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.
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 346 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 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.
Download or read book Lambda calculus Combinators and Functional Programming written by G. E. Revesz and published by Cambridge University Press. This book was released on 2009-06-25 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Originally published in 1988, this book presents an introduction to lambda-calculus and combinators without getting lost in the details of mathematical aspects of their theory. Lambda-calculus is treated here as a functional language and its relevance to computer science is clearly demonstrated. The main purpose of the book is to provide computer science students and researchers with a firm background in lambda-calculus and combinators and show the applicabillity of these theories to functional programming. The presentation of the material is self-contained. It can be used as a primary text for a course on functional programming. It can also be used as a supplementary text for courses on the structure and implementation of programming languages, theory of computing, or semantics of programming languages.
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.
Download or read book Lambda Calculus with Types written by Henk Barendregt and published by Cambridge University Press. This book was released on 2013-06-20 with total page 969 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book An Introduction to Functional Programming Through Lambda Calculus written by Greg Michaelson and published by Courier Corporation. This book was released on 2013-04-10 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: Well-respected text for computer science students provides an accessible introduction to functional programming. Cogent examples illuminate the central ideas, and numerous exercises offer reinforcement. Includes solutions. 1989 edition.
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:
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.
Download or read book The Lambda Calculus written by H.P. Barendregt and published by North Holland. This book was released on 1984 with total page 648 pages. Available in PDF, EPUB and Kindle. Book excerpt: The revised edition contains a new chapter which provides an elegant description of the semantics. The various classes of lambda calculus models are described in a uniform manner. Some didactical improvements have been made to this edition. An example of a simple model is given and then the general theory (of categorical models) is developed. Indications are given of those parts of the book which can be used to form a coherent course.
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.
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.
Download or read book Basic Simple Type Theory written by J. Roger Hindley and published by Cambridge University Press. This book was released on 1997 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: Type theory is one of the most important tools in the design of higher-level programming languages, such as ML. This book introduces and teaches its techniques by focusing on one particularly neat system and studying it in detail. By concentrating on the principles that make the theory work in practice, the author covers all the key ideas without getting involved in the complications of more advanced systems. This book takes a type-assignment approach to type theory, and the system considered is the simplest polymorphic one. The author covers all the basic ideas, including the system's relation to propositional logic, and gives a careful treatment of the type-checking algorithm that lies at the heart of every such system. Also featured are two other interesting algorithms that until now have been buried in inaccessible technical literature. The mathematical presentation is rigorous but clear, making it the first book at this level that can be used as an introduction to type theory for computer scientists.
Download or read book Lecture Notes on the Lambda Calculus written by Peter Selinger and published by . This book was released on 2018-10-04 with total page 108 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a set of lecture notes that developed out of courses on the lambda calculus that the author taught at the University of Ottawa in 2001 and at Dalhousie University in 2007 and 2013. Topics covered in these notes include the untyped lambda calculus, the Church-Rosser theorem, combinatory algebras, the simply-typed lambda calculus, the Curry-Howard isomorphism, weak and strong normalization, polymorphism, type inference, denotational semantics, complete partial orders, and the language PCF.
Download or read book Combinators written by Stephen Wolfram and published by Wolfram Media. This book was released on 2021 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Combinators have inspired ideas about computation ever since they were first invented in 1920, and in this innovative book, Stephen Wolfram provides a modern view of combinators and their significance. Informed by his work on the computational universe of possible programs and on computational language design, Wolfram explains new and existing ideas about combinators with unique clarity and stunning visualizations, as well as provides insights on their historical connections and the curious story of Moses Schèonfinkel, inventor of combinators. Though invented well before Turing machines, combinators have often been viewed as an inaccessibly abstract approach to computation. This book brings them to life as never before in a thought-provoking and broadly accessible exposition of interest across mathematics and computer science, as well as to those concerned with the foundations of formal and computational thinking, and with the history of ideas"--
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
Download or read book Lambda calculus Types and Models written by Jean Louis Krivine and published by Prentice Hall. This book was released on 1993 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introduction to lambda-calculus looks at aspects of the theory: combinatory logic, models, and type streams, showing how they interlink and underpin computer science.
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.
