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arXiv:1804.00596cs.AI

TacticToe: Learning to Prove with Tactics

Thibault Gauthier, Cezary Kaliszyk, Josef Urban, Ramana Kumar, Michael Norrish

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Abstract

We implement a automated tactical prover TacticToe on top of the HOL4 interactive theorem prover. TacticToe learns from human proofs which mathematical technique is suitable in each proof situation. This knowledge is then used in a Monte Carlo tree search algorithm to explore promising tactic-level proof paths. On a single CPU, with a time limit of 60 seconds, TacticToe proves 66.4 percent of the 7164 theorems in HOL4's standard library, whereas E prover with auto-schedule solves 34.5 percent. The success rate rises to 69.0 percent by combining the results of TacticToe and E prover.

arXiv comments
Journal reference
J. Automated Reasoning 65(2): 257-286, 2021
DOI
doi:10.1007/s10817-020-09580-x
Subjects
cs.AIArtificial Intelligence cs.LOLogic in Computer Science

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  1. Lean4 helped Terence Tao discover a small bug in his recent paper 1 comment

    • Sounds like you've stumbled into the wonderful world of machine-learning guided proof synthesis! While I don't think the full system you're describing has been built yet, many similar systems and pieces have. In terms of the initial phase of supervised learning on existing…

      aSanchezSternView on HNParent context

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