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Sharing HOL4 and HOL Light Proof Knowledge [chapter]

Thibault Gauthier, Cezary Kaliszyk
2015 Lecture Notes in Computer Science  
We evaluate the proposed knowledge-sharing methods by reproving the HOL Light and HOL4 standard libraries.  ...  The learning-reasoning system HOL(y)Hammer, whose single best strategy could automatically find proofs for 30% of the HOL Light problems, can prove 40% with the knowledge from HOL4.  ...  In this research we will focus on sharing proof knowledge between libraries of proof assistants based on higherorder logic, in particular HOL4 [23] and HOL Light [9] .  ... 
doi:10.1007/978-3-662-48899-7_26 fatcat:tdutfexmfzfdbjxla4mx4yvu7q

Sharing HOL4 and HOL Light proof knowledge [article]

Thibault Gauthier, Cezary Kaliszyk
2015 arXiv   pre-print
We evaluate the proposed knowledge-sharing methods by reproving the HOL Light and HOL4 standard libraries.  ...  The learning-reasoning system HOL(y)Hammer, whose single best strategy could automatically find proofs for 30% of the HOL Light problems, can prove 40% with the knowledge from HOL4.  ...  In this research we will focus on sharing proof knowledge between libraries of proof assistants based on higherorder logic, in particular HOL4 [23] and HOL Light [9] .  ... 
arXiv:1509.03527v1 fatcat:pguhm3mu75bhzi625u63jyaxbi

Matching Concepts across HOL Libraries [chapter]

Thibault Gauthier, Cezary Kaliszyk
2014 Lecture Notes in Computer Science  
We evaluate the approach on HOL based proof assistants HOL4, HOL Light and Isabelle/HOL, discovering 398 pairs of isomorphic constants and types. ⋆ The final publication is available at http://link.springer.com  ...  Many proof assistant libraries contain formalizations of the same mathematical concepts.  ...  We chose three proof assistants based on higher-order logic: HOL4 [18] , HOL Light [6] and Isabelle/HOL [21] .  ... 
doi:10.1007/978-3-319-08434-3_20 fatcat:nzsczwmuyrd7jnoe3ty5alvv34

Premise Selection and External Provers for HOL4

Thibault Gauthier, Cezary Kaliszyk
2015 Proceedings of the 2015 Conference on Certified Programs and Proofs - CPP '15  
Learning-assisted automated reasoning has recently gained popularity among the users of Isabelle/HOL, HOL Light, and Mizar.  ...  The results are combined accordingly and compared with the HOL Light experiments, showing a comparably high quality of predictions.  ...  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

Matching concepts across HOL libraries [article]

Thibault Gauthier, Cezary Kaliszyk
2014 arXiv   pre-print
We evaluate the approach on HOL based proof assistants HOL4, HOL Light and Isabelle/HOL, discovering 398 pairs of isomorphic constants and types.  ...  Many proof assistant libraries contain formalizations of the same mathematical concepts.  ...  We chose three proof assistants based on higher-order logic: HOL4 [18] , HOL Light [6] and Isabelle/HOL [21] .  ... 
arXiv:1405.3906v1 fatcat:t54pk7rj4bfufcccqwul2oqe3e

Reconstruction of Z3's Bit-Vector Proofs in HOL4 and Isabelle/HOL [chapter]

Sascha Böhme, Anthony C. J. Fox, Thomas Sewell, Tjark Weber
2011 Lecture Notes in Computer Science  
We thereby obtain high correctness assurances for Z3's results, and increase the degree of proof automation for bit-vector problems in HOL4 and Isabelle/HOL.  ...  We present independent reconstruction of unsatisfiability proofs for bit-vector theories in the theorem provers HOL4 and Isabelle/HOL.  ...  NICTA is funded by the Australian Government as represented by the Department of Broadband, Communications and the Digital Economy and the Australian Research Council through the ICT Centre of Excellence  ... 
doi:10.1007/978-3-642-25379-9_15 fatcat:gesxkp2cm5girliosyngzyuwmi

Learning to Reason with HOL4 tactics [article]

Thibault Gauthier, Cezary Kaliszyk, Josef Urban
2018 arXiv   pre-print
By combining tactic prediction and premise selection, TacticToe is able to re-prove 39 percent of 7902 HOL4 theorems in 5 seconds whereas the best single HOL(y)Hammer strategy solves 32 percent in the  ...  Such "hammer" tech- niques complement traditional proof assistant automation as implemented by tactics and decision procedures.  ...  Acknowledgments This work has been supported by the ERC Consolidator grant no. 649043 AI4REASON and ERC starting grant no. 714034 SMART.  ... 
arXiv:1804.00595v1 fatcat:p6oehxklwfdalokzeez3v6prga

Implicational Rewriting Tactics in HOL [chapter]

Vincent Aravantinos, Sofiène Tahar
2014 Lecture Notes in Computer Science  
We then provide solutions to deal with these situations automatically, which we implemented as HOL Light and HOL4 tactics.  ...  Reducing the distance between informal and formal proofs in interactive theorem proving is a long-standing matter.  ...  Peltier from the Laboratory of Informatics of Grenoble, and the contributors of the hol-info mailing list for fruitful discussions.  ... 
doi:10.1007/978-3-319-08970-6_4 fatcat:tbp4hfcwrfhl5nvs7up32xkm4i

HOL with Definitions: Semantics, Soundness, and a Verified Implementation [chapter]

Ramana Kumar, Rob Arthan, Magnus O. Myreen, Scott Owens
2014 Lecture Notes in Computer Science  
We present a mechanised semantics and soundness proof for the HOL Light kernel including its definitional principles, extending Harrison's verification of the kernel without definitions.  ...  We improve on Harrison's approach by making our model of HOL parametric on the universe of sets.  ...  We build on Harrison's proof of the consistency of HOL without definitions [4] , which shares our larger goal of verifying concrete HOL prover implementations, and advance this project by verifying an  ... 
doi:10.1007/978-3-319-08970-6_20 fatcat:36yemgi4w5g2dkg7jxnsux2epm

On the Formalization of Gamma Function in HOL

Umair Siddique, Osman Hasan
2014 Journal of automated reasoning  
Firstly, we extend the existing integration theory of HOL4 by formalizing a variant of improper integrals using sequential limits.  ...  This paper presents a higher-order logic formalization of the Gamma function using the HOL4 theorem prover. The contribution of this paper can be mainly divided into two parts.  ...  the required foundations from the HOL-Light theorem prover.  ... 
doi:10.1007/s10817-014-9311-3 fatcat:utrfokmtdzgwhk3fg7x5jnmzka

The 1st Verified Software Competition: Experience Report [chapter]

Vladimir Klebanov, Peter Müller, Natarajan Shankar, Gary T. Leavens, Valentin Wüstholz, Eyad Alkassar, Rob Arthan, Derek Bronish, Rod Chapman, Ernie Cohen, Mark Hillebrand, Bart Jacobs (+10 others)
2011 Lecture Notes in Computer Science  
We, the organizers and participants, report our experiences from the 1st Verified Software Competition, held in August 2010 in Edinburgh at the VSTTE 2010 conference.  ...  For example, for Invert we proved surjectivity of A from injectivity and boundedness.  ...  Completing Invert and N Queens required developing quite a bit of theory, which was labor-intensive but possible in VeriFast.  ... 
doi:10.1007/978-3-642-21437-0_14 fatcat:vkjleltbkrdchok44arrshxfua

A Verified Certificate Checker for Finite-Precision Error Bounds in Coq and HOL4 [article]

Heiko Becker, Nikita Zyuzin, Raphael Monat, Eva Darulova, Magnus O. Myreen, Anthony Fox
2018 arXiv   pre-print
We present implementations of certificate generation and checking for both Coq and HOL4 and evaluate it on a number of examples from the literature.  ...  The experiments use both in-logic evaluation of Coq and HOL4, and execution of extracted code outside of the logics: we benchmark Coq extracted unverified OCaml code and a CakeML-generated verified binary  ...  FPTaylor produces a proof certificate in HOL-Light, relying on an in-logic decision procedure [36] .  ... 
arXiv:1707.02115v2 fatcat:2c2jwcvlpfcsvnu4ncod2wuqdm

A Survey on Theorem Provers in Formal Methods [article]

M. Saqib Nawaz, Moin Malik, Yi Li, Meng Sun, M. Ikram Ullah Lali
2019 arXiv   pre-print
Technically, mathematical formalisms and automated reasoning based-approaches are employed to perform inferences and to generate proofs in theorem provers.  ...  However, these tools evolved with time and now play vital role in the modeling and reasoning about complex and large-scale systems, especially safety-critical systems.  ...  ACKNOWLEDGMENTS The work has been supported by the National Natural Science Foundation of China under grant no. 61772038, 61532019 and 61272160, and the Guandong Science and Technology Department (Grant  ... 
arXiv:1912.03028v1 fatcat:fabxqg75xjhxlh7u3uyypgyzdy

Translating HOL to Dedukti

Ali Assaf, Guillaume Burel
2015 Electronic Proceedings in Theoretical Computer Science  
In this paper, we show how to translate the proofs of a family of HOL proof assistants to Dedukti. The translation preserves binding, typing, and reduction.  ...  We implemented this translation in an automated tool and used it to successfully translate the OpenTheory standard library.  ...  Acknowledgments We thank Gilles Dowek for his support, as well as Mathieu Boespflug and Chantal Keller for their comments and suggestions.  ... 
doi:10.4204/eptcs.186.8 fatcat:waxjxyucf5clflo2mz5oqnqa7u

Formal Kinematic Analysis of a General 6R Manipulator Using the Screw Theory

Aixuan Wu, Zhiping Shi, Yongdong Li, Minhua Wu, Yong Guan, Jie Zhang, Hongxing Wei
2015 Mathematical Problems in Engineering  
Based on the screw theory in HOL4, which is newly developed by our research institute, we utilize the geometrical theory of HOL4 to develop formal reasoning support for the kinematic analysis of a robotic  ...  The main idea behind kinematic analysis is to study the motion of the robot based on the geometrical relationship of the robotic links and their joints, such as the Denavit-Hartenberg parameters.  ...  Acknowledgments First and foremost the authors thank Professor Shengzhen Jin for the guidance and encouragement that he gave them.  ... 
doi:10.1155/2015/549797 fatcat:33onpizdyna6pknebffondikku
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