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Learning how to Prove: From the Coq Proof Assistant to Textbook Style
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System Description: Russell  A Logical Framework for Deductive Systems
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Learning to Prove Theorems via Interacting with Proof Assistants
Humans prove theorems by relying on substantial highlevel reasoning and problemspecific insights. Proof assistants offer a formalism that resembles human mathematical reasoning, representing theorems in higherorder logic and proofs as highlevel 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 largescale dataset and learning environment containing 71K humanwritten proofs from 123 projects developed with the Coq proof assistant. We develop ASTactic, a deep learningbased 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 https://github.com/princetonvl/CoqGym.
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