Combinatory Logic

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Lambda-Calculus and Combinators

Author : J. Roger Hindley
Publisher : Cambridge University Press
ISBN 13 : 9780521898850
Total Pages : 358 pages
Book Rating : 4.8/5 (988 download)

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Book Synopsis Lambda-Calculus and Combinators by : J. Roger Hindley

Download or read book Lambda-Calculus and Combinators written by J. Roger Hindley and published by Cambridge University Press. This book was released on 2008-07-24 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt: Combinatory logic and lambda-calculus, originally devised in the 1920's, 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 long-awaited new version is thoroughly revised and offers a fully up-to-date 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 covered. Lambda-calculus models, which lie behind much of the semantics of programming languages, are also explained in depth. The treatment is as non-technical as possible, with the main ideas emphasized and illustrated by examples. Many exercises are included, from routine to advanced, with solutions to most at the end of the book.

Combinatory Logic

Author : Katalin Bimbo
Publisher : CRC Press
ISBN 13 : 1439800014
Total Pages : 357 pages
Book Rating : 4.4/5 (398 download)

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Book Synopsis Combinatory Logic by : Katalin Bimbo

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

Introduction to Combinatory Logic

Author : J. Roger Hindley
Publisher : CUP Archive
ISBN 13 : 9780521096973
Total Pages : 182 pages
Book Rating : 4.0/5 (969 download)

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Book Synopsis Introduction to Combinatory Logic by : J. Roger Hindley

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.

Combinatory Logic

Author : Katalin Bimbó
Publisher : CRC Press
ISBN 13 : 1439800006
Total Pages : 359 pages
Book Rating : 4.4/5 (398 download)

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Book Synopsis Combinatory Logic by : Katalin Bimbó

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.

To Mock a Mockingbird

Author : Raymond M. Smullyan
Publisher : Oxford University Press, USA
ISBN 13 : 0192801422
Total Pages : 258 pages
Book Rating : 4.1/5 (928 download)

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Book Synopsis To Mock a Mockingbird by : Raymond M. Smullyan

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.

Foundations of Mathematical Logic

Author : Haskell Brooks Curry
Publisher : Courier Corporation
ISBN 13 : 9780486634623
Total Pages : 420 pages
Book Rating : 4.6/5 (346 download)

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Book Synopsis Foundations of Mathematical Logic by : Haskell Brooks Curry

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.

Introduction to Combinatory Logic

Author : Sören Stenlund
Publisher :
ISBN 13 :
Total Pages : 238 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Introduction to Combinatory Logic by : Sören Stenlund

Download or read book Introduction to Combinatory Logic written by Sören Stenlund and published by . This book was released on 1971 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Categorical Combinators, Sequential Algorithms, and Functional Programming

Author : P.-L. Curien
Publisher : Springer Science & Business Media
ISBN 13 : 9780817636548
Total Pages : 434 pages
Book Rating : 4.6/5 (365 download)

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Book Synopsis Categorical Combinators, Sequential Algorithms, and Functional Programming by : P.-L. Curien

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 1993-01-01 with total page 434 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).

Randomness and Complexity

Author : Cristian Calude
Publisher : World Scientific
ISBN 13 : 9812770828
Total Pages : 466 pages
Book Rating : 4.8/5 (127 download)

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Book Synopsis Randomness and Complexity by : Cristian Calude

Download or read book Randomness and Complexity written by Cristian Calude and published by World Scientific. This book was released on 2007 with total page 466 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is a collection of papers written by a selection of eminent authors from around the world in honour of Gregory Chaitin's 60th birthday. This is a unique volume including technical contributions, philosophical papers and essays.

Introduction to Combinators and (lambda) Calculus

Author : J. R. Hindley
Publisher : CUP Archive
ISBN 13 : 9780521318396
Total Pages : 376 pages
Book Rating : 4.3/5 (183 download)

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Book Synopsis Introduction to Combinators and (lambda) Calculus by : J. R. Hindley

Download or read book Introduction to Combinators and (lambda) Calculus written by J. R. Hindley and published by CUP Archive. This book was released on 1986-05-29 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: Combinatory logic and lambda-conversion were originally devised in the 1920s for investigating the foundations of mathematics using the basic concept of 'operation' instead of 'set'. They have now developed into linguistic tools, useful in several branches of logic and computer science, especially in the study of programming languages. These notes form a simple introduction to the two topics, suitable for a reader who has no previous knowledge of combinatory logic, but has taken an undergraduate course in predicate calculus and recursive functions. The key ideas and basic results are presented, as well as a number of more specialised topics, and man), exercises are included to provide manipulative practice.

Lectures on the Curry-Howard Isomorphism

Author : Morten Heine Sørensen
Publisher : Elsevier
ISBN 13 : 0080478921
Total Pages : 457 pages
Book Rating : 4.0/5 (84 download)

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Book Synopsis Lectures on the Curry-Howard Isomorphism by : Morten Heine Sørensen

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

Combinatory Linguistics

Author : Cem Bozsahin
Publisher : Walter de Gruyter
ISBN 13 : 311029687X
Total Pages : 304 pages
Book Rating : 4.1/5 (12 download)

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Book Synopsis Combinatory Linguistics by : Cem Bozsahin

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.

Combinatory Logic

Author : Haskell Brooks Curry
Publisher :
ISBN 13 :
Total Pages : 544 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Combinatory Logic by : Haskell Brooks Curry

Download or read book Combinatory Logic written by Haskell Brooks Curry and published by . This book was released on 1958 with total page 544 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Combinators

Author : Sören Stenlund
Publisher :
ISBN 13 :
Total Pages : 194 pages
Book Rating : 4.:/5 (26 download)

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Book Synopsis Combinators by : Sören Stenlund

Download or read book Combinators written by Sören Stenlund and published by . This book was released on 1972 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt:

A Beginner's Further Guide To Mathematical Logic

Author : Raymond M Smullyan
Publisher : World Scientific Publishing Company
ISBN 13 : 9814733016
Total Pages : 288 pages
Book Rating : 4.8/5 (147 download)

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Book Synopsis A Beginner's Further Guide To Mathematical Logic by : Raymond M Smullyan

Download or read book A Beginner's Further Guide To Mathematical Logic written by Raymond M Smullyan and published by World Scientific Publishing Company. This book was released on 2016-11-11 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: 'A wealth of examples to which solutions are given permeate the text so the reader will certainly be active.'The Mathematical GazetteThis is the final book written by the late great puzzle master and logician, Dr. Raymond Smullyan.This book is a sequel to my Beginner's Guide to Mathematical Logic.The previous volume deals with elements of propositional and first-order logic, contains a bit on formal systems and recursion, and concludes with chapters on Gödel's famous incompleteness theorem, along with related results.The present volume begins with a bit more on propositional and first-order logic, followed by what I would call a 'fein' chapter, which simultaneously generalizes some results from recursion theory, first-order arithmetic systems, and what I dub a 'decision machine.' Then come five chapters on formal systems, recursion theory and metamathematical applications in a general setting. The concluding five chapters are on the beautiful subject of combinatory logic, which is not only intriguing in its own right, but has important applications to computer science. Argonne National Laboratory is especially involved in these applications, and I am proud to say that its members have found use for some of my results in combinatory logic.This book does not cover such important subjects as set theory, model theory, proof theory, and modern developments in recursion theory, but the reader, after studying this volume, will be amply prepared for the study of these more advanced topics.

Set Theory Based on Combinatory Logic

Author : Maarten Wicher Visser Bunder
Publisher :
ISBN 13 :
Total Pages : 96 pages
Book Rating : 4.:/5 (26 download)

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Book Synopsis Set Theory Based on Combinatory Logic by : Maarten Wicher Visser Bunder

Download or read book Set Theory Based on Combinatory Logic written by Maarten Wicher Visser Bunder and published by . This book was released on 1969 with total page 96 pages. Available in PDF, EPUB and Kindle. Book excerpt:

A New Kind of Science

Author : Stephen Wolfram
Publisher :
ISBN 13 : 9780713991161
Total Pages : 1197 pages
Book Rating : 4.9/5 (911 download)

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Book Synopsis A New Kind of Science by : Stephen Wolfram

Download or read book A New Kind of Science written by Stephen Wolfram and published by . This book was released on 2002 with total page 1197 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work presents a series of dramatic discoveries never before made public. Starting from a collection of simple computer experiments---illustrated in the book by striking computer graphics---Wolfram shows how their unexpected results force a whole new way of looking at the operation of our universe. Wolfram uses his approach to tackle a remarkable array of fundamental problems in science: from the origin of the Second Law of thermodynamics, to the development of complexity in biology, the computational limitations of mathematics, the possibility of a truly fundamental theory of physics, and the interplay between free will and determinism.