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Learning to Reason with HOL4 tactics [article]

Thibault Gauthier, Cezary Kaliszyk, Josef Urban
2018 arXiv   pre-print
Techniques combining machine learning with translation to automated reasoning have recently become an important component of formal proof assistants.  ...  It implements a modified A*-algorithm directly in HOL4 that explores different tactic-level proof paths, guiding their selection by learning from a large number of previous tactic-level proofs.  ...  As external automated reasoning techniques often outperform the combined power of the tactics, we would like to combine the TacticToe search with HOL(y)Hammer for HOL4 [9] .  ... 
arXiv:1804.00595v1 fatcat:p6oehxklwfdalokzeez3v6prga

Learning to Prove with Tactics [article]

Thibault Gauthier, Cezary Kaliszyk, Josef Urban, Ramana Kumar, Michael Norrish
2018 arXiv   pre-print
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.  ...  Acknowledgments We would like to thank Lasse Blaauwbroek and Yutaka Nagashima for their insightful comments which contributed to improve the quality of this paper.  ... 
arXiv:1804.00596v1 fatcat:twmo2yoiwrfaxmj2onudf6sw7a

Premise Selection and External Provers for HOL4

Thibault Gauthier, Cezary Kaliszyk
2015 Proceedings of the 2015 Conference on Certified Programs and Proofs - CPP '15  
In this paper, we present an add-on to the HOL4 proof assistant and an adaptation of the HOLyHammer system that provides machine learning-based premise selection and automated reasoning also for HOL4.  ...  Learning-assisted automated reasoning has recently gained popularity among the users of Isabelle/HOL, HOL Light, and Mizar.  ...  Acknowledgments We would like to thank Josef Urban and Michael Färber for their comments on the previous version of this paper. This work has been supported by the Austrian Science Fund (FWF): P26201.  ... 
doi:10.1145/2676724.2693173 dblp:conf/cpp/GauthierK15 fatcat:p5jxweitsvbvndliq465gsinra

Deep Reinforcement Learning for Synthesizing Functions in Higher-Order Logic [article]

Thibault Gauthier
2020 arXiv   pre-print
A close interaction between the machine learning modules and the HOL4 library is achieved by the choice of tree neural networks (TNNs) as machine learning models and the internal use of HOL4 terms to represent  ...  The paper describes a deep reinforcement learning framework based on self-supervised learning within the proof assistant HOL4.  ...  To solve this issue, the tactical prover TacticToe [16, 17] , also implemented in HOL4, learns to apply tactics extracted from existing proof scripts.  ... 
arXiv:1910.11797v3 fatcat:bqtdfbrcxrcc5p6e3tzygogxsy

Tactic Learning and Proving for the Coq Proof Assistant [article]

Lasse Blaauwbroek, Josef Urban, Herman Geuvers
2020 arXiv   pre-print
To do this, it learns from previous tactic scripts and how they are applied to proof states. The performance of the system is evaluated on the Coq Standard Library.  ...  In a similar vein as the TacticToe project for HOL4, our system predicts appropriate tactics and finds proofs in the form of tactic scripts.  ...  For this reason, a proof search must be performed, where not only the first predicted tactic is chosen.  ... 
arXiv:2003.09140v1 fatcat:vozpbh5w4fgrboqnrkju7odxza

GRUNGE: A Grand Unified ATP Challenge [article]

Chad E. Brown, Thibault Gauthier, Cezary Kaliszyk, Geoff Sutcliffe, Josef Urban
2019 arXiv   pre-print
The formalisms are in higher-order logic (with and without type variables) and first-order logic (possibly with multiple types, and possibly with type variables).  ...  This paper describes a large set of related theorem proving problems obtained by translating theorems from the HOL4 standard library into multiple logical formalisms.  ...  TacticToe is a machine-learning guided prover that searches for a tactical proof by selecting suitable tactics and theorems learned from humanwritten tactical proofs.  ... 
arXiv:1903.02539v1 fatcat:w2py2275rzc4rh5s3v45fff5vi

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

Kshitij Bansal, Sarah M. Loos, Markus N. Rabe, Christian Szegedy, and Stewart Wilcox
2019 arXiv   pre-print
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.  ...  Acknowledgements We would like to thank Alex Alemi, Geoffrey Irving, Cezary Kaliszyk, Thibault Gauthier, Ramana Kumar, Viktor Toman, and Josef Urban for their insightful comments and contributions to early  ... 
arXiv:1904.03241v3 fatcat:ih4fizuonrbvzk2oyu4pekhftu

TacticZero: Learning to Prove Theorems from Scratch with Deep Reinforcement Learning [article]

Minchao Wu, Michael Norrish, Christian Walder, Amir Dezfouli
2021 arXiv   pre-print
The proposed framework is able to learn proof search strategies as well as tactic and arguments prediction in an end-to-end manner.  ...  We propose a novel approach to interactive theorem-proving (ITP) using deep reinforcement learning.  ...  Our agent learns proof search strategies in a similar manner by learning to choose promising derivations and subgoals to attack, as well as the tactics and their arguments to apply to the goals, without  ... 
arXiv:2102.09756v2 fatcat:hyz573txjjauje2ucfpm2ufw54

Automatic Derivation of Platform Noninterference Properties [chapter]

Oliver Schwarz, Mads Dam
2016 Lecture Notes in Computer Science  
The analysis is represented in HOL4 using a direct semantical embedding of noninterference, and does not use an explicit type system, in order to (i) minimize the trusted computing base, and to (ii) support  ...  Thus, they can be used to guarantee that user processes cannot infer the state of privileged system components, such as secure partitions.  ...  Thanks to Anthony C. J. Fox, Roberto Guanciale, Nicolae Paladi, and the anonymous reviewers for their helpful comments.  ... 
doi:10.1007/978-3-319-41591-8_3 fatcat:c2m6q5xl3rhbvpsjkilo4dmjqm

Selected Extended Papers of ITP 2017

Mauricio Ayala-Rincón, César Muñoz
2018 Journal of automated reasoning  
The reviewers guaranteed both significant additional contributions with respect to the LNCS proceedings and assured the quality standards of the Journal of Automated Reasoning, for which the guest editors  ...  The ITP conference series is concerned with all topics related to interactive theorem proving, ranging from theoretical foundations to implementation aspects and applications in program verification, security  ...  The auto2 prover is packaged as a tactic in Isabelle. The proposed framework allows the entire development chain to be formalized in Isabelle/FOL with a high automation level.  ... 
doi:10.1007/s10817-018-09500-0 fatcat:no6wykx3jrdphd2kalkgqnocqi

Learning to Reason in Large Theories without Imitation [article]

Kshitij Bansal, Christian Szegedy, Markus N. Rabe, Sarah M. Loos, Viktor Toman
2020 arXiv   pre-print
This helps with exploring and learning which premises are relevant for proving a new theorem.  ...  In this paper, we demonstrate how to do automated theorem proving in the presence of a large knowledge base of potential premises without learning from human proofs.  ...  However, any open-ended system for mathematical reasoning needs to be able to learn which premises are relevant without human guidance.  ... 
arXiv:1905.10501v3 fatcat:ft65xynsgbfdxkzlcy4omg7ov4

Formalization of real analysis: a survey of proof assistants and libraries

2015 Mathematical Structures in Computer Science  
We have chosen to look into the formalizations provided in standard by the following systems: Coq, HOL4, HOL Light, Isabelle/HOL, Mizar, ProofPower-HOL, and PVS.  ...  They, however, have different purposes and it is not always easy to choose which one is adapted to undertake a formalization effort.  ...  We are also grateful to the anonymous reviewers for their constructive remarks.  ... 
doi:10.1017/s0960129514000437 fatcat:qjnpetpbcbb4rbvm26geem3jai

A Formalization of the Process Algebra CCS in HOL4 [article]

Chun Tian
2017 arXiv   pre-print
An old formalization of the Process Algebra CCS (no value passing, with explicit relabeling operator) on has been ported from HOL88 theorem prover to HOL4 (Kananaskis-11 and later).  ...  We have used HOL4's new co-inductive relation support to re-define strong and weak bisimulation equivalances, and shows that the new definitions are equivalent with old ones.  ...  The author saved these code and continued learning HOL4. Finally, starting from Jan 2017, the author was able to read proof scripts written in HOL4 and prove some new theorems in it.  ... 
arXiv:1705.07313v2 fatcat:atvk2h3jfbghtpqcldme3ahkiy

The Tactician [chapter]

Lasse Blaauwbroek, Josef Urban, Herman Geuvers
2020 Lecture Notes in Computer Science  
To this end, Tactician learns from previously written tactic scripts and gives users either suggestions about the next tactic to be executed or altogether takes over the burden of proof synthesis.  ...  Tactician's goal is to provide users with a seamless, interactive, and intuitive experience together with robust and adaptive proof automation.  ...  This work was supported by the European Regional Development Fund under the project AI&Reasoning (reg. no. CZ.02.1.01/0.0/0.0/15 003/0000466) and by the AI4REASON ERC Consolidator grant nr. 649043.  ... 
doi:10.1007/978-3-030-53518-6_17 fatcat:u7o7b4ne2zghdctir6cp6zs2lm

Proof Learning in PVS with Utility Pattern Mining

M. Saqib Nawaz, Philippe Fournier-Viger, Ji Zhang
2020 IEEE Access  
Experimental results suggest that combining frequent pattern mining techniques, such as sequential pattern mining and high utility itemset mining, with proof assistants, such as PVS, is useful to learn  ...  HUIM techniques are then applied on the corpus to discover frequent proof steps/high utility patterns and their relationships with each other.  ...  The SPMF software has been used in more than 800 articles, since 2010, for many applications from chemistry, smartphone usage analysis restaurant recommendation, to malware detection. He is the  ... 
doi:10.1109/access.2020.3004199 fatcat:l5lly5fmrjbwdi2jurwfogci6y
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