gym-saturation: Gymnasium environments for saturation provers (System description)

TL;DR

This paper introduces gym-saturation, a Python package with OpenAI Gym environments for saturation provers, enabling reinforcement learning integration with theorem proving tools like Vampire and iProver.

Contribution

It provides a flexible framework for applying reinforcement learning to saturation provers, including environment wrappers and proof state representations.

Findings

Successfully integrated reinforcement learning algorithms with provers.

Demonstrated transformation of provers into bandit-like problems.

Provided practical examples with Vampire and iProver.

Abstract

This work describes a new version of a previously published Python package - gym-saturation: a collection of OpenAI Gym environments for guiding saturation-style provers based on the given clause algorithm with reinforcement learning. We contribute usage examples with two different provers: Vampire and iProver. We also have decoupled the proof state representation from reinforcement learning per se and provided examples of using a known ast2vec Python code embedding model as a first-order logic representation. In addition, we demonstrate how environment wrappers can transform a prover into a problem similar to a multi-armed bandit. We applied two reinforcement learning algorithms (Thompson sampling and Proximal policy optimisation) implemented in Ray RLlib to show the ease of experimentation with the new release of our package.