TacticToe: Learning to Prove with Tactics

TL;DR

TacticToe is an automated tactic-based prover built on HOL4 that learns from human proofs and uses Monte Carlo tree search to efficiently prove theorems, significantly outperforming traditional automated provers.

Contribution

It introduces a machine learning approach combined with Monte Carlo tree search for tactic selection in theorem proving, enhancing proof automation in HOL4.

Findings

TacticToe proves 66.4% of theorems in 60 seconds.

E prover with auto-schedule proves 34.5%.

Combined approach proves 69.0%.

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.