GamePad: A learning environment for theorem proving
OpenAI has introduced GamePad, a system designed to explore the application of machine learning to theorem proving using the Coq proof assistant. By leveraging the step-by-step nature of interactive theorem provers, GamePad enables the exploration of formal proofs under human supervision.
Integration with the Coq Proof Assistant
GamePad utilizes Coq, an interactive theorem prover that allows users to construct machine-checkable proofs incrementally. This structured environment transforms theorem proving into a sequence of steps, creating a viable framework for applying machine learning models to automate the discovery and verification of mathematical proofs.
Core Technical Tasks
GamePad focuses on two primary machine learning tasks inherent to tactic-based theorem proving:
- Tactic Prediction: The system predicts the next proof step (tactic) required to advance the proof.
- Position Evaluation: The system predicts the number of proof steps remaining to reach the conclusion.
Application and Validation
To demonstrate the utility of the environment, OpenAI applied GamePad to two specific mathematical contexts:
- Algebraic Rewrite Problems: The system was used to synthesize proofs for simple algebraic rewrite problems.
- Feit-Thompson Theorem: The system was used to train baseline models based on a formalization of the Feit-Thompson theorem.
Implications for Automated Reasoning
By providing a standardized learning environment for Coq, GamePad facilitates the development of models that can assist mathematicians and computer scientists in formalizing complex theorems. The ability to predict both the optimal next step and the distance to a solution allows for more efficient search and synthesis of formal proofs.