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… 
Learned Provability Likelihood for Tactical Search
  • Thibault Gauthier
  • Computer Science
    Electronic Proceedings in Theoretical Computer Science
  • 2021
TLDR
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
  • Hanwei Qian
  • Computer Science, Mathematics
    Advances in Artificial Intelligence and Security
  • 2021
TLDR
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
TLDR
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
TLDR
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
TLDR
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
TLDR
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
TLDR
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
TLDR
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
TLDR
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
TLDR
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.
...
1
2
...

References

SHOWING 1-10 OF 51 REFERENCES
TacticToe: Learning to Reason with HOL4 Tactics
TLDR
A unified proof assistant automation approach which attempts to automate the selection of appropriate tactics and tactic-sequences with an optimized small-scale hammering approach, implemented as a tactic-level automation for HOL4: TacticToe.
Refactoring Proofs with Tactician
TLDR
An overview of Tactician's core capabilities is given and insight into how it is implemented is provided to help novices and experienced users maintain their proofs.
A Learning-Based Fact Selector for Isabelle/HOL
TLDR
This work introduces MaSh, an alternative that learns from successful proofs, and outperforms the old fact selector on large formalizations.
The Use of Explicit Plans to Guide Inductive Proofs
  • A. Bundy
  • Computer Science, Mathematics
    CADE
  • 1988
We propose the use of explicit proof plans to guide the search for a proof in automatic theorem proving. By representing proof plans as the specifications of LCF-like tactics, [Gordon et al 79], and
MaLeCoP Machine Learning Connection Prover
TLDR
Probabilistic guidance based on learned knowledge is added to the connection tableau calculus and implemented on top of the lean-CoP theorem prover, linking it to an external advisor system, bringing interesting possibilities for further construction and training of self-learning AI mathematical experts on large mathematical libraries.
Internal Guidance for Satallax
TLDR
An efficient scheme for Naive Bayesian classification by generalising label occurrences to types with monoid structure is presented, which makes it possible to extend existing fast classifiers, which consider only positive examples, with negative ones.
Learning-Assisted Automated Reasoning with Flyspeck
TLDR
It is shown that 39 % of the 14185 theorems could be proved in a push-button mode (without any high-level advice and user interaction) in 30 seconds of real time on a fourteen-CPU workstation.
FEMaLeCoP: Fairly Efficient Machine Learning Connection Prover
TLDR
FEMaLeCoP is the first AI/ATP system convincingly demonstrating that guiding the internal inference algorithms of theorem provers by knowledge learned from previous proofs can significantly improve the performance of the provers.
MaLARea: a Metasystem for Automated Reasoning in Large Theories
TLDR
A simple metasystem iteratively combining deductive Automated Reasoning tools (now the E and the SPASS ATP systems) with a machine learning component, intended use is in large theories, i.e. on a large number of problems which in a consistent fashion use many axioms, lemmas, theorems, definitions and symbols.
Hammering towards QED
This paper surveys the emerging methods to automate reasoning over large libraries developed with formal proof assistants. We call these methods hammers. They give the authors of formal proofs a
...
1
2
3
4
5
...