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In this paper, we introduce a system called GamePad that can be used toexplore the application of machine learning methods to theorem proving in theCoq proof assistant. Interactive theorem provers such as Coq enable users toconstruct machine-checkable proofs in a step-by-step manner. Hence, theyprovide an opportunity to explore theorem proving with human supervision. Weuse GamePad to synthesize proofs for a simple algebraic rewrite problem andtrain baseline models for a formalization of the Feit-Thompson theorem. Weaddress position evaluation (i.e., predict the number of proof steps left) andtactic prediction (i.e., predict the next proof step) tasks, which arisenaturally in tactic-based theorem proving.

GamePad: A Learning Environment for Theorem Proving