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Introduction to Combinators and (lambda) Calculus

Author : J. R. Hindley

Publisher : CUP Archive

Page : 376 pages

File Size : 35,72 MB

Release : 1986-05-29

Category : Mathematics

ISBN : 9780521318396

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Book Description

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

Author : G. E. Revesz

Publisher : Cambridge University Press

Page : 0 pages

File Size : 46,68 MB

Release : 2009-06-25

Category : Computers

ISBN : 9780521114295

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Book Description

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

Author : Greg Michaelson

Publisher : Courier Corporation

Page : 338 pages

File Size : 19,56 MB

Release : 2013-04-10

Category : Mathematics

ISBN : 0486280292

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Book Description

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

Author : Henk Barendregt

Publisher : Cambridge University Press

Page : 969 pages

File Size : 26,18 MB

Release : 2013-06-20

Category : Mathematics

ISBN : 1107276349

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Book Description

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.



Introduction to Combinators and [lambda]-calculus

Author : J. Roger Hindley

Publisher : Cambridge [Cambridgeshire] ; New York : Cambridge University Press

Page : 360 pages

File Size : 13,71 MB

Release : 1986

Category : Mathematics

ISBN : 9780521318396

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Book Description

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 and Combinators

Author : J. Roger Hindley

Publisher : Cambridge University Press

Page : 346 pages

File Size : 16,32 MB

Release : 2008-07-24

Category : Computers

ISBN : 1139473247

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Book Description

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.



Lambda-Calculus and Combinators

Author : J. Roger Hindley

Publisher :

Page : 359 pages

File Size : 49,19 MB

Release : 2008

Category : Combinatory logic

ISBN : 9780511412363

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Book Description

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.



Basic Simple Type Theory

Author : J. Roger Hindley

Publisher : Cambridge University Press

Page : 200 pages

File Size : 28,94 MB

Release : 1997

Category : Computers

ISBN : 0521465184

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Book Description

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.



The Lambda Calculus

Author : H.P. Barendregt

Publisher : North Holland

Page : 648 pages

File Size : 43,50 MB

Release : 1984

Category : Mathematics

ISBN :

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Book Description

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.



An Introduction to Lambda Calculi for Computer Scientists

Author : Chris Hankin

Publisher : College Publications

Page : 164 pages

File Size : 16,31 MB

Release : 2004

Category : Computers

ISBN : 9780954300654

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Book Description

The lambda-calculus lies at the very foundations of computer science. Besides its historical role in computability theory it has had significant influence on programming language design and implementation, denotational semantics, and domain theory. The book emphasises the proof theory for the type-free lambda-calculus. The first six chapters concern this calculus and cover the basic theory, reduction, models, computability, and the relationship between the lambda-calculus and combinatory logic. Chapter 7 presents a variety of typed calculi; first the simply typed lambda-calculus, then Milner-style polymorphism and, finally, the polymorphic lambda-calculus. Chapter 8 concerns two variants of the type-free lambda-calculus that have appeared in the research literature: the lazy lambda-calculus, and the lambda sigma-calculus. The final chapter contains references and a guide to further reading. There are exercises throughout. In contrast to earlier books on these topics, which were written by logicians, this book is written from a computer science perspective and emphasises the practical relevance of many of the key theoretical ideas. The book is intended as a course text for final year undergraduates or first year graduate students in computer science. Research students should find it a useful introduction to more specialist literature.