Search Results: lambda-calculus-and-combinators-an-introduction

Introduction to Combinators and (lambda) Calculus

Author: J. R. Hindley,J. P. Seldin

Publisher: CUP Archive

ISBN: 9780521268967

Category: Mathematics

Page: 360

View: 2183

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

An Introduction

Author: J. Roger Hindley,Jonathan P. Seldin

Publisher: Cambridge University Press

ISBN: 1139473247

Category: Computers

Page: N.A

View: 3200

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, Combinators and Functional Programming

Author: G. E. Revesz

Publisher: Cambridge University Press

ISBN: 9780521114295

Category: Computers

Page: 192

View: 5480

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

ISBN: 0486280292

Category: Mathematics

Page: 336

View: 8469

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.

Combinatory Logic

Pure, Applied and Typed

Author: Katalin Bimbó

Publisher: CRC Press

ISBN: 1439800006

Category: Computers

Page: 357

View: 7681

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.

Introduction to Combinatory Logic

Author: J. Roger Hindley,B. Lercher,J. P. Seldin

Publisher: CUP Archive

ISBN: 9780521096973

Category: Combinations

Page: 170

View: 8352

Lambda Calculus with Types

Author: Henk Barendregt,Wil Dekkers,Richard Statman

Publisher: Cambridge University Press

ISBN: 1107276349

Category: Mathematics

Page: N.A

View: 1061

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.

Basic Simple Type Theory

Author: J. Roger Hindley

Publisher: Cambridge University Press

ISBN: 9780521465182

Category: Computers

Page: 186

View: 2100

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

Its Syntax and Semantics

Author: H.P. Barendregt

Publisher: Elsevier

ISBN: 9780080933757

Category: Mathematics

Page: 654

View: 2951

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 Calculi

A Guide for Computer Scientists

Author: Chris Hankin

Publisher: Oxford University Press, USA

ISBN: 9780198538417

Category: Mathematics

Page: 162

View: 3105

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 emphasizes 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 three variants of the type-free [lambda]-calculus that have recently appeared in the research literature: the lazy [lambda]-calculus, the concurrent [gamma]-calculus and the [lambda][sigma]-calculus. The final chapter contains references and a guide to further reading. There are exercises throughout.

Abstract Computing Machines

A Lambda Calculus Perspective

Author: Werner Kluge

Publisher: Springer Science & Business Media

ISBN: 354027359X

Category: Computers

Page: 384

View: 1907

The book emphasizes the design of full-fledged, fully normalizing lambda calculus machinery, as opposed to the just weakly normalizing machines.

Interactive Theorem Proving and Program Development

Coq’Art: The Calculus of Inductive Constructions

Author: Yves Bertot,Pierre Castéran

Publisher: Springer Science & Business Media

ISBN: 366207964X

Category: Mathematics

Page: 472

View: 7880

A practical introduction to the development of proofs and certified programs using Coq. An invaluable tool for researchers, students, and engineers interested in formal methods and the development of zero-fault software.

Type-logical Semantics

Author: Bob Carpenter

Publisher: MIT Press

ISBN: 9780262531498

Category: Language Arts & Disciplines

Page: 575

View: 5509

The book, which stepwise develops successively more powerful logical and grammatical systems, covers an unusually broad range of material.

Types and Programming Languages

Author: Benjamin C. Pierce,Benjamin C. (Professor Pierce, University of Pennsylvania)

Publisher: MIT Press

ISBN: 9780262162098

Category: Computers

Page: 623

View: 5540

Mathematical Preliminaries - Untyped Systems - Untyped Arithmetic Expressions - An ML Implementation of Arithmetic Expressions - The Untyped Lambda-Calculus - Nameless Representation of Terms - An ML Implementation of the Lambda-Calculus - Types Arithmetic Expressions - Simply Typed Lambda-Calculus - An ML Implementation of Simple Types - Simple Extensions - Normalization - Exceptions - Subtyping - Metatheory of Subtyping - An ML Implementation of Subtyping - Recursive Types - Metatheory of Recursive Types - Polymorphism - Type Reconstruction - Universal Types - Existential Types - An ML Implementation of System F - Bounded Quantification - Higher-Order Systems - Higher-Order Polymorphism - Higher-Order Subtyping.

Introduction to Functional Programming Systems Using Haskell

Author: Antony J. T. Davie

Publisher: Cambridge University Press

ISBN: 9780521277242

Category: Computers

Page: 290

View: 6358

Here is an introduction to functional programming and its associated systems. A unique feature is its use of the language Haskell for teaching both the rudiments and the finer points of the functional technique. Haskell is a new, internationally agreed and accepted functional language that is designed for teaching, research and applications, that has a complete formal description, that is freely available, and that is based on ideas that have a wide consensus. Thus it encapsulates some of the main thrusts of functional programming itself, which is a style of programming designed to confront the software crisis directly. Programs written in functional languages can be built up from smaller parts, and they can also be proved correct, important when software has to be reliable. Moreover, a certain amount of parallelism can be extracted from functional languages automatically. This book serves as an introduction both to functional programming and Haskell, and will be most useful to students, teachers and researchers in either of these areas. An especially valuable feature are the chapters on programming and implementation, along with a large number of exercises.

Lambda-calculus, Types and Models

Author: Jean Louis Krivine

Publisher: Ellis Horwood Limited


Category: Computers

Page: 180

View: 5869

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.

Learn You a Haskell for Great Good!

A Beginner's Guide

Author: Miran Lipovaca

Publisher: No Starch Press

ISBN: 1593272952

Category: Computers

Page: 400

View: 9768

It's all in the name: Learn You a Haskell for Great Good! is a hilarious, illustrated guide to this complex functional language. Packed with the author's original artwork, pop culture references, and most importantly, useful example code, this book teaches functional fundamentals in a way you never thought possible. You'll start with the kid stuff: basic syntax, recursion, types and type classes. Then once you've got the basics down, the real black belt master-class begins: you'll learn to use applicative functors, monads, zippers, and all the other mythical Haskell constructs you've only read about in storybooks. As you work your way through the author's imaginative (and occasionally insane) examples, you'll learn to: –Laugh in the face of side effects as you wield purely functional programming techniques –Use the magic of Haskell's "laziness" to play with infinite sets of data –Organize your programs by creating your own types, type classes, and modules –Use Haskell's elegant input/output system to share the genius of your programs with the outside world Short of eating the author's brain, you will not find a better way to learn this powerful language than reading Learn You a Haskell for Great Good!

Proofs and Types

Author: Jean-Yves Girard,Yves Lafont,Paul Taylor

Publisher: Cambridge University Press

ISBN: 9780521371810

Category: Computers

Page: 192

View: 9861

This text is an outgrowth of notes prepared by J. Y. Girard for a course at the University of Paris VII. It deals with the mathematical background of the application to computer science of aspects of logic (namely the correspondence between proposition & types). Combined with the conceptual perspectives of Girard's ideas, this sheds light on both the traditional logic material & its prospective applications to computer science. The book covers a very active & exciting research area, & it will be essential reading for all those working in logic & computer science.

An Architecture for Combinator Graph Reduction

Author: Philip John Koopman

Publisher: Elsevier

ISBN: 1483270467

Category: Computers

Page: 172

View: 6469

An Architecture for Combinator Graph Reduction examines existing methods of evaluating lazy functional programs using combinator reduction techniques, implementation, and characterization of a means for accomplishing graph reduction on uniprocessors, and analysis of the potential for special-purpose hardware implementations. Comprised of eight chapters, the book begins by providing a background on functional programming languages and existing implementation technology. Subsequent chapters discuss the TIGRE (Threaded Interpretive Graph Reduction Engine) methodology for implementing combinator graph reduction; the TIGRE abstract machine, which is used to implement the graph reduction methodology; the results of performance measurements of TIGRE on a variety of platforms; architectural metrics for TIGRE executing on the MIPS R2000 processor; and the potential for special-purpose hardware to yield further speed improvements. The final chapter summarizes the results of the research, and suggests areas for further investigation. Computer engineers, programmers, and computer scientists will find the book interesting.

To Mock a Mocking Bird

Author: Raymond M. Smullyan

Publisher: Knopf

ISBN: 0307819795

Category: Games & Activities

Page: 256

View: 8437

In this entertaining and challenging new collection of logic puzzles, Raymond Smullyan—author of What Is the Name of This Book? And The Lady or the Tiger?—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. In the first part of the book, he transports us once again to that wonderful realm where knights, knaves, twin sisters, quadruplet brothers, gods, demons, and mortals either always tell the truth or always lie, and where truth-seekers are set a variety of fascinating problems. The section culminates in an enchanting and profound metapuzzle (a puzzle about a puzzle), in which Inspector Craig of Scotland Yard gets involved in a search of the Fountain of Youth on the Island of Knights and Knaves. In the second and larger section, we accompany the Inspector on a summer-long adventure into the field of combinatory logic (a branch of logic that plays an important role in computer science and artificial intelligence). His adventure, which includes enchanted forests, talking birds, bird sociologists, and a classic quest, provides for us along the way the pleasure of solving puzzles of increasing complexity until we reach the Master Forest and—thanks to Gödel’s famous theorem—the final revelation. To Mock a Mockingbird will delight all puzzle lovers—the curious neophytes as well as the serious students of logic, mathematics, or computer science.

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