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Author: Fernando Ferreira
Publisher: Springer Science & Business Media
ISBN: 3642139612
Category : Computers
Languages : en
Pages : 464
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Book Description
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.
Author: Fernando Ferreira
Publisher: Springer Science & Business Media
ISBN: 3642139612
Category : Computers
Languages : en
Pages : 464
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Book Description
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.
Author: Samuel Mimram
Publisher:
ISBN:
Category :
Languages : en
Pages : 539
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Book Description
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.
Author: Konstantine Arkoudas
Publisher: MIT Press
ISBN: 0262342502
Category : Computers
Languages : en
Pages : 1223
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Book Description
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.
Author: Hendrik Pieter Barendregt
Publisher: Springer Science & Business Media
ISBN: 9783540580850
Category : Computers
Languages : en
Pages : 404
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Book Description
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.
Author: Daniel J. Velleman
Publisher: Cambridge University Press
ISBN: 0521861241
Category : Mathematics
Languages : en
Pages : 401
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Book Description
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.
Author: Jean-Pierre Jouannaud
Publisher: Springer Science & Business Media
ISBN: 3642253784
Category : Business & Economics
Languages : en
Pages : 414
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Book Description
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.
Author: Edsger W. Dijkstra
Publisher: Addison-Wesley Professional
ISBN:
Category : Computers
Languages : en
Pages : 264
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Book Description
In 1987, The University of Texas at Austin sponsored the Year of Programming, which consisted of six institutes on selected topics in computer programming. Leading scientists and practitioners were invited from around the world for lectures and tutorials, for discussion and collaboration. The general objectives of these institutes were to advance the art and science of programming and to disseminate the best of what is known about programming theory and practice.
Author: Thorsten Altenkirch
Publisher: Springer
ISBN: 3540744649
Category : Computers
Languages : en
Pages : 277
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Book Description
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.
Author: Benjamin C. Pierce
Publisher: MIT Press
ISBN: 0262326450
Category : Computers
Languages : en
Pages : 117
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Book Description
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
Author: Theodore A. Sundstrom
Publisher: Prentice Hall
ISBN: 9780131877184
Category : Logic, Symbolic and mathematical
Languages : en
Pages : 0
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Book Description
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
