Deep Reinforcement Learning for Synthesizing Functions in Higher-Order Logic
This work addresses the challenge of automated theorem proving and function synthesis for formal verification, representing an incremental improvement with specific domain applications.
The paper tackles the problem of synthesizing functions in higher-order logic using a deep reinforcement learning framework integrated with the HOL4 proof assistant, achieving a 65% success rate on combinator synthesis problems and 78.5% on Diophantine equations.
The paper describes a deep reinforcement learning framework based on self-supervised learning within the proof assistant HOL4. A close interaction between the machine learning modules and the HOL4 library is achieved by the choice of tree neural networks (TNNs) as machine learning models and the internal use of HOL4 terms to represent tree structures of TNNs. Recursive improvement is possible when a task is expressed as a search problem. In this case, a Monte Carlo Tree Search (MCTS) algorithm guided by a TNN can be used to explore the search space and produce better examples for training the next TNN. As an illustration, term synthesis tasks on combinators and Diophantine equations are specified and learned. We achieve a success rate of 65% on combinator synthesis problems outperforming state-of-the-art ATPs run with their best general set of strategies. We set a precedent for statistically guided synthesis of Diophantine equations by solving 78.5% of the generated test problems.