TY - GEN

T1 - Learning to prove theorems via interacting with proof assistants

AU - Yang, Kaiyu

AU - Deng, Jia

PY - 2019/1/1

Y1 - 2019/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85071947577&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85071947577&partnerID=8YFLogxK

M3 - Conference contribution

T3 - 36th International Conference on Machine Learning, ICML 2019

SP - 12079

EP - 12094

BT - 36th International Conference on Machine Learning, ICML 2019

PB - International Machine Learning Society (IMLS)

T2 - 36th International Conference on Machine Learning, ICML 2019

Y2 - 9 June 2019 through 15 June 2019

ER -