Introduction To Combinatory Logic
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Introduction To Combinatory Logic
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Author : J. Roger Hindley
language : en
Publisher: CUP Archive
Release Date : 1972-06
Introduction To Combinatory Logic written by J. Roger Hindley and has been published by CUP Archive this book supported file pdf, txt, epub, kindle and other format this book has been release on 1972-06 with Mathematics categories.
These notes present some of the basic techniques and results in the subject of combinatory logic. This subject will first be treated with an introduction via lambda-conversion. Chapter two is an introduction to combinators. Chapters three and four will deal with recursive functions. Chapters five, six, and seven deal with extensional theory of combinators. Chapters nine and ten deal with combinator-based systems of logic . Chapters eight and eleven deal with proof-theoretic application.
Introduction To Combinators And Lambda Calculus
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Author : J. R. Hindley
language : en
Publisher: CUP Archive
Release Date : 1986-05-29
Introduction To Combinators And Lambda Calculus written by J. R. Hindley and has been published by CUP Archive this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986-05-29 with Mathematics categories.
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.
Introduction To Combinatory Logic
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Author : J. Roger Hindley
language : en
Publisher:
Release Date : 1972
Introduction To Combinatory Logic written by J. Roger Hindley and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1972 with Combinatory logic categories.
Combinatory Logic
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Author : Katalin Bimbó
language : en
Publisher: CRC Press
Release Date : 2011-07-27
Combinatory Logic written by Katalin Bimbó and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-07-27 with Computers categories.
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.
Lambda Calculus And Combinators
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Author : J. Roger Hindley
language : en
Publisher:
Release Date : 2008
Lambda Calculus And Combinators written by J. Roger Hindley and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Combinatory logic categories.
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.
Combinators Terms And Proof Theory
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Author : S. Stenlund
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Combinators Terms And Proof Theory written by S. Stenlund and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Philosophy categories.
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.
Lambda Calculus And Combinators
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Author : J. Roger Hindley
language : en
Publisher:
Release Date : 2008
Lambda Calculus And Combinators written by J. Roger Hindley and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Combinatory logic categories.
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.
Foundations Of Combinatory Logic
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Author : Haskell Curry
language : en
Publisher:
Release Date : 2017-04-19
Foundations Of Combinatory Logic written by Haskell Curry and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-04-19 with categories.
Curry's PhD dissertation Introduction to Combinatory Logic, represents a first major work on a new subject. Curry's interest in the subject started when he noticed the complicated form of substitution in Principia Mathematica and set about trying to find a simpler form of this rule. This led him by 1926 to some of the combinators. In 1928 Curry went to G\"ottingen and completed his dissertation in 1929 under the direction of David Hilbert. This book is a translation of the dissertation. Curry's dissertation was the first publication to give a complete formal development of combinatory logic as a formal system in which the terms are built up from variables and a number of constants (combinators including B, C and K) by means of application. The proof of the consistency of the system faced the major difficulty that the only reduction relation Curry had was what we now call weak reduction. This made it impossible to prove the Church-Rosser Theorem, which is now the standard way one proves the consistency of systems of this kind. Instead, Curry was looking at sequences based on what we now call weak contractions with strings of variables added on the right. After his dissertation, Curry developed further ground-breaking ideas that continue to be very influential. These include, functionality (which became the basis of what we now call type assignment), the correspondence between types and implication formulas (the beginning of the idea of "propositions as types") and generalised functionality (a form of dependent types in modern type systems). Curry's ideas continue to influence developments in mathematics, logic and computation. We hope that making his original thesis available in English will help make his ideas clearer. We have made use of all information we could find by Curry, mostly from marginal notes in his copy of the dissertation, indicating corrections to the original German.
Lambda Calculus And Combinators
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Author : J. Roger Hindley
language : en
Publisher: Cambridge University Press
Release Date : 2008-07-24
Lambda Calculus And Combinators written by J. Roger Hindley and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-07-24 with Computers categories.
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.
An Introduction To Lambda Calculi For Computer Scientists
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Author : Chris Hankin
language : en
Publisher: College Publications
Release Date : 2004
An Introduction To Lambda Calculi For Computer Scientists written by Chris Hankin and has been published by College Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Computers categories.
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.
