Wellfounded And Non Wellfounded Types Of Continuous Functionals
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Wellfounded And Non Wellfounded Types Of Continuous Functionals
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Author : Dag Normann
language : en
Publisher:
Release Date : 1992
Wellfounded And Non Wellfounded Types Of Continuous Functionals written by Dag Normann and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Functions, Continuous categories.
Computability Enumerability Unsolvability
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Author : S. B. Cooper
language : en
Publisher: Cambridge University Press
Release Date : 1996-01-11
Computability Enumerability Unsolvability written by S. B. Cooper and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-01-11 with Mathematics categories.
The fundamental ideas concerning computation and recursion naturally find their place at the interface between logic and theoretical computer science. The contributions in this book, by leaders in the field, provide a picture of current ideas and methods in the ongoing investigations into the pure mathematical foundations of computability theory. The topics range over computable functions, enumerable sets, degree structures, complexity, subrecursiveness, domains and inductive inference. A number of the articles contain introductory and background material which it is hoped will make this volume an invaluable resource.
Models And Computability
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Author : S. Barry Cooper
language : en
Publisher: Cambridge University Press
Release Date : 1999-06-17
Models And Computability written by S. Barry Cooper and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-06-17 with Computers categories.
Second of two volumes providing a comprehensive guide to the current state of mathematical logic.
Typed Lambda Calculi And Applications
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Author : Jean-Yves Girard
language : en
Publisher: Springer
Release Date : 2003-07-31
Typed Lambda Calculi And Applications written by Jean-Yves Girard and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-07-31 with Computers categories.
This book constitutes the refereed proceedings of the 4th International Conference on Typed Lambda Calculi and Applications, TLCA'99, held in L'Aquila, Italy in April 1999. The 25 revised full papers presented were carefully reviewed and selected from a total of 50 submissions. Also included are two invited demonstrations. The volume reports research results on various aspects of typed lambda calculi. Among the topics addressed are noncommutative logics, type theory, algebraic data types, logical calculi, abstract data types, and subtyping.
Handbook Of Computability Theory
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Author : E.R. Griffor
language : en
Publisher: Elsevier
Release Date : 1999-10-01
Handbook Of Computability Theory written by E.R. Griffor and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-10-01 with Mathematics categories.
The chapters of this volume all have their own level of presentation. The topics have been chosen based on the active research interest associated with them. Since the interest in some topics is older than that in others, some presentations contain fundamental definitions and basic results while others relate very little of the elementary theory behind them and aim directly toward an exposition of advanced results. Presentations of the latter sort are in some cases restricted to a short survey of recent results (due to the complexity of the methods and proofs themselves). Hence the variation in level of presentation from chapter to chapter only reflects the conceptual situation itself. One example of this is the collective efforts to develop an acceptable theory of computation on the real numbers. The last two decades has seen at least two new definitions of effective operations on the real numbers.
Foundations Of Software Science And Computation Structures
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Author : Bart Jacobs
language : en
Publisher: Springer
Release Date : 2016-03-22
Foundations Of Software Science And Computation Structures written by Bart Jacobs and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-03-22 with Computers categories.
This book constitutes the proceedings of the 19th International Conference on Foundations of Software Science and Computation Structures, FOSSACS 2016, which took place in Eindhoven, The Netherlands, in April 2016, held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2016. The 31 full papers presented in this volume were carefully reviewed and selected from 85 submissions. They were organized in topical sections named: types; recursion and fixed-points; verification and program analysis; automata, logic, games; probabilistic and timed systems; proof theory and lambda calculus; algorithms for infinite systems; and monads.
From Sets And Types To Topology And Analysis
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Author : Laura Crosilla
language : en
Publisher: Clarendon Press
Release Date : 2005-10-06
From Sets And Types To Topology And Analysis written by Laura Crosilla and has been published by Clarendon Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-10-06 with Mathematics categories.
This edited collection bridges the foundations and practice of constructive mathematics and focusses on the contrast between the theoretical developments, which have been most useful for computer science (eg constructive set and type theories), and more specific efforts on constructive analysis, algebra and topology. Aimed at academic logicians, mathematicians, philosophers and computer scientists Including, with contributions from leading researchers, it is up-to-date, highly topical and broad in scope. This is the latest volume in the Oxford Logic Guides, which also includes: 41. J.M. Dunn and G. Hardegree: Algebraic Methods in Philosophical Logic 42. H. Rott: Change, Choice and Inference: A study of belief revision and nonmonotoic reasoning 43. Johnstone: Sketches of an Elephant: A topos theory compendium, volume 1 44. Johnstone: Sketches of an Elephant: A topos theory compendium, volume 2 45. David J. Pym and Eike Ritter: Reductive Logic and Proof Search: Proof theory, semantics and control 46. D.M. Gabbay and L. Maksimova: Interpolation and Definability: Modal and Intuitionistic Logics 47. John L. Bell: Set Theory: Boolean-valued models and independence proofs, third edition
Lambda Calculus With Types
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Author : Henk Barendregt
language : en
Publisher: Cambridge University Press
Release Date : 2013-06-20
Lambda Calculus With Types written by Henk Barendregt and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-20 with Mathematics categories.
This handbook with exercises reveals in formalisms, hitherto mainly used for hardware and software design and verification, unexpected mathematical beauty. The lambda calculus forms a prototype universal programming language, which in its untyped version is related to Lisp, and was treated in the first author's classic The Lambda Calculus (1984). The formalism has since been extended with types and used in functional programming (Haskell, Clean) and proof assistants (Coq, Isabelle, HOL), used in designing and verifying IT products and mathematical proofs. In this book, the authors focus on three classes of typing for lambda terms: simple types, recursive types and intersection types. It is in these three formalisms of terms and types that the unexpected mathematical beauty is revealed. The treatment is authoritative and comprehensive, complemented by an exhaustive bibliography, and numerous exercises are provided to deepen the readers' understanding and increase their confidence using types.
Concepts Of Proof In Mathematics Philosophy And Computer Science
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Author : Dieter Probst
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2016-07-25
Concepts Of Proof In Mathematics Philosophy And Computer Science written by Dieter Probst and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-07-25 with Philosophy categories.
A proof is a successful demonstration that a conclusion necessarily follows by logical reasoning from axioms which are considered evident for the given context and agreed upon by the community. It is this concept that sets mathematics apart from other disciplines and distinguishes it as the prototype of a deductive science. Proofs thus are utterly relevant for research, teaching and communication in mathematics and of particular interest for the philosophy of mathematics. In computer science, moreover, proofs have proved to be a rich source for already certified algorithms. This book provides the reader with a collection of articles covering relevant current research topics circled around the concept 'proof'. It tries to give due consideration to the depth and breadth of the subject by discussing its philosophical and methodological aspects, addressing foundational issues induced by Hilbert's Programme and the benefits of the arising formal notions of proof, without neglecting reasoning in natural language proofs and applications in computer science such as program extraction.
Higher Order Computability
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Author : John Longley
language : en
Publisher: Springer
Release Date : 2015-11-06
Higher Order Computability written by John Longley and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-11-06 with Computers categories.
This book offers a self-contained exposition of the theory of computability in a higher-order context, where 'computable operations' may themselves be passed as arguments to other computable operations. The subject originated in the 1950s with the work of Kleene, Kreisel and others, and has since expanded in many different directions under the influence of workers from both mathematical logic and computer science. The ideas of higher-order computability have proved valuable both for elucidating the constructive content of logical systems, and for investigating the expressive power of various higher-order programming languages. In contrast to the well-known situation for first-order functions, it turns out that at higher types there are several different notions of computability competing for our attention, and each of these has given rise to its own strand of research. In this book, the authors offer an integrated treatment that draws together many of these strands within a unifying framework, revealing not only the range of possible computability concepts but the relationships between them. The book will serve as an ideal introduction to the field for beginning graduate students, as well as a reference for advanced researchers