Combinatory Logic

Author : Katalin Bimbó
Publisher : CRC Press
ISBN 13 : 1439800006
Total Pages : 359 pages
Book Rating : 4.03/5 ( download)

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Download or read book Combinatory Logic written by Katalin Bimbó and published by CRC Press. This book was released on 2011-07-27 with total page 359 pages. Available in PDF, EPUB and Kindle. Book excerpt: Combinatory logic is one of the most versatile areas within logic that is tied to parts of philosophical, mathematical, and computational logic. Functioning as a comprehensive source for current developments of combinatory logic, this book is the only one of its kind to cover results of the last four decades. Using a reader-friendly style, the author presents the most up-to-date research studies. She includes an introduction to combinatory logic before progressing to its central theorems and proofs. The text makes intelligent and well-researched connections between combinatory logic and lambda calculi and presents models and applications to illustrate these connections.

Author : J. Roger Hindley
Publisher :
ISBN 13 : 9780511414909
Total Pages : 359 pages
Book Rating : 4.00/5 ( download)

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Download or read book Lambda-Calculus and Combinators written by J. Roger Hindley and published by . This book was released on 2008 with total page 359 pages. Available in PDF, EPUB and Kindle. Book excerpt: Combinatory logic and lambda-calculus, originally devised in the 1920s, have since developed into linguistic tools, especially useful in programming languages. The authors' previous book served as the main reference for introductory courses on lambda-calculus for over 20 years: this version is thoroughly revised and offers an account of the subject with the same authoritative exposition. The grammar and basic properties of both combinatory logic and lambda-calculus are discussed, followed by an introduction to type-theory. Typed and untyped versions of the systems, and their differences, are c.

Author : J. Roger Hindley
Publisher : CUP Archive
ISBN 13 : 9780521096973
Total Pages : 182 pages
Book Rating : 4.79/5 ( download)

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Download or read book Introduction to Combinatory Logic written by J. Roger Hindley and published by CUP Archive. This book was released on 1972-06 with total page 182 pages. Available in PDF, EPUB and Kindle. Book excerpt: These notes present some of the basic techniques and results in the subject of combinatory logic. This subject will first be treated with an introduction via lambda-conversion. Chapter two is an introduction to combinators. Chapters three and four will deal with recursive functions. Chapters five, six, and seven deal with extensional theory of combinators. Chapters nine and ten deal with combinator-based systems of logic . Chapters eight and eleven deal with proof-theoretic application.

Author : Raymond M. Smullyan
Publisher : Oxford University Press, USA
ISBN 13 : 0192801422
Total Pages : 258 pages
Book Rating : 4.25/5 ( download)

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Download or read book To Mock a Mockingbird written by Raymond M. Smullyan and published by Oxford University Press, USA. This book was released on 2000 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: The author of Forever Undecided, Raymond Smullyan continues to delight and astonish us with his gift for making available, in the thoroughly pleasurable form of puzzles, some of the most important mathematical thinking of our time.

Author : Katalin Bimbo
Publisher : CRC Press
ISBN 13 : 1439800014
Total Pages : 357 pages
Book Rating : 4.10/5 ( download)

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Download or read book Combinatory Logic written by Katalin Bimbo and published by CRC Press. This book was released on 2011-07-27 with total page 357 pages. Available in PDF, EPUB and Kindle. Book excerpt: Combinatory logic is one of the most versatile areas within logic that is tied to parts of philosophical, mathematical, and computational logic. Functioning as a comprehensive source for current developments of combinatory logic, this book is the only one of its kind to cover results of the last four decades. Using a reader-friendly style, the auth

Author : P.-L. Curien
Publisher : Springer Science & Business Media
ISBN 13 : 1461203171
Total Pages : 425 pages
Book Rating : 4.79/5 ( download)

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Download or read book Categorical Combinators, Sequential Algorithms, and Functional Programming written by P.-L. Curien and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 425 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a revised edition of the monograph which appeared under the same title in the series Research Notes in Theoretical Computer Science, Pit man, in 1986. In addition to a general effort to improve typography, English, and presentation, the main novelty of this second edition is the integration of some new material. Part of it is mine (mostly jointly with coauthors). Here is brief guide to these additions. I have augmented the account of categorical combinatory logic with a description of the confluence properties of rewriting systems of categor ical combinators (Hardin, Yokouchi), and of the newly developed cal culi of explicit substitutions (Abadi, Cardelli, Curien, Hardin, Levy, and Rios), which are similar in spirit to the categorical combinatory logic, but are closer to the syntax of A-calculus (Section 1.2). The study of the full abstraction problem for PCF and extensions of it has been enriched with a new full abstraction result: the model of sequential algorithms is fully abstract with respect to an extension of PCF with a control operator (Cartwright, Felleisen, Curien). An order extensional model of error-sensitive sequential algorithms is also fully abstract for a corresponding extension of PCF with a control operator and errors (Sections 2.6 and 4.1). I suggest that sequential algorithms lend themselves to a decomposition of the function spaces that leads to models of linear logic (Lamarche, Curien), and that connects sequentiality with games (Joyal, Blass, Abramsky) (Sections 2.1 and 2.6).

Author : Haskell Brooks Curry
Publisher : Courier Corporation
ISBN 13 : 9780486634623
Total Pages : 420 pages
Book Rating : 4.20/5 ( download)

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Download or read book Foundations of Mathematical Logic written by Haskell Brooks Curry and published by Courier Corporation. This book was released on 1977-01-01 with total page 420 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written by a pioneer of mathematical logic, this comprehensive graduate-level text explores the constructive theory of first-order predicate calculus. It covers formal methods — including algorithms and epitheory — and offers a brief treatment of Markov's approach to algorithms. It also explains elementary facts about lattices and similar algebraic systems. 1963 edition.

Author : Cem Bozsahin
Publisher : Walter de Gruyter
ISBN 13 : 311029687X
Total Pages : 304 pages
Book Rating : 4.77/5 ( download)

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Download or read book Combinatory Linguistics written by Cem Bozsahin and published by Walter de Gruyter. This book was released on 2012-12-06 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book examines to what extent the mediating relation between constituents and their semantics can arise from combinatory knowledge of words. It traces the roots of Combinatory Categorial Grammar, and uses the theory to promote a Humean question in linguistics and cognitive science: Why do we see limited constituency and dependency in natural languages, despite their diversity and potential infinity? A potential answer is that constituents and dependencies might have arisen from a single resource: adjacency. The combinatory formulation of adjacency constrains possible grammars.

Author : Morten Heine Sørensen
Publisher : Elsevier
ISBN 13 : 0080478921
Total Pages : 457 pages
Book Rating : 4.20/5 ( download)

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Download or read book Lectures on the Curry-Howard Isomorphism written by Morten Heine Sørensen and published by Elsevier. This book was released on 2006-07-04 with total page 457 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Curry-Howard isomorphism states an amazing correspondence between systems of formal logic as encountered in proof theory and computational calculi as found in type theory. For instance,minimal propositional logic corresponds to simply typed lambda-calculus, first-order logic corresponds to dependent types, second-order logic corresponds to polymorphic types, sequent calculus is related to explicit substitution, etc.The isomorphism has many aspects, even at the syntactic level:formulas correspond to types, proofs correspond to terms, provability corresponds to inhabitation, proof normalization corresponds to term reduction, etc.But there is more to the isomorphism than this. For instance, it is an old idea---due to Brouwer, Kolmogorov, and Heyting---that a constructive proof of an implication is a procedure that transformsproofs of the antecedent into proofs of the succedent; the Curry-Howard isomorphism gives syntactic representations of such procedures. The Curry-Howard isomorphism also provides theoretical foundations for many modern proof-assistant systems (e.g. Coq).This book give an introduction to parts of proof theory and related aspects of type theory relevant for the Curry-Howard isomorphism. It can serve as an introduction to any or both of typed lambda-calculus and intuitionistic logic. Key features- The Curry-Howard Isomorphism treated as common theme- Reader-friendly introduction to two complementary subjects: Lambda-calculus and constructive logics- Thorough study of the connection between calculi and logics- Elaborate study of classical logics and control operators- Account of dialogue games for classical and intuitionistic logic- Theoretical foundations of computer-assisted reasoning · The Curry-Howard Isomorphism treated as the common theme.· Reader-friendly introduction to two complementary subjects: lambda-calculus and constructive logics · Thorough study of the connection between calculi and logics.· Elaborate study of classical logics and control operators.· Account of dialogue games for classical and intuitionistic logic.· Theoretical foundations of computer-assisted reasoning

Author : V.E. Wolfengagen
Publisher : ООО «ЮрИнфоР-Пресс»
ISBN 13 : 5891581779
Total Pages : 15 pages
Book Rating : 4.77/5 ( download)

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Download or read book Applicative computing Its quarks, atoms and molecules written by V.E. Wolfengagen and published by ООО «ЮрИнфоР-Пресс». This book was released on 2010 with total page 15 pages. Available in PDF, EPUB and Kindle. Book excerpt: