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


Kshitij Bansal, Sarah Loos, Markus Rabe, Christian Szegedy, Stewart Wilcox ;
Proceedings of the 36th International Conference on Machine Learning, PMLR 97:454-463, 2019.


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 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 approaches. We also present a deep reinforcement learning driven automated theorem prover, DeepHOL, that gives strong initial results on this benchmark.

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