HOList: An Environment for Machine Learning of Higher-Order Theorem Proving
This work addresses the problem of automating complex mathematical reasoning for researchers in AI and formal verification, representing an incremental step by applying existing deep learning methods to a new domain.
The authors tackled the challenge of automated theorem proving in higher-order logic by introducing HOList, an environment and benchmark based on HOL Light, and DeepHOL, a deep reinforcement learning prover that achieved strong initial results on this benchmark.
We present an environment, benchmark, and deep learning driven automated theorem prover for higher-order logic. Higher-order interactive theorem provers enable the formalization of arbitrary mathematical theories and thereby present an interesting, open-ended challenge for deep learning. We provide an open-source framework based on the HOL Light theorem prover that can be used as a reinforcement learning environment. HOL Light comes with a broad coverage of basic mathematical theorems on calculus and the formal proof of the Kepler conjecture, from which we derive a challenging benchmark for automated reasoning. We also present a deep reinforcement learning driven automated theorem prover, DeepHOL, with strong initial results on this benchmark.