Introduction to Combinators and (lambda) Calculus

Introduction to Combinators and (lambda) Calculus
Title Introduction to Combinators and (lambda) Calculus PDF eBook
Author J. R. Hindley
Publisher CUP Archive
Pages 376
Release 1986-05-29
Genre Mathematics
ISBN 9780521318396

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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.

Lambda-calculus, Combinators and Functional Programming

Lambda-calculus, Combinators and Functional Programming
Title Lambda-calculus, Combinators and Functional Programming PDF eBook
Author G. E. Revesz
Publisher Cambridge University Press
Pages 0
Release 2009-06-25
Genre Computers
ISBN 9780521114295

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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.

An Introduction to Functional Programming Through Lambda Calculus

An Introduction to Functional Programming Through Lambda Calculus
Title An Introduction to Functional Programming Through Lambda Calculus PDF eBook
Author Greg Michaelson
Publisher Courier Corporation
Pages 338
Release 2013-04-10
Genre Mathematics
ISBN 0486280292

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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.

Lambda Calculus with Types

Lambda Calculus with Types
Title Lambda Calculus with Types PDF eBook
Author Henk Barendregt
Publisher Cambridge University Press
Pages 969
Release 2013-06-20
Genre Mathematics
ISBN 1107276349

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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.

Combinators

Combinators
Title Combinators PDF eBook
Author Sören Stenlund
Publisher
Pages 194
Release 1972
Genre Combinatory logic
ISBN

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To Mock a Mockingbird

To Mock a Mockingbird
Title To Mock a Mockingbird PDF eBook
Author Raymond M. Smullyan
Publisher Oxford University Press, USA
Pages 258
Release 2000
Genre Games & Activities
ISBN 0192801422

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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.

Lambda-Calculus and Combinators

Lambda-Calculus and Combinators
Title Lambda-Calculus and Combinators PDF eBook
Author J. Roger Hindley
Publisher Cambridge University Press
Pages 346
Release 2008-07-24
Genre Computers
ISBN 1139473247

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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.