Foundations Of Combinatory Logic
DOWNLOAD
Download Foundations Of Combinatory Logic PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Foundations Of Combinatory Logic book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page
Foundations Of Combinatory Logic
DOWNLOAD
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.
Foundations Of Mathematical Logic
DOWNLOAD
Author : Haskell Brooks Curry
language : en
Publisher: Courier Corporation
Release Date : 1977-01-01
Foundations Of Mathematical Logic written by Haskell Brooks Curry and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 1977-01-01 with Mathematics categories.
Written by a pioneer of mathematical logic, this comprehensive graduate-level text explores the constructive theory of first-order predicate calculus. It covers formal methods — including algorithms and epitheory — and offers a brief treatment of Markov's approach to algorithms. It also explains elementary facts about lattices and similar algebraic systems. 1963 edition.
Combinatory Logic
DOWNLOAD
Author : Haskell Brooks Curry
language : en
Publisher:
Release Date : 1958
Combinatory Logic written by Haskell Brooks Curry and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1958 with Combinatory logic categories.
The Combinatory Foundations Of Mathematical Logic
DOWNLOAD
Author : Haskell B. Curry
language : en
Publisher:
Release Date : 1942
The Combinatory Foundations Of Mathematical Logic written by Haskell B. Curry and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1942 with categories.
Systems Of Combinatory Logic Related To Quine S New Foundations
DOWNLOAD
Author : Melvin Randall Holmes
language : en
Publisher:
Release Date : 1989
Systems Of Combinatory Logic Related To Quine S New Foundations written by Melvin Randall Holmes and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with Logic, Symbolic and mathematical categories.
Lambda Calculus And Combinators
DOWNLOAD
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 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 Combinatory Programme
DOWNLOAD
Author : Erwin Engeler
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
The Combinatory Programme written by Erwin Engeler 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 Computers categories.
Combinatory logic started as a programme in the foundation of mathematics and in an historical context at a time when such endeavours attracted the most gifted among the mathematicians. This small volume arose under quite differ ent circumstances, namely within the context of reworking the mathematical foundations of computer science. I have been very lucky in finding gifted students who agreed to work with me and chose, for their Ph. D. theses, subjects that arose from my own attempts 1 to create a coherent mathematical view of these foundations. The result of this collaborative work is presented here in the hope that it does justice to the individual contributor and that the reader has a chance of judging the work as a whole. E. Engeler ETH Zurich, April 1994 lCollected in Chapter III, An Algebraization of Algorithmics, in Algorithmic Properties of Structures, Selected Papers of Erwin Engeler, World Scientific PubJ. Co. , Singapore, 1993, pp. 183-257. I Historical and Philosophical Background Erwin Engeler In the fall of 1928 a young American turned up at the Mathematical Institute of Gottingen, a mecca of mathematicians at the time; he was a young man with a dream and his name was H. B. Curry. He felt that he had the tools in hand with which to solve the problem of foundations of mathematics mice and for all. His was an approach that came to be called "formalist" and embodied that later became known as Combinatory Logic.
Combinatory Logic
DOWNLOAD
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.
Introduction To Combinators And Lambda Calculus
DOWNLOAD
Author : J. Roger Hindley
language : en
Publisher: Cambridge [Cambridgeshire] ; New York : Cambridge University Press
Release Date : 1986
Introduction To Combinators And Lambda Calculus written by J. Roger Hindley and has been published by Cambridge [Cambridgeshire] ; New York : Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986 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.
Foundations Of Mathematics
DOWNLOAD
Author : Erwin Engeler
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Foundations Of Mathematics written by Erwin Engeler 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 Mathematics categories.
This book appeared about ten years ago in Gennan. It started as notes for a course which I gave intermittently at the ETH over a number of years. Following repeated suggestions, this English translation was commissioned by Springer; they were most fortunate in finding translators whose mathemati cal stature, grasp of the language and unselfish dedication to the essentially thankless task of rendering the text comprehensible in a second language, both impresses and shames me. Therefore, my thanks go to Dr. Roberto Minio, now Darmstadt and Professor Charles Thomas, Cambridge. The task of preparing a La'JEX-version of the text was extremely daunting, owing to the complexity and diversity of the symbolisms inherent in the various parts of the book. Here, my warm thanks go to Barbara Aquilino of the Mathematics Department of the ETH, who spent tedious but exacting hours in front of her Olivetti. The present book is not primarily intended to teach logic and axiomat ics as such, nor is it a complete survey of what was once called "elementary mathematics from a higher standpoint". Rather, its goal is to awaken a certain critical attitude in the student and to help give this attitude some solid foun dation. Our mathematics students, having been drilled for years in high-school and college, and having studied the immense edifice of analysis, regrettably come away convinced that they understand the concepts of real numbers, Euclidean space, and algorithm.