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Programs Proofs Processes
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Book Synopsis Programs, Proofs, Processes by : Fernando Ferreira
Download or read book Programs, Proofs, Processes written by Fernando Ferreira and published by Springer Science & Business Media. This book was released on 2010-06-17 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 6th Conference on Computability in Europe, CiE 2010, held in Ponta Delgada, Azores, Portugal, in June/July 2010. The 28 revised papers presented together with 20 invited lectures were carefully reviewed and selected from 90 submissions. The papers address not only the more established lines of research of computational complexity and the interplay between proofs and computation, but also novel views that rely on physical and biological processes and models to find new ways of tackling computations and improving their efficiency.
Book Synopsis Fundamental Proof Methods in Computer Science by : Konstantine Arkoudas
Download or read book Fundamental Proof Methods in Computer Science written by Konstantine Arkoudas and published by MIT Press. This book was released on 2017-04-28 with total page 1223 pages. Available in PDF, EPUB and Kindle. Book excerpt: A textbook that teaches students to read and write proofs using Athena. Proof is the primary vehicle for knowledge generation in mathematics. In computer science, proof has found an additional use: verifying that a particular system (or component, or algorithm) has certain desirable properties. This book teaches students how to read and write proofs using Athena, a freely downloadable computer language. Athena proofs are machine-checkable and written in an intuitive natural-deduction style. The book contains more than 300 exercises, most with full solutions. By putting proofs into practice, it demonstrates the fundamental role of logic and proof in computer science as no other existing text does. Guided by examples and exercises, students are quickly immersed in the most useful high-level proof methods, including equational reasoning, several forms of induction, case analysis, proof by contradiction, and abstraction/specialization. The book includes auxiliary material on SAT and SMT solving, automated theorem proving, and logic programming. The book can be used by upper undergraduate or graduate computer science students with a basic level of programming and mathematical experience. Professional programmers, practitioners of formal methods, and researchers in logic-related branches of computer science will find it a valuable reference.
Book Synopsis How to Prove It by : Daniel J. Velleman
Download or read book How to Prove It written by Daniel J. Velleman and published by Cambridge University Press. This book was released on 2006-01-16 with total page 401 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many students have trouble the first time they take a mathematics course in which proofs play a significant role. This new edition of Velleman's successful text will prepare students to make the transition from solving problems to proving theorems by teaching them the techniques needed to read and write proofs. The book begins with the basic concepts of logic and set theory, to familiarize students with the language of mathematics and how it is interpreted. These concepts are used as the basis for a step-by-step breakdown of the most important techniques used in constructing proofs. The author shows how complex proofs are built up from these smaller steps, using detailed 'scratch work' sections to expose the machinery of proofs about the natural numbers, relations, functions, and infinite sets. To give students the opportunity to construct their own proofs, this new edition contains over 200 new exercises, selected solutions, and an introduction to Proof Designer software. No background beyond standard high school mathematics is assumed. This book will be useful to anyone interested in logic and proofs: computer scientists, philosophers, linguists, and of course mathematicians.
Download or read book Program = Proof written by Samuel Mimram and published by . This book was released on 2020-07-03 with total page 539 pages. Available in PDF, EPUB and Kindle. Book excerpt: This course provides a first introduction to the Curry-Howard correspondence between programs and proofs, from a theoretical programmer's perspective: we want to understand the theory behind logic and programming languages, but also to write concrete programs (in OCaml) and proofs (in Agda). After an introduction to functional programming languages, we present propositional logic, λ-calculus, the Curry-Howard correspondence, first-order logic, Agda, dependent types and homotopy type theory.
Book Synopsis Program Verification by : Timothy T.R. Colburn
Download or read book Program Verification written by Timothy T.R. Colburn and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 454 pages. Available in PDF, EPUB and Kindle. Book excerpt: Among the most important problems confronting computer science is that of developing a paradigm appropriate to the discipline. Proponents of formal methods - such as John McCarthy, C.A.R. Hoare, and Edgar Dijkstra - have advanced the position that computing is a mathematical activity and that computer science should model itself after mathematics. Opponents of formal methods - by contrast, suggest that programming is the activity which is fundamental to computer science and that there are important differences that distinguish it from mathematics, which therefore cannot provide a suitable paradigm. Disagreement over the place of formal methods in computer science has recently arisen in the form of renewed interest in the nature and capacity of program verification as a method for establishing the reliability of software systems. A paper that appeared in Communications of the ACM entitled, `Program Verification: The Very Idea', by James H. Fetzer triggered an extended debate that has been discussed in several journals and that has endured for several years, engaging the interest of computer scientists (both theoretical and applied) and of other thinkers from a wide range of backgrounds who want to understand computer science as a domain of inquiry. The editors of this collection have brought together many of the most interesting and important studies that contribute to answering questions about the nature and the limits of computer science. These include early papers advocating the mathematical paradigm by McCarthy, Naur, R. Floyd, and Hoare (in Part I), others that elaborate the paradigm by Hoare, Meyer, Naur, and Scherlis and Scott (in Part II), challenges, limits and alternatives explored by C. Floyd, Smith, Blum, and Naur (in Part III), and recent work focusing on formal verification by DeMillo, Lipton, and Perlis, Fetzer, Cohn, and Colburn (in Part IV). It provides essential resources for further study. This volume will appeal to scientists, philosophers, and laypersons who want to understand the theoretical foundations of computer science and be appropriately positioned to evaluate the scope and limits of the discipline.
Book Synopsis Social Processes and Proofs of Theorems and Programs by : Richard A. De Millo
Download or read book Social Processes and Proofs of Theorems and Programs written by Richard A. De Millo and published by . This book was released on 1978 with total page 34 pages. Available in PDF, EPUB and Kindle. Book excerpt: It has been extensively argued that the art and science of programming should strive to become more like mathematics. In this paper we argue that this point of view is correct, but that the reasons usually given for it are wrong. We present our view that mathematics is, rather than a formal process, an ongoing social process and that the formalistic view of mathematics is misleading and destructive for proving software. (Author).
Author :Jean-Pierre Jouannaud Publisher :Springer Science & Business Media ISBN 13 :3642253784 Total Pages :414 pages Book Rating :4.6/5 (422 download)
Book Synopsis Certified Programs and Proofs by : Jean-Pierre Jouannaud
Download or read book Certified Programs and Proofs written by Jean-Pierre Jouannaud and published by Springer Science & Business Media. This book was released on 2011-11-18 with total page 414 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the referred proceedings of the First International Conference on Certified Programs and Proofs, CPP 2011, held in Kenting, Taiwan, in December 2011. The 24 revised regular papers presented together with 4 invited talks were carefully reviewed and selected from 49 submissions. They are organized in topical sections on logic and types, certificates, formalization, proof assistants, teaching, programming languages, hardware certification, miscellaneous, and proof perls.
Book Synopsis Types for Proofs and Programs by : Stefano Berardi
Download or read book Types for Proofs and Programs written by Stefano Berardi and published by Springer. This book was released on 2009-06-07 with total page 331 pages. Available in PDF, EPUB and Kindle. Book excerpt: These proceedings contain a selection of refereed papers presented at or - lated to the Annual Workshop of the TYPES project (EU coordination action 510996), which was held during March 26–29, 2008 in Turin, Italy. The topic of this workshop, and of all previous workshops of the same project, was f- mal reasoning and computer programming based on type theory: languages and computerized tools for reasoning, and applications in several domains such as analysis of programming languages, certi?ed software, mobile code, formali- tion of mathematics, mathematics education. The workshop was attended by more than 100 researchers and included more than 40 presentations. We also had three invited lectures, from A. Asperti (University of Bologna), G. Dowek (LIX, Ecole polytechnique, France) and J. W. Klop (Vrije Universiteit, A- terdam, The Netherlands). From 27 submitted papers, 19 were selected after a reviewing process. Each submitted paper was reviewed by three referees; the ?nal decisions were made by the editors. This workshop is the last of a series of meetings of the TYPES working group funded by the European Union (IST project 29001, ESPRIT Working Group 21900, ESPRIT BRA 6435).
Author :Hendrik Pieter Barendregt Publisher :Springer Science & Business Media ISBN 13 :9783540580850 Total Pages :404 pages Book Rating :4.5/5 (88 download)
Book Synopsis Types for Proofs and Programs by : Hendrik Pieter Barendregt
Download or read book Types for Proofs and Programs written by Hendrik Pieter Barendregt and published by Springer Science & Business Media. This book was released on 1994-05-20 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains thoroughly refereed and revised full papers selected from the presentations at the first workshop held under the auspices of the ESPRIT Basic Research Action 6453 Types for Proofs and Programs in Nijmegen, The Netherlands, in May 1993. As the whole ESPRIT BRA 6453, this volume is devoted to the theoretical foundations, design and applications of systems for theory development. Such systems help in designing mathematical axiomatisation, performing computer-aided logical reasoning, and managing databases of mathematical facts; they are also known as proof assistants or proof checkers.
Book Synopsis Fundamental Proof Methods in Computer Science by : Konstantine Arkoudas
Download or read book Fundamental Proof Methods in Computer Science written by Konstantine Arkoudas and published by MIT Press. This book was released on 2017-05-05 with total page 1223 pages. Available in PDF, EPUB and Kindle. Book excerpt: A textbook that teaches students to read and write proofs using Athena. Proof is the primary vehicle for knowledge generation in mathematics. In computer science, proof has found an additional use: verifying that a particular system (or component, or algorithm) has certain desirable properties. This book teaches students how to read and write proofs using Athena, a freely downloadable computer language. Athena proofs are machine-checkable and written in an intuitive natural-deduction style. The book contains more than 300 exercises, most with full solutions. By putting proofs into practice, it demonstrates the fundamental role of logic and proof in computer science as no other existing text does. Guided by examples and exercises, students are quickly immersed in the most useful high-level proof methods, including equational reasoning, several forms of induction, case analysis, proof by contradiction, and abstraction/specialization. The book includes auxiliary material on SAT and SMT solving, automated theorem proving, and logic programming. The book can be used by upper undergraduate or graduate computer science students with a basic level of programming and mathematical experience. Professional programmers, practitioners of formal methods, and researchers in logic-related branches of computer science will find it a valuable reference.
Book Synopsis Mathematical Reasoning by : Theodore A. Sundstrom
Download or read book Mathematical Reasoning written by Theodore A. Sundstrom and published by Prentice Hall. This book was released on 2007 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Focusing on the formal development of mathematics, this book shows readers how to read, understand, write, and construct mathematical proofs.Uses elementary number theory and congruence arithmetic throughout. Focuses on writing in mathematics. Reviews prior mathematical work with “Preview Activities” at the start of each section. Includes “Activities” throughout that relate to the material contained in each section. Focuses on Congruence Notation and Elementary Number Theorythroughout.For professionals in the sciences or engineering who need to brush up on their advanced mathematics skills. Mathematical Reasoning: Writing and Proof, 2/E Theodore Sundstrom
Book Synopsis Basic Category Theory for Computer Scientists by : Benjamin C. Pierce
Download or read book Basic Category Theory for Computer Scientists written by Benjamin C. Pierce and published by MIT Press. This book was released on 1991-08-07 with total page 117 pages. Available in PDF, EPUB and Kindle. Book excerpt: Basic Category Theory for Computer Scientists provides a straightforward presentation of the basic constructions and terminology of category theory, including limits, functors, natural transformations, adjoints, and cartesian closed categories. Category theory is a branch of pure mathematics that is becoming an increasingly important tool in theoretical computer science, especially in programming language semantics, domain theory, and concurrency, where it is already a standard language of discourse. Assuming a minimum of mathematical preparation, Basic Category Theory for Computer Scientists provides a straightforward presentation of the basic constructions and terminology of category theory, including limits, functors, natural transformations, adjoints, and cartesian closed categories. Four case studies illustrate applications of category theory to programming language design, semantics, and the solution of recursive domain equations. A brief literature survey offers suggestions for further study in more advanced texts. Contents Tutorial • Applications • Further Reading
Book Synopsis The Axiom of Choice by : Thomas J. Jech
Download or read book The Axiom of Choice written by Thomas J. Jech and published by Courier Corporation. This book was released on 2008-01-01 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: Comprehensive and self-contained text examines the axiom's relative strengths and consequences, including its consistency and independence, relation to permutation models, and examples and counterexamples of its use. 1973 edition.
Book Synopsis Types for Proofs and Programs by : Thorsten Altenkirch
Download or read book Types for Proofs and Programs written by Thorsten Altenkirch and published by Springer. This book was released on 2007-09-13 with total page 277 pages. Available in PDF, EPUB and Kindle. Book excerpt: The refereed post-proceedings of the International Workshop of the Types Working Group are presented in this volume. The 17 papers address all current issues in formal reasoning and computer programming based on type theory, including languages and computerized tools for reasoning; applications in several domains, such as analysis of programming languages; certified software; formalization of mathematics; and mathematics education.
Book Synopsis Types for Proofs and Programs by : Stefano Berardi
Download or read book Types for Proofs and Programs written by Stefano Berardi and published by Springer. This book was released on 2004-05-17 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: These proceedings contain a selection of refereed papers presented at or related to the 3rd Annual Workshop of the Types Working Group (Computer-Assisted Reasoning Based on Type Theory, EU IST project 29001), which was held d- ing April 30 to May 4, 2003, in Villa Gualino, Turin, Italy. The workshop was attended by about 100 researchers. Out of 37 submitted papers, 25 were selected after a refereeing process. The ?nal choices were made by the editors. Two previous workshops of the Types Working Group under EU IST project 29001 were held in 2000 in Durham, UK, and in 2002 in Berg en Dal (close to Nijmegen), The Netherlands. These workshops followed a series of meetings organized in the period 1993–2002 within previous Types projects (ESPRIT BRA 6435 and ESPRIT Working Group 21900). The proceedings of these e- lier workshops were also published in the LNCS series, as volumes 806, 996, 1158, 1512, 1657, 2277, and 2646. ESPRIT BRA 6453 was a continuation of ESPRIT Action 3245, Logical Frameworks: Design, Implementation and Ex- riments. Proceedings for annual meetings under that action were published by Cambridge University Press in the books “Logical Frameworks”, and “Logical Environments”, edited by G. Huet and G. Plotkin. We are very grateful to the members of the research group “Semantics and Logics of Computation” of the Computer Science Department of the University of Turin, who helped organize the Types 2003 meeting in Torino.
Book Synopsis Proofs and Algorithms by : Gilles Dowek
Download or read book Proofs and Algorithms written by Gilles Dowek and published by Springer Science & Business Media. This book was released on 2011-01-11 with total page 161 pages. Available in PDF, EPUB and Kindle. Book excerpt: Logic is a branch of philosophy, mathematics and computer science. It studies the required methods to determine whether a statement is true, such as reasoning and computation. Proofs and Algorithms: Introduction to Logic and Computability is an introduction to the fundamental concepts of contemporary logic - those of a proof, a computable function, a model and a set. It presents a series of results, both positive and negative, - Church's undecidability theorem, Gödel’s incompleteness theorem, the theorem asserting the semi-decidability of provability - that have profoundly changed our vision of reasoning, computation, and finally truth itself. Designed for undergraduate students, this book presents all that philosophers, mathematicians and computer scientists should know about logic.
Book Synopsis Social Processes and Proofs of Theorems and Programs by : Richard A. Demillo
Download or read book Social Processes and Proofs of Theorems and Programs written by Richard A. Demillo and published by . This book was released on 1976 with total page 21 pages. Available in PDF, EPUB and Kindle. Book excerpt:
