Download or read book Generic Automatic Proof Tools written by Lawrence C. Paulson and published by . This book was released on 1996 with total page 36 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Automated Deduction A Basis for Applications Volume I Foundations Calculi and Methods Volume II Systems and Implementation Techniques Volume III Applications written by Wolfgang Bibel and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: 1. BASIC CONCEPTS OF INTERACTIVE THEOREM PROVING Interactive Theorem Proving ultimately aims at the construction of powerful reasoning tools that let us (computer scientists) prove things we cannot prove without the tools, and the tools cannot prove without us. Interaction typi cally is needed, for example, to direct and control the reasoning, to speculate or generalize strategic lemmas, and sometimes simply because the conjec ture to be proved does not hold. In software verification, for example, correct versions of specifications and programs typically are obtained only after a number of failed proof attempts and subsequent error corrections. Different interactive theorem provers may actually look quite different: They may support different logics (first-or higher-order, logics of programs, type theory etc.), may be generic or special-purpose tools, or may be tar geted to different applications. Nevertheless, they share common concepts and paradigms (e.g. architectural design, tactics, tactical reasoning etc.). The aim of this chapter is to describe the common concepts, design principles, and basic requirements of interactive theorem provers, and to explore the band width of variations. Having a 'person in the loop', strongly influences the design of the proof tool: proofs must remain comprehensible, - proof rules must be high-level and human-oriented, - persistent proof presentation and visualization becomes very important.
Download or read book Generic Proof Tools and Finite Group Theory written by François Garillot and published by . This book was released on 2011 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Automated Deduction and Proof Certification for the B Method written by Pierre Halmagrand and published by . This book was released on 2016 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The B Method is a formal method heavily used in the railway industry to specify and develop safety-critical software. It allows the development of correct-by-construction programs, thanks to a refinement process from an abstract specification to a deterministic implementation of the program. The soundness of the refinement steps depends on the validity of logical formulas called proof obligations, expressed in a specific typed set theory. Typical industrial projects using the B Method generate thousands of proof obligations, thereby relying on automated tools to discharge as many as possible proof obligations. A specific tool, called Atelier B, designed to implement the B Method and provided with a theorem prover, helps users verify the validity of proof obligations, automatically or interactively. Improving the automated verification of proof obligations is a crucial task for the speed and ease of development. The solution developed in our work is to use Zenon, a first-orderlogic automated theorem prover based on the tableaux method. The particular feature of Zenon is to generate proof certificates, i.e. proof objects that can be verified by external tools. The B Method is based on first-order logic and a specific typed set theory. To improve automated theorem proving in this theory, we extend the proof-search algorithm of Zenon to polymorphism and deduction modulo theory, leading to a new tool called Zenon Modulo which is the main contribution of our work. The extension to polymorphism allows us to deal with problems combining several sorts, like booleans and integers, and generic axioms, like B set theory axioms, without relying on encodings. Deduction modulo theory is an extension of first-order logic with rewriting both on terms and propositions. It is well suited for proof search in axiomatic theories, as it turns axioms into rewrite rules. This way, we turn proof search among axioms into computations, avoiding unnecessary combinatorial explosion, and reducing the size of proofs by recording only their meaningful steps. To certify Zenon Modulo proofs, we choose to rely on Dedukti, a proof-checker used as a universal backend to verify proofs coming from different theorem provers,and based on deduction modulo theory. This work is part of a larger project called BWare, which gathers academic entities and industrial companies around automated theorem proving for the B Method. These industrial partners provide to BWare a large benchmark of proof obligations coming from real industrial projects using the B Method and allowing us to test our tool Zenon Modulo. The experimental results obtained on this benchmark are particularly conclusive since Zenon Modulo proves more proof obligations than state-of-the-art first-order provers. In addition, all the proof certificates produced by Zenon Modulo on this benchmark are well checked by Dedukti, increasing our confidence in the soundness of our work.
Download or read book Automated Reasoning and Its Applications written by Robert Veroff and published by MIT Press. This book was released on 1997 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: The contributors are among the world's leading researchers inautomated reasoning. Their essays cover the theory, software system design, and use of these systems to solve real problems. The primary objective of automated reasoning (which includes automated deduction and automated theorem proving) is to develop computer programs that use logical reasoning for the solution of a wide variety of problems, including open questions. The essays in Automated Reasoning and Its Applications were written in honor of Larry Wos, one of the founders of the field. Wos played a central role in forming the culture of automated reasoning at Argonne National Laboratory. He and his colleagues consistently seek to build systems that search huge spaces for solutions to difficult problems and proofs of significant theorems. They have had numerous notable successes. The contributors are among the world's leading researchers in automated reasoning. Their essays cover the theory, software system design, and use of these systems to solve real problems. Contributors Robert S. Boyer, Shang-Ching Chou, Xiao-Shan Gao, Lawrence Henschen, Deepak Kapur, Kenneth Kunen, Ewing Lusk, William McCune, J Strother Moore, Ross Overbeek, Lawrence C. Paulson, Hantao Zhang, Jing-Zhong Zhang
Download or read book Theorem Proving in Higher Order Logics written by Yves Bertot and published by Springer. This book was released on 2003-07-31 with total page 363 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 12th International Conference on Theorem Proving in Higher Order Logics, TPHOLs '99, held in Nice, France, in September 1999. The 20 revised full papers presented together with three invited contributions were carefully reviewed and selected from 35 papers submitted. All current aspects of higher order theorem proving, formal verification, and specification are discussed. Among the theorem provers evaluated are COQ, HOL, Isabelle, Isabelle/ZF, and OpenMath.
Download or read book Automated Deduction CADE 19 written by Franz Baader and published by Springer Science & Business Media. This book was released on 2003-07-16 with total page 517 pages. Available in PDF, EPUB and Kindle. Book excerpt: The refereed proceedings of the 19th International Conference on Automated Deduction, CADE 2003, held in Miami Beach, FL, USA in July 2003. The 29 revised full papers and 7 system description papers presented together with an invited paper and 3 abstracts of invited talks were carefully reviewed and selected from 83 submissions. All current aspects of automated deduction are discussed, ranging from theoretical and methodological issues to the presentation of new theorem provers and systems.
Download or read book Theorem Proving in Higher Order Logics written by Otmane Ait Mohamed and published by Springer Science & Business Media. This book was released on 2008-07-30 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 21st International Conference on Theorem Proving in Higher Order Logics, TPHOLs 2008, held in Montreal, Canada, in August 2008. The 17 revised full papers presented together with 1 proof pearl (concise and elegant presentations of interesting examples), 5 tool presentations, and 2 invited papers were carefully reviewed and selected from 40 submissions. The papers cover all aspects of theorem proving in higher order logics as well as related topics in theorem proving and verification such as formal semantics of specification, modeling, and programming languages, specification and verification of hardware and software, formalisation of mathematical theories, advances in theorem prover technology, as well as industrial application of theorem provers.
Download or read book Frontiers of Combining Systems written by Cesare Tinelli and published by Springer Science & Business Media. This book was released on 2011-09-23 with total page 283 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 8th International Symposium on Frontiers of Combining Systems, FroCoS 2011, held in Saarbrücken, Germany, in October 2011. The 15 revised full papers presented together with three invited papers were carefully reviewed and selected from 22 submissions. The event builds a common forum for research activities in the general area of combination, modularization and integration of systems, with emphasis on logic-based ones, and of their practical use.
Download or read book A Generic Tableau Prover and Its Integration with Isabelle written by Lawrence C. Paulson and published by . This book was released on 1998 with total page 32 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: "A generic tableau prover has been implemented and integrated with Isabelle [14]. It is based on leantap [3] but is much more complicated, with numerous modifications to allow it to reason with any supplied set of tableau rules. It has a higher-order syntax in order to support the binding operators of set theory; unification is first-order (extended for bound variables in obvious ways) instead of higher-order, for simplicity. When a proof is found, it is returned to Isabelle as a list of tactics. Because Isabelle verifies the proof, the prover can cut corners for efficiency's sake without compromising soundness. For example, it knows almost nothing about types."
Download or read book Theorem Proving in Higher Order Logics written by Jim Grundy and published by Springer Science & Business Media. This book was released on 1998-09-09 with total page 516 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 11th International Conference on Theorem Proving in Higher Order Logics, TPHOLs '98, held in Canberra, Australia, in September/October 1998. The 26 revised full papers presented were carefully reviewed and selected from a total of 52 submissions. Also included are two invited papers. The papers address all current aspects of theorem proving in higher order logics and formal verification and program analysis. Besides the HOL system, the theorem provers Coq, Isabelle, LAMBDA, LEGO, NuPrl, and PVS are discussed.
Download or read book Computational Logic CL 2000 written by John Lloyd and published by Springer. This book was released on 2003-06-26 with total page 1399 pages. Available in PDF, EPUB and Kindle. Book excerpt: These are the proceedings of the First International Conference on Compu- tional Logic (CL 2000) which was held at Imperial College in London from 24th to 28th July, 2000. The theme of the conference covered all aspects of the theory, implementation, and application of computational logic, where computational logic is to be understood broadly as the use of logic in computer science. The conference was collocated with the following events: { 6th International Conference on Rules and Objects in Databases (DOOD 2000) { 10th International Workshop on Logic-based Program Synthesis and Tra- formation (LOPSTR 2000) { 10th International Conference on Inductive Logic Programming (ILP 2000). CL 2000 consisted of seven streams: { Program Development (LOPSTR 2000) { Logic Programming: Theory and Extensions { Constraints { Automated Deduction: Putting Theory into Practice { Knowledge Representation and Non-monotonic Reasoning { Database Systems (DOOD 2000) { Logic Programming: Implementations and Applications. The LOPSTR 2000 workshop constituted the program development stream and the DOOD 2000 conference constituted the database systems stream. Each stream had its own chair and program committee, which autonomously selected the papers in the area of the stream. Overall, 176 papers were submitted, of which 86 were selected to be presented at the conference and appear in these proceedings. The acceptance rate was uniform across the streams. In addition, LOPSTR 2000 accepted about 15 extended abstracts to be presented at the conference in the program development stream.
Download or read book Mathematical Methods in Program Development written by Manfred Broy and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 538 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modern information processing systems show such complex properties as distribution, parallelism, interaction, time dependency, and nondeterminism. For critical applications, mathematical methods are needed to model the systems and to support their development and validation. Impressive progress in mathematical methods for programming software systems makes it possible to think about unifying the different approaches. This book gives a comprehensive overview of existing methods and presents some of the most recent results in applying them. The main topics are: advanced programming techniques, foundations of systems engineering, mathematical support methods, and application of the methods. The approaches presented are illustrated by examples and related to other approaches.
Download or read book Formal Methods and Hybrid Real Time Systems written by Cliff B. Jones and published by Springer. This book was released on 2007-09-04 with total page 551 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Festschrift volume is published to honour both Dines Bjørner and Zhou Chaochen on the occasion of their 70th birthdays. The volume includes 25 refereed papers by leading researchers, current and former colleagues, who congregated at a celebratory symposium held in Macao, China, in the course of the International Colloquium on Theoretical Aspects of Computing, ICTAC 2007. The papers cover a broad spectrum of subjects.
Download or read book Interactive Theorem Proving written by Marko Van Eekelen and published by Springer Science & Business Media. This book was released on 2011-08-02 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the Second International Conference on Interactive Theorem proving, ITP 2011, held in Berg en Dal, The Netherlands, in August 2011. The 25 revised full papers presented were carefully reviewed and selected from 50 submissions. Among the topics covered are counterexample generation, verification, validation, term rewriting, theorem proving, computability theory, translations from one formalism to another, and cooperation between tools. Several verification case studies were presented, with applications to computational geometry, unification, real analysis, etc.
Download or read book Verified Software Theories Tools and Experiments written by Dimitra Giannakopoulou and published by Springer. This book was released on 2014-10-13 with total page 291 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume constitutes the thoroughly refereed post-conference proceedings of the 6th International Conference on Verified Software: Theories, Tools and Experiments, VSTTE 2014, held in July 2014 at the Vienna Summer of Logic in Vienna, Austria, as an associated event of CAV 2014, the International Conference on Computer-Aided Verification. The 17 revised full papers presented were carefully revised and selected from 34 submissions. The papers are organized in topical sections such as analysis: understanding and explanation; verification frameworks and applications; hypervisors and dynamic data structures; certification; real time and security.
Download or read book Towards Mechanized Mathematical Assistants written by Manuel Kauers and published by Springer. This book was released on 2007-08-15 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 6th International Conference on Mathematical Knowledge Management, MKM 2007, and the 14th Symposium on the Integration of Symbolic Computation and Mechanized Reasoning, Calculemus 2006, held in Hagenberg, Austria in June 2007 as events of the RISC Summer 2007, organized by the Research Institute for Symbolic Computation.
