conference on Machine Learning, ICML 2019 |

Publisher | International Machine Learning Society (IMLS) |

Pages | 12079-12094 |

Number of pages | 16 |

ISBN (Electronic) | 9781510886988 |

State | Published - Jan 1 2019 |

Event | 36th International Conference on Machine Learning, ICML 2019 - Long Beach, United States Duration: Jun 9 2019 → Jun 15 2019 |

### Publication series

Name | 36th International Conference on Machine Learning, ICML 2019 |
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Volume | 2019-June |

### Conference

Conference | 36th International Conference on Machine Learning, ICML 2019 |
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Country | United States |

City | Long Beach |

Period | 6/9/19 → 6/15/19 |

### All Science Journal Classification (ASJC) codes

- Education
- Computer Science Applications
- Human-Computer Interaction

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## Cite this

*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).