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HOList: An Environment for Machine Learning of Higher Order Logic Theorem Proving

Kshitij Bansal
Sarah Loos
Markus Rabe
Christian Szegedy
Stewart James Wilcox
Thirty-sixth International Conference on Machine Learning (ICML) (2019) (to appear)


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.