# TacticToe: Learning to Prove with Tactics

@article{Gauthier2020TacticToeLT, title={TacticToe: Learning to Prove with Tactics}, author={Thibault Gauthier and C. Kaliszyk and Josef Urban and Ramana Kumar and Michael Norrish}, journal={Journal of Automated Reasoning}, year={2020}, volume={65}, pages={257-286} }

We implement an 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 s, TacticToe proves 66.4% of the 7164 theorems in HOL4’s standard library, whereas E prover with auto-schedule solves 34.5%. The success rate…

## 18 Citations

Learned Provability Likelihood for Tactical Search

- Computer ScienceElectronic Proceedings in Theoretical Computer Science
- 2021

A method to estimate the provability of a mathematical formula is presented and the tactical theorem prover TacticToe is adapted to factor in these estimations, leading to an improvement in performance and an improved user experience.

Research on Automation Strategy of Coq

- Computer Science, MathematicsAdvances in Artificial Intelligence and Security
- 2021

The use of machine learning and concurrent search methods are proposed to improve the degree of automation of theorem proofs, which can help theorem assistants find suitable proof strategies faster and reduce the workload of constructing proofs.

Lassie: HOL4 tactics by example

- Computer ScienceCPP
- 2021

Lassie is presented, a tactic framework for the HOL4 theorem prover that allows individual users to define their own tactic language by example and give frequently used tactics or tactic combinations easier-to-remember names.

The Isabelle ENIGMA

- Computer ScienceArXiv
- 2022

The authors' best single-strategy ENIGMA and premise selection system improves the best previous version of E by 25.3% in 15 seconds, outperforming also all other previous ATP and SMT systems.

Faster Smarter Proof by Induction in Isabelle/HOL

- Computer ScienceIJCAI
- 2021

Evaluation of sem ind, a recommendation tool for proof by induction in Isabelle/HOL, shows that it improves the accuracy of recommendation and increases the median value of execution time for the most promising candidates within 5.0 seconds of timeout.

ING WITH LANGUAGE MODELS

- Computer Science
- 2021

This work proposes PACT (Proof Artifact Co-Training), a general methodology for extracting abundant self-supervised data from kernel-level proof terms for joint training alongside the usual tactic prediction objective and applies this methodology to Lean, a proof assistant host to some of the most sophisticated formalized mathematics to date.

SCRATCH WITH DEEP REINFORCEMENT LEARNING

- Computer Science
- 2021

A novel approach to interactive theorem-proving (ITP) using deep reinforcement learning that is able to prove theorems both end-to-end and from scratch (i.e., without relying on example proofs from human experts).

The Role of Entropy in Guiding a Connection Prover

- Computer ScienceTABLEAUX
- 2021

This work starts by incorporating a state-of-the-art learning algorithm – a graph neural network (GNN) – into the plCoP theorem prover, and shows that a proper entropy regularization, i.e., training the GNN not to be overconfident, greatly improves pl coP’s performance on a large mathematical corpus.

Learning Equational Theorem Proving

- Computer ScienceArXiv
- 2021

Stratified Shortest Solution Imitation Learning (3SIL) is developed to learn equational theorem proving in a deep reinforcement learning (RL) setting and is shown to significantly outperform several established RL and imitation learning methods.

The design of mathematical language

- Computer Science
- 2021

This chapter begins to map out the design features of mathematical language without descending to the level of formal implementation, drawing on examples from the mathematical literature and insights from the design of computational proof assistants.

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