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A comparative study of Coq and HOL [chapter]

Vincent Zammit
1997 Lecture Notes in Computer Science  
This paper illustrates the di erences between the style of theory mechanisation of Coq and of HOL.  ...  This comparative study is based on the mechanisation of fragments of the theory of computation in these systems.  ...  Acknowledgements I would like to thank my supervisor, Simon Thompson, for his support and encouragement as well as the anonymous referees for their comments and suggestions on an earlier draft of this  ... 
doi:10.1007/bfb0028403 fatcat:m5emdvn2qncudmbfy2hpe33sfe

Concrete Semantics with Coq and CoqHammer [chapter]

Łukasz Czajka, Burak Ekici, Cezary Kaliszyk
2018 Lecture Notes in Computer Science  
We compare the formalization efficiency, compactness, and the readability of the proof scripts originating from a Coq re-formalization of two chapters from the book.  ...  In this paper we discuss a re-formalization of the book using the Coq proof assistant.  ...  Case Studies In this section, we illustrate a set of goals that are discharged using the Coq automation techniques, presented in Section 3, together with a comparison to their original versions, in an  ... 
doi:10.1007/978-3-319-96812-4_5 fatcat:hinv6upr4zfk5kuo6se5fjel2q

Comparing Mathematical Provers [chapter]

Freek Wiedijk
2003 Lecture Notes in Computer Science  
The three main dimensions on which we compare these systems are: the size of their library, the strength of their logic and their level of automation.  ...  We compare fifteen systems for the formalizations of mathematics with the computer. We present several tables that list various properties of these programs.  ...  For instance, there are comparisons between NuPRL and Nqthm [5] , HOL and Isabelle [2] , HOL and ALF [1] , Coq and HOL [12] , and HOL and PVS [11] . a square] is incommensurable [with the side] because  ... 
doi:10.1007/3-540-36469-2_15 fatcat:bo4hoan5zrgajada3ejhd7jyni

Comparison of Two Theorem Provers: Isabelle/HOL and Coq [article]

Artem Yushkovskiy
2018 arXiv   pre-print
This paper compares two widespread tools for automated theorem proving, Isabelle/HOL and Coq, with respect to expressiveness, limitations and usability.  ...  For this reason, it firstly gives a brief introduction to the bases of formal systems and automated deduction theory, their main problems and challenges, and then provides detailed comparison of most notable  ...  Stavros Tripakis for letting me dive into the exciting world of Logic, for providing feedback on my paper at all stages of the work, for answering all my countless questions and supporting me.  ... 
arXiv:1808.09701v2 fatcat:ffesxt4esffgjottsxmwjykjri

Ott: Effective tool support for the working semanticist

2010 Journal of functional programming  
We present a metalanguage specifically designed for this problem, and a tool, Ott, that sanity-checks such definitions and compiles them into proof assistant code for Coq, HOL, and Isabelle/HOL, together  ...  This has been tested in substantial case studies, including modular specifications of calculi from the TAPL text, a Lightweight Java with Java JSR 277/294 module system proposals, and a large fragment  ...  We acknowledge the support of EPSRC grants GR/T11715, EP/C510712 and EP/F036345, and a Royal Society University Research Fellowship (Sewell).  ... 
doi:10.1017/s0956796809990293 fatcat:wtvqxpi3arb6xiwsotyktqiicu

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.  ...  We have also accounted for large developments that play a similar role or extend standard libraries: ACL2(r) for ACL2, C-CoRN/MathClasses for Coq, and the NASA PVS library.  ...  The authors are grateful to Assia Mahboubi, Micaela Mayero, César Muñoz, Bas Spitters, and Makarius Wenzel, for their numerous and helpful comments on this survey.  ... 
doi:10.1017/s0960129514000437 fatcat:qjnpetpbcbb4rbvm26geem3jai

QED at Large: A Survey of Engineering of Formally Verified Software

Talia Ringer, Karl Palmskog, Ilya Sergey, Milos Gligoric, Zachary Tatlock
2019 Foundations and Trends® in Programming Languages  
This survey of the literature presents a holistic understanding of proof engineering for program correctness, covering impact in practice, foundations, proof automation, proof organization, and practical  ...  Projects based on construction of machine-checked formal proofs are now reaching an unprecedented scale, comparable to large software projects, which leads to new challenges in proof development and maintenance  ...  -N. and J. Malenfant. 1995. "Reflection in logic, functional and object-oriented programming: A Short Comparative Study".  ... 
doi:10.1561/2500000045 fatcat:gb4mbpqn4jbufplrbk2y75huzu

A General Formal Memory Framework for Smart Contracts Verification based on Higher-Order Logic Theorem Proving

Yang Zheng, Lei Hang
2019 International Journal of Performability Engineering  
One of the most reliable methods for s the security and reliability of smart contracts is a formal symbolic virtual machine based on higher-order logic proof system.  ...  Simple case studies are employed to demonstrate its effectiveness. Finally, the proposed GERM framework is verified in Coq.  ...  Here, we present a brief discussion of the most significant studies that have inspired the present work.  ... 
doi:10.23940/ijpe.19.11.p19.29983007 fatcat:obcrrcxhvfcb3cbx32xokv4nfq

Experiences from Exporting Major Proof Assistant Libraries

Michael Kohlhase, Florian Rabe
2021 Journal of automated reasoning  
As a preparatory step, in previous work, we translated the libraries of multiple proof assistants, specifically the ones of Coq, HOL Light, IMPS, Isabelle, Mizar, and PVS into a universal format: OMDoc  ...  In this paper, we survey these challenges and compare and evaluate the solutions we chose.  ...  We gratefully acknowledge project support by the German Research Council (DFG) under grants KO 2428/13-1 and RA 18723/1-1 and from the European Union under Project OpenDreamKit.  ... 
doi:10.1007/s10817-021-09604-0 fatcat:3umqoajd3befvkbsixearflcuu

Coquelicot: A User-Friendly Library of Real Analysis for Coq

Sylvie Boldo, Catherine Lelay, Guillaume Melquiond
2014 Mathematics in Computer Science  
The Coq system comes with an axiomatization of standard real numbers and a library of theorems on real analysis. Unfortunately, this standard library is lacking some widely used results.  ...  Moreover, Coquelicot is a conservative extension of Coq's standard library and we provide correspondence theorems between the two libraries.  ...  Acknowledgements The authors are grateful to Pierre Michalak andÉvelyne Roudneff for allowing us to take the Baccalaureate exam in real-life conditions in a high school in Massy, and for organizing the  ... 
doi:10.1007/s11786-014-0181-1 fatcat:eptv7v543bg63nlm6gzyakcctu

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
In this work, more than 40 theorem provers are studied in detail and compared to present a comprehensive analysis and evaluation of these tools.  ...  Mechanical reasoning is a key area of research that lies at the crossroads of mathematical logic and artificial intelligence.  ...  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

Experiences from Exporting Major Proof Assistant Libraries [article]

Michael Kohlhase, Florian Rabe
2020 arXiv   pre-print
As a preparatory step, in previous work, we translated the libraries of multiple proof assistants, specifically the ones of Coq, HOL Light, IMPS, Isabelle, Mizar, and PVS into a universal format: OMDoc  ...  The interoperability of proof assistants and the integration of their libraries is a highly valued but elusive goal in the field of theorem proving.  ...  We gratefully acknowledge project support by the German Research Council (DFG) under grants KO 2428/13-1 and RA 18723/1-1 and from the European Union under Project OpenDreamKit.  ... 
arXiv:2005.03089v1 fatcat:h2dzkdjpprd75eqzk3fausgthq

Program Extraction from Normalization Proofs

Ulrich Berger, Stefan Berghofer, Pierre Letouzey, Helmut Schwichtenberg
2006 Studia Logica: An International Journal for Symbolic Logic  
The case study is used to test and compare the program extraction machineries of the three proof assistants in a non-trivial setting.  ...  This paper describes formalizations of Tait's normalization proof for the simply typed λ-calculus in the proof assistants Minlog, Coq and Isabelle/HOL.  ...  After manually implementing these remarks in the extracted code, we have noticed a new improvement of about Conclusion This case study turned out to be extremely useful for testing and comparing the  ... 
doi:10.1007/s11225-006-6604-5 fatcat:6e35esi3gvdrzevonerxrmiw7u

Formal Proofs of Tarjan's Strongly Connected Components Algorithm in Why3, Coq and Isabelle

Ran Chen, Cyril Cohen, Jean-Jacques Lévy, Stephan Merz, Laurent Théry, Michael Wagner
2019 International Conference on Interactive Theorem Proving  
In this paper, we present the formal proof of correctness of a non-trivial algorithm from graph theory that was carried out in three proof assistants: Why3, Coq, and Isabelle.  ...  Comparing provers on a formalization of the same problem is always a valuable exercise.  ...  The Isabelle/HOL proof can be seen as a mid-point between the Why3 and Coq proofs.  ... 
doi:10.4230/lipics.itp.2019.13 dblp:conf/itp/ChenCLMT19 fatcat:az25cxxzizhnzoggtl4jdlnxpi
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