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Author: Stephen Wolfram
Publisher: Wolfram Media
ISBN: 9781579550431
Category : Computers
Languages : en
Pages : 0
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Book Description
"Combinators have inspired ideas about computation ever since they were first invented in 1920, and in this innovative book, Stephen Wolfram provides a modern view of combinators and their significance. Informed by his work on the computational universe of possible programs and on computational language design, Wolfram explains new and existing ideas about combinators with unique clarity and stunning visualizations, as well as provides insights on their historical connections and the curious story of Moses Schèonfinkel, inventor of combinators. Though invented well before Turing machines, combinators have often been viewed as an inaccessibly abstract approach to computation. This book brings them to life as never before in a thought-provoking and broadly accessible exposition of interest across mathematics and computer science, as well as to those concerned with the foundations of formal and computational thinking, and with the history of ideas"--
Author: Stephen Wolfram
Publisher: Wolfram Media
ISBN: 9781579550431
Category : Computers
Languages : en
Pages : 0
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Book Description
"Combinators have inspired ideas about computation ever since they were first invented in 1920, and in this innovative book, Stephen Wolfram provides a modern view of combinators and their significance. Informed by his work on the computational universe of possible programs and on computational language design, Wolfram explains new and existing ideas about combinators with unique clarity and stunning visualizations, as well as provides insights on their historical connections and the curious story of Moses Schèonfinkel, inventor of combinators. Though invented well before Turing machines, combinators have often been viewed as an inaccessibly abstract approach to computation. This book brings them to life as never before in a thought-provoking and broadly accessible exposition of interest across mathematics and computer science, as well as to those concerned with the foundations of formal and computational thinking, and with the history of ideas"--
Author: S. Stenlund
Publisher: Springer Science & Business Media
ISBN: 940102913X
Category : Philosophy
Languages : en
Pages : 186
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Book Description
The aim of this monograph is to present some of the basic ideas and results in pure combinatory logic and their applications to some topics in proof theory, and also to present some work of my own. Some of the material in chapter 1 and 3 has already appeared in my notes Introduction to Combinatory Logic. It appears here in revised form since the presen tation in my notes is inaccurate in several respects. I would like to express my gratitude to Stig Kanger for his invalu able advice and encouragement and also for his assistance in a wide variety of matters concerned with my study in Uppsala. I am also in debted to Per Martin-USf for many valuable and instructive conversa tions. As will be seen in chapter 4 and 5, I also owe much to the work of Dag Prawitz and W. W. Tait. My thanks also to Craig McKay who read the manuscript and made valuable suggestions. I want, however, to emphasize that the shortcomings that no doubt can be found, are my sole responsibility. Uppsala, February 1972.
Author: Philip John Koopman
Publisher: Elsevier
ISBN: 1483270467
Category : Computers
Languages : en
Pages : 172
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Book Description
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.
Author: J. Roger Hindley
Publisher: Cambridge University Press
ISBN: 9780521898850
Category : Computers
Languages : en
Pages : 358
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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.
Author: Sören Stenlund
Publisher:
ISBN:
Category : Combinatory logic
Languages : en
Pages : 194
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Book Description
Author: Katalin Bimbo
Publisher: CRC Press
ISBN: 1439800014
Category : Computers
Languages : en
Pages : 357
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Book Description
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 auth
Author: P.-L. Curien
Publisher: Springer Science & Business Media
ISBN: 9780817636548
Category : Computers
Languages : en
Pages : 434
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Book Description
This book is a revised edition of the monograph which appeared under the same title in the series Research Notes in Theoretical Computer Science, Pit man, in 1986. In addition to a general effort to improve typography, English, and presentation, the main novelty of this second edition is the integration of some new material. Part of it is mine (mostly jointly with coauthors). Here is brief guide to these additions. I have augmented the account of categorical combinatory logic with a description of the confluence properties of rewriting systems of categor ical combinators (Hardin, Yokouchi), and of the newly developed cal culi of explicit substitutions (Abadi, Cardelli, Curien, Hardin, Levy, and Rios), which are similar in spirit to the categorical combinatory logic, but are closer to the syntax of A-calculus (Section 1.2). The study of the full abstraction problem for PCF and extensions of it has been enriched with a new full abstraction result: the model of sequential algorithms is fully abstract with respect to an extension of PCF with a control operator (Cartwright, Felleisen, Curien). An order extensional model of error-sensitive sequential algorithms is also fully abstract for a corresponding extension of PCF with a control operator and errors (Sections 2.6 and 4.1). I suggest that sequential algorithms lend themselves to a decomposition of the function spaces that leads to models of linear logic (Lamarche, Curien), and that connects sequentiality with games (Joyal, Blass, Abramsky) (Sections 2.1 and 2.6).
Author: Pierre-Louis Curien
Publisher:
ISBN:
Category : Computer programming
Languages : en
Pages : 330
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Book Description
Author: Guy Cousineau
Publisher: Springer
ISBN:
Category : Computers
Languages : en
Pages : 222
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Book Description
Author: Raymond M Smullyan
Publisher: World Scientific Publishing Company
ISBN: 9814733016
Category : Mathematics
Languages : en
Pages : 288
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Book Description
'A wealth of examples to which solutions are given permeate the text so the reader will certainly be active.'The Mathematical GazetteThis is the final book written by the late great puzzle master and logician, Dr. Raymond Smullyan.This book is a sequel to my Beginner's Guide to Mathematical Logic.The previous volume deals with elements of propositional and first-order logic, contains a bit on formal systems and recursion, and concludes with chapters on Gödel's famous incompleteness theorem, along with related results.The present volume begins with a bit more on propositional and first-order logic, followed by what I would call a 'fein' chapter, which simultaneously generalizes some results from recursion theory, first-order arithmetic systems, and what I dub a 'decision machine.' Then come five chapters on formal systems, recursion theory and metamathematical applications in a general setting. The concluding five chapters are on the beautiful subject of combinatory logic, which is not only intriguing in its own right, but has important applications to computer science. Argonne National Laboratory is especially involved in these applications, and I am proud to say that its members have found use for some of my results in combinatory logic.This book does not cover such important subjects as set theory, model theory, proof theory, and modern developments in recursion theory, but the reader, after studying this volume, will be amply prepared for the study of these more advanced topics.
