The Lambda Calculus

Author: H.P. Barendregt
Publisher: North Holland
ISBN:
Category : Mathematics
Languages : en
Pages : 648

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.

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.

The Lambda Calculus

Author: Henk Barendregt
Publisher:
ISBN: 9781848900660
Category : Computers
Languages : en
Pages : 656

Book Description
The Lambda Calculus, treated in this book mainly in its untyped version, consists of a collection of expressions, called lambda terms, together with ways how to rewrite and identify these. In the parts conversion, reduction, theories, and models the view is respectively 'algebraic', computational, with more ('coinductive') identifications, and finally set-theoretic. The lambda terms are built up from variables, using application and abstraction. Applying a term F to M has as intention that F is a function, M its argument, and FM the result of the application. This is only the intention: to actually obtain the result one has to rewrite the expression FM according to the reduction rules. Abstraction provides a way to create functions according to the effect when applying them. The power of the theory comes from the fact that computations, both terminating and infinite, can be expressed by lambda terms at a 'comfortable' level of abstraction.

The Parametric Lambda Calculus

Author: Simona Ronchi Della Rocca
Publisher: Springer Science & Business Media
ISBN: 9783540200321
Category : Mathematics
Languages : en
Pages : 280

Book Description
The parametric lambda calculus is a metamodel for reasoning about various kinds of computations. Its syntactic definition is based on the notion of "sets of input values", and different lambda calculi can be obtained from it by instantiating such sets in suitable ways. The parametric lambda calculus is used as a tool for presenting in a uniform way basic notions of programming languages, and for studying with a uniform approach some lambda calculi modeling different kinds of computations, such as call-by-name, both in its lazy and non-lazy versions, and call-by-value. The parametric presentation allows us both to prove in one step all the fundamental properties of different calculi, and to compare them with each other. The book includes some classical results in the field of lambda calculi, but completely rephrased using the parametric approach, together with some new results. The lambda calculi are presented from a computer science viewpoint, with particular emphasis on their semantics, both operational and denotational. This book is dedicated to researchers, and can be used as a textbook for masters or Ph.D. courses on the foundations of computer science.

Semantic Techniques in Quantum Computation

Author: Simon Gay
Publisher: Cambridge University Press
ISBN: 052151374X
Category : Computers
Languages : en
Pages : 497

Book Description
Explores quantum computation from the perspective of the branch of theoretical computer science known as semantics.

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.

Semantics Engineering with PLT Redex

Author: Matthias Felleisen
Publisher: MIT Press
ISBN: 0262062755
Category : Computers
Languages : en
Pages : 515

Book Description
The first comprehensive presentation of reduction semantics in one volume, and the first tool set for such forms of semantics. This text is the first comprehensive presentation of reduction semantics in one volume; it also introduces the first reliable and easy-to-use tool set for such forms of semantics. Software engineers have long known that automatic tool support is critical for rapid prototyping and modeling, and this book is addressed to the working semantics engineer (graduate student or professional language designer). The book comes with a prototyping tool suite to develop, explore, test, debug, and publish semantic models of programming languages. With PLT Redex, semanticists can formulate models as grammars and reduction models on their computers with the ease of paper and pencil. The text first presents a framework for the formulation of language models, focusing on equational calculi and abstract machines, then introduces PLT Redex, a suite of software tools for expressing these models as PLT Redex models. Finally, experts describe a range of models formulated in Redex. PLT Redex comes with the PLT Scheme implementation, available free at http://www.plt-scheme.org/. Readers can download the software and experiment with Redex as they work their way through the book.

Lecture Notes on the Lambda Calculus

Author: Peter Selinger
Publisher:
ISBN: 9780359158850
Category : Science
Languages : en
Pages : 108

Book Description
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.