research-article

Proof searching in HOL4 with genetic algorithm

Authors:

M. Zohaib Nawaz,

M. Saqib Nawaz,

Philippe Fournier-Viger, and

Meng SunAuthors Info & Claims

SAC '20: Proceedings of the 35th Annual ACM Symposium on Applied Computing

March 2020

Pages 513 - 520

https://doi.org/10.1145/3341105.3373917

Published: 30 March 2020 Publication History

Abstract

Proof searching and proof automation are the two most desired properties in interactive theorem provers (ITPs) as they generally require manual user guidance, which can be quite cumbersome. In this paper, we provide an evolutionary proof searching approach for the HOL4 proof assistant, where a genetic algorithm (GA) with different crossover and mutation operators is used to search and optimize the proofs in different HOL theories. Random proof sequences are first generated from a population of frequently occurring HOL4 proof steps that are discovered with sequential pattern mining. Generated proof sequences are then evolved with GA operators (three crossover and two mutation) till their fitness match the fitness of the target proof sequences. Various crossover and mutation operators are used to compare their effect on the performance of GAs in proof searching. Obtained results suggest that integrating GAs with HOL4 allows us to efficiently support proof finding and optimization.

References

[1]

Y. Bertot and P. Casteran. 2003. Interactive theorem proving and program development: Coq'Art: The calculus of inductive construction. Springer.

[2]

H. Duncan. 2007. The use of data-mining for the automatic formation of tactics. Ph.D. Dissertation. University of Edinburgh, UK.

[3]

M. Färber and C. E. Brown. 2016. Internal guidance for Satallax. In Proceedings of IJCAR, 2016 (LNCS), Vol. 9706. Springer, 349--361.

[4]

P. Fournier-Viger, J. C. W. Lin, R. U. Kiran, Y. S. Koh, and R. Thomas. 2017. A survey of sequential pattern mining. Data Science and Pattern Recognition 1(1) (2017), 54--77.

[5]

GA implementation. [n.d.]. Available at: github.com/muhammadzohaibnawaz/GAHOL4.

[6]

T. Gauthier, C. Kaliszyk, and J. Urban. 2017. TacticToe: Learning to reason with HOL4 tactics. In Proceedings of LPAR, 2017 (EPiC Series in Computing), Vol. 46. 125--143.

[7]

O. Hasan and S. Tahar. 2015. Formal verification methods. In Encyclopedia of Information Science & Technology, 3rd edition. IGI Global, 7162--7170.

[8]

J. H. Holland. 1975. Adaptation in natural and artificial systems. University of Michigan Press, Ann Arbor, MI, USA.

Digital Library

[9]

S. Y. Huang and Y. P. Chen. 2017. Proving theorems by using evolutionary search with human involvement. In Proceedings of CEC, 2017. IEEE, 1495--1502.

[10]

G. Irving, C. Szegedy, A. A. Alemi, N. Eén, F. Chollet, and J. Urban. 2016. DeepMath - Deep sequence models for premise selection. In Proceedings of NIPS, 2016. ACM, 2235--2243.

[11]

C. Kaliszyk, F. Chollet, and C. Szegedy. 2017. HolStep: A machine learning dataset for Higher-Order Logic theorem proving. CoRR abs/1703.00426 (2017).

[12]

C. Kaliszyk, L. Mamane, and J. Urban. 2014. Machine Learning of Coq Proof Guidance: First Experiments. In Proceedings of SCSS, 2014 (EPiC Series in Computing), Vol. 30. 27--34.

[13]

J. R. Koza. 1993. Genetic programming - On the programming of computers by means of natural selection. MIT Press.

Digital Library

[14]

M. Mitchell. 1996. An introduction to genetic algorithms. MIT Press.

[15]

M. S. Nawaz, M. Malik, Y. Li, M. Sun, and M. I. Lali. 2019. A survey on theorem provers in Formal methods. arXiv:cs.SE/1912.03028.

[16]

M. S. Nawaz and M. Sun. 2018. A formal design model for genetic algorithms operators and its encoding in PVS. In Proceedings of BDIOT, 2018. ACM, 186--190.

[17]

M. S. Nawaz, M. Sun, and P. Fournier-Viger. 2019. Proof guidance in PVS with sequential pattern mining. In Proceedings of FSEN, 2019 (LNCS), Vol. 11761. Springer, 45--60.

[18]

A. L. Nsakanda, W. L. Price, M. Diaby, and M. Gravel. 2007. Ensuring population diversity in genetic algorithms: A technical note with application to the cell formation problem. European Journal of Operational Research 178 (2007), 634--638.

[19]

S. Owre, N. Shankar, J. M. Rushby, and D. W. J. Stringer-Calvert. 2001. PVS system guide, PVS prover guide, PVS language reference. Technical Report. SRI International.

[20]

J. E. Santo. 2015. Curry-Howard for sequent calculus at last!. In Proceedings of TLCA, 2015 (LIPIcs), Vol. 38. 165--179.

[21]

K. Slind and M. Norrish. 2008. A brief overview of HOL4. In Proceedings of TPHOL, 2008. Springer, 28--32.

[22]

L. A. Yang, J. P. Liu, C. H. Chen, and Y. P. Chen. 2016. Automatically proving mathematical theorems with evolutionary algorithms and proof assistants. In Proceddings of CEC, 2016. IEEE, 4421--4428.

Cited By

Nagashima Y(2023)Genetic Algorithm for Program SynthesisFundamentals of Software Engineering10.1007/978-3-031-42441-0_8(104-111)Online publication date: 30-Aug-2023
https://doi.org/10.1007/978-3-031-42441-0_8
Nawaz MNawaz MHasan OFournier-Viger PSun M(2021)Proof searching and prediction in HOL4 with evolutionary/heuristic and deep learning techniquesApplied Intelligence10.1007/s10489-020-01837-751:3(1580-1601)Online publication date: 1-Mar-2021
https://dl.acm.org/doi/10.1007/s10489-020-01837-7
Nawaz MSun MFournier-Viger P(2021)Proof Searching in PVS Theorem Prover Using Simulated AnnealingAdvances in Swarm Intelligence10.1007/978-3-030-78811-7_24(253-262)Online publication date: 17-Jul-2021
https://dl.acm.org/doi/10.1007/978-3-030-78811-7_24
Show More Cited By

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Proof searching in HOL4 with genetic algorithm

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cover image ACM Conferences

SAC '20: Proceedings of the 35th Annual ACM Symposium on Applied Computing

March 2020

2348 pages

ISBN:9781450368667

DOI:10.1145/3341105

Conference Chairs:
Chih-Cheng Hung
Kennesaw State University
,
Tomas Cerny
Baylor University
,
Program Chairs:
Dongwan Shin
New Mexico Tech
,
Alessio Bechini
University of Pisa, Italy

Copyright © 2020 ACM.

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SIGAPP: ACM Special Interest Group on Applied Computing

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Association for Computing Machinery

New York, NY, United States

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Published: 30 March 2020

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SAC '20: The 35th ACM/SIGAPP Symposium on Applied Computing

March 30 - April 3, 2020

Brno, Czech Republic

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Overall Acceptance Rate 1,650 of 6,669 submissions, 25%

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Cited By

Nagashima Y(2023)Genetic Algorithm for Program SynthesisFundamentals of Software Engineering10.1007/978-3-031-42441-0_8(104-111)Online publication date: 30-Aug-2023
https://doi.org/10.1007/978-3-031-42441-0_8
Nawaz MNawaz MHasan OFournier-Viger PSun M(2021)Proof searching and prediction in HOL4 with evolutionary/heuristic and deep learning techniquesApplied Intelligence10.1007/s10489-020-01837-751:3(1580-1601)Online publication date: 1-Mar-2021
https://dl.acm.org/doi/10.1007/s10489-020-01837-7
Nawaz MSun MFournier-Viger P(2021)Proof Searching in PVS Theorem Prover Using Simulated AnnealingAdvances in Swarm Intelligence10.1007/978-3-030-78811-7_24(253-262)Online publication date: 17-Jul-2021
https://dl.acm.org/doi/10.1007/978-3-030-78811-7_24
Nawaz MFournier-Viger PZhang J(2020)Proof Learning in PVS With Utility Pattern MiningIEEE Access10.1109/ACCESS.2020.30041998(119806-119818)Online publication date: 2020
https://doi.org/10.1109/ACCESS.2020.3004199

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