Reinforcement learning to improve proof-automation in theorem proving

Developing generic proof automation methods for interactive theorem provers (ITPs) is challenging but valuable.

Applications range from performance improvements in the verification of safety-critical systems to the certification of famous, long, and hard-to-prove theorems.

We propose using recently successful reinforcement learning (RL) algorithms to learn proof strategies employed in vast ITP libraries and use them as generic methods to automate the ITP proving process.

Specifically, the project aims to create a tactic for one of the most popular and automated ITPs, Isabelle/HOL, and train the RL algorithms with theorems from the two largest Isabelle libraries: HOL-Library and the Archive of Formal Proofs (AFP).

We identify three gaps in the state of the art that such an RL-and-Isabelle approach would close and describe the work packages that will achieve the corresponding three research objectives.

The project will be done under the guidance of Dr Josef Urban, who holds a Distinguished Researcher position at the Czech Institute of Informatics, Robotics and Cybernetics (CIIRC) within the Czech Technical University (CTU) in Prague. Dr Urban and the CIIRC group are experts in integrating machine learning (ML) and interactive theorem proving.

Their infrastructure and expertise targeted to ML and ITPs provide the best research environment for this project.

Jonathan Julián Huerta y Munive, the researcher carrying out the project, complements this expertise with his Isabelle/HOL experience and knowledge of ITP applications.