Theorem Proving With The Real Numbers
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Theorem Proving With The Real Numbers
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Author : John Robert Harrison
language : en
Publisher:
Release Date : 1996
Theorem Proving With The Real Numbers written by John Robert Harrison and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with Automatic theorem proving categories.
Abstract: "This thesis discusses the use of the real numbers in theorem proving. Typically, theorem provers only support a few 'discrete' datatypes such as the natural numbers. However the availability of the real numbers opens up many interesting and important application areas, such as the verification of floating point hardware and hybrid systems. It also allows the formalization of many more branches of classical mathematics, which is particularly relevant for attempts to inject more rigour into computer algebra systems. Our work is conducted in a version of the HOL theorem prover. We describe the rigorous definitional construction of the real numbers, using a new version of Cantor's method, and the formalization of a significant portion of real analysis. We also describe an advanced derived decision procedure for the 'Tarski subset' of real algebra as well as some more modest but practically useful tools for automating explicit calculations and routine linear arithmetic reasoning. Finally, we consider in more detail two interesting application areas. We discuss the desirability of combining the rigour of theorem provers with the power and convenience of computer algebra systems, and explain a method we have used in practice to achieve this. We then move on to the verification of floating point hardware. After a careful discussion of possible correctness specifications, we report on two case studies, one involving a transcendental function. We aim to show that a theory of real numbers is useful in practice and interesting in theory, and that the 'LCF style' of theorem proving is well suited to the kind of work we describe. We hope also to convince the reader that the kind of mathematics needed for applications is well within the abilities of current theorem proving technology."
Theorem Proving With The Real Numbers
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Author : John Harrison
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Theorem Proving With The Real Numbers written by John Harrison and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Computers categories.
This book discusses the use of the real numbers in theorem proving. Typ ically, theorem provers only support a few 'discrete' datatypes such as the natural numbers. However the availability of the real numbers opens up many interesting and important application areas, such as the verification of float ing point hardware and hybrid systems. It also allows the formalization of many more branches of classical mathematics, which is particularly relevant for attempts to inject more rigour into computer algebra systems. Our work is conducted in a version of the HOL theorem prover. We de scribe the rigorous definitional construction of the real numbers, using a new version of Cantor's method, and the formalization of a significant portion of real analysis. We also describe an advanced derived decision procedure for the 'Tarski subset' of real algebra as well as some more modest but practically useful tools for automating explicit calculations and routine linear arithmetic reasoning. Finally, we consider in more detail two interesting application areas. We discuss the desirability of combining the rigour of theorem provers with the power and convenience of computer algebra systems, and explain a method we have used in practice to achieve this. We then move on to the verification of floating point hardware. After a careful discussion of possible correctness specifications, we report on two case studies, one involving a transcendental function.
Interactive Theorem Proving
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Author : Lennart Beringer
language : en
Publisher: Springer
Release Date : 2012-08-10
Interactive Theorem Proving written by Lennart Beringer and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-08-10 with Mathematics categories.
This book constitutes the thoroughly refereed proceedings of the Third International Conference on Interactive Theorem Proving, ITP 2012, held in Princeton, NJ, USA, in August 2012. The 21 revised full papers presented together with 4 rough diamond papers, 3 invited talks, and one invited tutorial were carefully reviewed and selected from 40 submissions. Among the topics covered are formalization of mathematics; program abstraction and logics; data structures and synthesis; security; (non-)termination and automata; program verification; theorem prover development; reasoning about program execution; and prover infrastructure and modeling styles.
Higher Order Logic Theorem Proving And Its Applications
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Author : L.J.M. Claesen
language : en
Publisher: Elsevier
Release Date : 2014-05-23
Higher Order Logic Theorem Proving And Its Applications written by L.J.M. Claesen and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-23 with Mathematics categories.
The HOL system is a higher order logic theorem proving system implemented at Edinburgh University, Cambridge University and INRIA. Its many applications, from the verification of hardware designs at all levels to the verification of programs and communication protocols are considered in depth in this volume. Other systems based on higher order logic, namely Nuprl and LAMBDA are also discussed. Features given particular consideration are: novel developments in higher order logic and its implementations in HOL; formal design and verification methodologies for hardware and software; public domain availability of the HOL system. Papers addressing these issues have been divided as follows: Mathematical Logic; Induction; General Modelling and Proofs; Formalizing and Modelling of Automata; Program Verification; Hardware Description Language Semantics; Hardware Verification Methodologies; Simulation in Higher Order Logic; Extended Uses of Higher Order Logic. Academic and industrial researchers involved in formal hardware and software design and verification methods should find the publication especially interesting and it is hoped it will also provide a useful reference tool for those working at software institutes and within the electronics industries.
Theorem Proving In Higher Order Logics
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Author : Otmane Ait Mohamed
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-07-30
Theorem Proving In Higher Order Logics written by Otmane Ait Mohamed and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-07-30 with Computers categories.
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.
Theorem Proving In Higher Order Logics
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Author : Joe Hurd
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-08-08
Theorem Proving In Higher Order Logics written by Joe Hurd and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-08-08 with Computers categories.
This book constitutes the refereed proceedings of the 18th International Conference on Theorem Proving in Higher Order Logics, TPHOLs 2005, held in Oxford, UK, in August 2005. The 20 revised full papers presented together with 2 invited papers and 4 proof pearls (concise and elegant presentations of interesting examples) were carefully reviewed and selected from 49 submissions. All current issues in HOL theorem proving and formal verification of software and hardware systems are addressed. Among the topics of this volume are theorem proving, verification, recursion and induction, mechanized proofs, mathematical logic, proof theory, type systems, program verification, and proving systems like HOL, Coq, ACL2, Isabelle/HOL and Isabelle/HOLCF.
Interactive Theorem Proving
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Author : Matt Kaufmann
language : en
Publisher: Springer
Release Date : 2010-07-13
Interactive Theorem Proving written by Matt Kaufmann and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-07-13 with Computers categories.
This book constitutes the refereed proceedings of the First International Conference on Interactive Theorem proving, ITP 2010, held in Edinburgh, UK, in July 2010. The 33 revised full papers presented were carefully reviewed and selected from 74 submissions. The papers are organized in topics such as counterexample generation, hybrid system verification, 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.
Interactive Theorem Proving
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Author : Gerwin Klein
language : en
Publisher: Springer
Release Date : 2014-06-28
Interactive Theorem Proving written by Gerwin Klein and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-06-28 with Mathematics categories.
This book constitutes the proceedings of the 5th International Conference on Interactive Theorem Proving, ITP 2014, Held as Part of the Vienna Summer of Logic, VSL 2014, in Vienna, Austria, in July 2014. The 35 papers presented in this volume were carefully reviewed and selected from 59 submissions. The topics range from theoretical foundations to implementation aspects and applications in program verification, security and formalization of mathematics.
Theorem Proving In Higher Order Logics
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Author : Stefan Berghofer
language : en
Publisher: Springer
Release Date : 2009-08-20
Theorem Proving In Higher Order Logics written by Stefan Berghofer and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-08-20 with Computers categories.
This book constitutes the refereed proceedings of the 22nd International Conference on Theorem Proving in Higher Order Logics, TPHOLs 200, held in Munich, Germany, in August 2009. The 26 revised full papers presented together with 1 proof pearl, 4 tool presentations, and 3 invited papers were carefully reviewed and selected from 55 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, formalization of mathematical theories, advances in theorem prover technology, as well as industrial application of theorem provers.
Interactive Theorem Proving
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Author : Marko Van Eekelen
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-08-02
Interactive Theorem Proving written by Marko Van Eekelen and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-08-02 with Computers categories.
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.