An Introduction to Lambda Calculi for Computer Scientists

Author: Chris Hankin
Publisher: College Publications
ISBN: 9780954300654
Category : Computers
Languages : en
Pages : 164

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.

Lambda Calculi

Author: Chris Hankin
Publisher:
ISBN:
Category : Computers
Languages : en
Pages : 184

Book Description
This is a textbook for final year undergraduates/first year graduates in computer science, as well as a useful introduction for research students seeking a solid introduction to more specialist literature. This text emphasises the role of calculus in programming language design and implementation, denotational semantics, and domain theory. Alternative books on the subject have been written by logicians, but this is the first to have been written from a computer science prespective, invaluable in emphasising the practical relevance of the key theortical ideas.

Domains and Lambda-Calculi

Author: Roberto M. Amadio
Publisher: Cambridge University Press
ISBN: 0521622778
Category : Computers
Languages : en
Pages : 504

Book Description
Graduate text on mathematical foundations of programming languages, and operational and denotational semantics.

Lambda Calculus with Types

Author: Henk Barendregt
Publisher: Cambridge University Press
ISBN: 1107276349
Category : Mathematics
Languages : en
Pages : 969

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.

An Introduction to Functional Programming Through Lambda Calculus

Author: Greg Michaelson
Publisher: Courier Corporation
ISBN: 0486280292
Category : Mathematics
Languages : en
Pages : 338

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 and Combinators

Author: J. Roger Hindley
Publisher: Cambridge University Press
ISBN: 9780521898850
Category : Computers
Languages : en
Pages : 358

Book Description
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.

Lambda-calculus, Combinators and Functional Programming

Author: G. E. Revesz
Publisher: Cambridge University Press
ISBN: 9780521114295
Category : Computers
Languages : en
Pages : 0

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.

The Calculi of Lambda-conversion

Author: Alonzo Church
Publisher: Princeton University Press
ISBN: 9780691083940
Category : Mathematics
Languages : en
Pages : 112

Book Description
The description for this book, The Calculi of Lambda Conversion. (AM-6), Volume 6, will be forthcoming.

Basic Category Theory for Computer Scientists

Author: Benjamin C. Pierce
Publisher: MIT Press
ISBN: 0262326450
Category : Computers
Languages : en
Pages : 117

Book Description
Basic Category Theory for Computer Scientists provides a straightforward presentation of the basic constructions and terminology of category theory, including limits, functors, natural transformations, adjoints, and cartesian closed categories. Category theory is a branch of pure mathematics that is becoming an increasingly important tool in theoretical computer science, especially in programming language semantics, domain theory, and concurrency, where it is already a standard language of discourse. Assuming a minimum of mathematical preparation, Basic Category Theory for Computer Scientists provides a straightforward presentation of the basic constructions and terminology of category theory, including limits, functors, natural transformations, adjoints, and cartesian closed categories. Four case studies illustrate applications of category theory to programming language design, semantics, and the solution of recursive domain equations. A brief literature survey offers suggestions for further study in more advanced texts. Contents Tutorial • Applications • Further Reading

Central European Functional Programming School

Author: Zoltán Horváth
Publisher: Springer Science & Business Media
ISBN: 3540880585
Category : Computers
Languages : en
Pages : 309

Book Description
This volume presents eight carefully revised texts from selected lectures given by leading researchers at the Second Central European Functional Programming School, CEFP 2007, held in Cluj-Napoca, Romania, in June 2007. The eight revised full papers presented were carefully selected during two rounds of reviewing and improvement for inclusion in the book. The lectures cover a wide range of topics such as interactive workflows, lazy functional programs, lambda calculus, and object-oriented functional programming.