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

5 Apr 2019  ·  Kshitij Bansal, Sarah M. Loos, Markus N. Rabe, Christian Szegedy, Stewart Wilcox ·

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.

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Introduced in the Paper:

Task Dataset Model Metric Name Metric Value Global Rank Result Benchmark
Automated Theorem Proving HOList benchmark Tactic Dependent Loop Percentage correct 38.88 # 2
Automated Theorem Proving HOList benchmark Deeper Wider WaveNet Percentage correct 32.65 # 4


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