Some Extensional Term Models For Combinatory Logics And Lambda Calculi 1971
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Some Extensional Term Models For Combinatory Logics And Lambda Calculi 1971
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Author : Henk Barendregt
language : en
Publisher:
Release Date : 2020-12-22
Some Extensional Term Models For Combinatory Logics And Lambda Calculi 1971 written by Henk Barendregt and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-12-22 with categories.
This book is an extended version of the author's 1971 PhD thesis, containing a facsimile of the original and several extensions: motivation, hindsight and the making of. It is concerned with consistency of equating unsolvable terms and adding the omega-rule as strengthening of the principle of extensionality. The republication is put in context of the transition of lambda-calculus from an academic theory to a major foundation for fruitful aspects of logic, having an impact on mathematics and computer science and technology with a societal impact by securing correctness of complex systems.
Some Extensional Term Models For Combinatory Logics And Lambda Calculi
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Author : Hendrik Pieter Barendregt
language : en
Publisher:
Release Date : 1971
Some Extensional Term Models For Combinatory Logics And Lambda Calculi written by Hendrik Pieter Barendregt and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1971 with Combinatory logic categories.
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.
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.
Programs As Diagrams
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Author : Dusko Pavlovic
language : en
Publisher: Springer Nature
Release Date : 2023-09-19
Programs As Diagrams written by Dusko Pavlovic and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-09-19 with Computers categories.
It is not always clear what computer programs mean in the various languages in which they can be written, yet a picture can be worth 1000 words, a diagram 1000 instructions. In this unique textbook/reference, programs are drawn as string diagrams in the language of categories, which display a universal syntax of mathematics (Computer scientists use them to analyze the program semantics; programmers to display the syntax of computations). Here, the string-diagrammatic depictions of computations are construed as programs in a single-instruction programming language. Such programs as diagrams show how functions are packed in boxes and tied by strings. Readers familiar with categories will learn about the foundations of computability; readers familiar with computability gain access to category theory. Additionally, readers familiar with both are offered many opportunities to improve the approach. Topics and features: Delivers a ‘crash’ diagram-based course in theory of computation Uses single-instruction diagrammatic programming language Offers a practical introduction into categories and string diagrams as computational tools Reveals how computability is programmability, rather than an ‘ether’ permeating computers Provides a categorical model of intensional computation is unique up to isomorphism Serves as a stepping stone into research of computable categories In addition to its early chapters introducing computability for beginners, this flexible textbook/resource also contains both middle chapters that expand for suitability to a graduate course as well as final chapters opening up new research. Dusko Pavlovic is a professor at the Department of Information and Computer Sciences at the University of Hawaii at Manoa, and by courtesy at the Department of Mathematics and the College of Engineering. He completed this book as an Excellence Professor at Radboud University in Nijmegen, The Netherlands.
Foundations Of Software Science And Computation Structures
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Author : Naoki Kobayashi
language : en
Publisher: Springer Nature
Release Date :
Foundations Of Software Science And Computation Structures written by Naoki Kobayashi and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
Raymond Smullyan On Self Reference
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Author : Melvin Fitting
language : en
Publisher: Springer
Release Date : 2018-01-11
Raymond Smullyan On Self Reference written by Melvin Fitting and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-01-11 with Philosophy categories.
This book collects, for the first time in one volume, contributions honoring Professor Raymond Smullyan’s work on self-reference. It serves not only as a tribute to one of the great thinkers in logic, but also as a celebration of self-reference in general, to be enjoyed by all lovers of this field. Raymond Smullyan, mathematician, philosopher, musician and inventor of logic puzzles, made a lasting impact on the study of mathematical logic; accordingly, this book spans the many personalities through which Professor Smullyan operated, offering extensions and re-evaluations of his academic work on self-reference, applying self-referential logic to art and nature, and lastly, offering new puzzles designed to communicate otherwise esoteric concepts in mathematical logic, in the manner for which Professor Smullyan was so well known. This book is suitable for students, scholars and logicians who are interested in learning more about Raymond Smullyan's work and life.
Computer Science Logic
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Author : Leszek Pacholski
language : en
Publisher: Springer Science & Business Media
Release Date : 1995-07-18
Computer Science Logic written by Leszek Pacholski 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 1995-07-18 with Computers categories.
This volume contains revised refereed versions of the best papers presented during the CSL '94 conference, held in Kazimierz, Poland in September 1994; CSL '94 is the eighth event in the series of workshops held for the third time as the Annual Conference of the European Association for Computer Science Logic. The 38 papers presented were selected from a total of 151 submissions. All important aspects of the methods of mathematical logic in computer science are addressed: lambda calculus, proof theory, finite model theory, logic programming, semantics, category theory, and other logical systems. Together, these papers give a representative snapshot of the area of logical foundations of computer science.
Nature Cognition And System I
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Author : M.E. Carvallo
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Nature Cognition And System I written by M.E. Carvallo 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 Science categories.
usually called the classical (scientific) attitude (according to which there is a dichotomy between nature and cognition) and suggestions for better understanding of their mutual encroach ment. The authors belong more or less to the non-standard systems science, the third order cybernetics, or find themselves already beyond the third stage in the history of artificial intelli 1 gence ). They take the inescapability of the mutual implication of the description of nature and that of cognition seriously. Fourth ly, closely linking up with the previous, it emphatically calls attention to the forgotten microscopic dimension of science. If I am not mistaken we have at this moment reached the historic stage where the tremendous renascence of the mechanistic-structural paradigm, remarkably enough, calls for its functional-dynamic counterparts. The volume strives to respond to this secret trend in various disciplines and to put into words that which is tacitly alive in the minds of the ever increasing number of people in this systemsage. The investigation on the intertwinement of nature and cognition finds itself in this very paradoxical niche structured by those two opposite developments.
Fundamenta Mathematicae
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Author :
language : en
Publisher:
Release Date : 1974
Fundamenta Mathematicae written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1974 with Electronic journals categories.