Combinators Lambda Terms And Proof Theory

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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.

Combinators Lambda Terms And Proof Theory

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Author : S. Stenlund
language : en
Publisher: Springer
Release Date : 1972-09-30

Combinators Lambda Terms And Proof Theory written by S. Stenlund and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1972-09-30 with Philosophy categories.

Combinators Lambda Terms And Proof Theory

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Author : Soren Stenlund
language : it
Publisher:
Release Date : 1972

Combinators Lambda Terms And Proof Theory written by Soren Stenlund and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1972 with categories.

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.

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.

Typed Lambda Calculi And Applications

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Author : Luke Ong
language : en
Publisher: Springer
Release Date : 2011-06-12

Typed Lambda Calculi And Applications written by Luke Ong and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-06-12 with Mathematics categories.

This book constitutes the refereed proceedings of the 10th International Conference on Typed Lambda Calculi and Applications, TLCA 2011, held in Novi Sad, Serbia, in June 2011 as part of RDP 2011, the 6th Federated Conference on Rewriting, Deduction, and Programming. The 15 revised full papers presented were carefully reviewed and selected from 44 submissions. The papers provide prevailing research results on all current aspects of typed lambda calculi, ranging from theoretical and methodological issues to applications in various contexts addressing a wide variety of topics such as proof-theory, semantics, implementation, types, and programming.

The Lambda Calculus

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Author : Hendrik Pieter Barendregt
language : en
Publisher: North Holland
Release Date : 1981

The Lambda Calculus written by Hendrik Pieter Barendregt and has been published by North Holland this book supported file pdf, txt, epub, kindle and other format this book has been release on 1981 with Mathematics categories.

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.

The Lambda Calculus

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Author : H.P. Barendregt
language : en
Publisher: North Holland
Release Date : 1984

The Lambda Calculus written by H.P. Barendregt and has been published by North Holland this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984 with Mathematics categories.

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.

Witness Theory

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Author : Adrian Rezus
language : en
Publisher:
Release Date : 2020-03-06

Witness Theory written by Adrian Rezus and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-03-06 with Mathematics categories.

This book is concerned with the mathematical analysis of the concept of formal proof in classical logic, and records - in substance - a longer exercise in applied λ-calculus. Following colloquialisms going back to L. E. J. Brouwer, the objects of study in this enterprise are called witnesses. A witness is meant to represent the logical proof of a classically valid formula, in a given proof-context. The formalisms used to express witnesses and their equational behaviour are extensions of the pure `typed' λ-calculus, considered as equational theories. Formally, a witness is generated from decorated - or `typed' - witness variables, representing assumptions, and witness operators, representing logical rules of inference. The equational specifications serve to define the witness operators. In general, this can be done by ignoring the `typing', i.e., the logic formulas themselves. Model-theoretically, the witnesses are objects of an extensional Scott λ-model. The approach - called, generically, `witness theory' - is inspired from work of N. G. de Bruijn, on a mathematical theory of proving, done during the late 1960s and the early 1970s, at the University of Eindhoven (The Netherlands), and is similar to the approach behind the Curry-Howard Correspondence, familiar from intuitionistic logic. For the classical case, the decorations - oft called `types' - are classical logic formulas. At quantifier-free level, the equational theory of concern is the λ-calculus with `surjective pairing' and some subsystens thereof, appropriately decorated. The extension to propositional, first- and second-order quantifiers is straightforward. The book consists of a collection of notes and papers written and circulated during the last ten years, as a continuation of previous research done by the author during the nineteen eighties. Among other things, it includes a survey of the origins of modern proof theory - Frege to Gentzen - from a witness-theoretical point of view, as well as a characteristic application of witness theory to a practical logic problem concerning axiomatisability.

Lectures On The Curry Howard Isomorphism

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Author : Morten Heine Sørensen
language : en
Publisher: Elsevier
Release Date : 2006-07-04

Lectures On The Curry Howard Isomorphism written by Morten Heine Sørensen and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-07-04 with Mathematics categories.

The Curry-Howard isomorphism states an amazing correspondence between systems of formal logic as encountered in proof theory and computational calculi as found in type theory. For instance,minimal propositional logic corresponds to simply typed lambda-calculus, first-order logic corresponds to dependent types, second-order logic corresponds to polymorphic types, sequent calculus is related to explicit substitution, etc.The isomorphism has many aspects, even at the syntactic level:formulas correspond to types, proofs correspond to terms, provability corresponds to inhabitation, proof normalization corresponds to term reduction, etc.But there is more to the isomorphism than this. For instance, it is an old idea---due to Brouwer, Kolmogorov, and Heyting---that a constructive proof of an implication is a procedure that transformsproofs of the antecedent into proofs of the succedent; the Curry-Howard isomorphism gives syntactic representations of such procedures. The Curry-Howard isomorphism also provides theoretical foundations for many modern proof-assistant systems (e.g. Coq).This book give an introduction to parts of proof theory and related aspects of type theory relevant for the Curry-Howard isomorphism. It can serve as an introduction to any or both of typed lambda-calculus and intuitionistic logic. Key features- The Curry-Howard Isomorphism treated as common theme- Reader-friendly introduction to two complementary subjects: Lambda-calculus and constructive logics- Thorough study of the connection between calculi and logics- Elaborate study of classical logics and control operators- Account of dialogue games for classical and intuitionistic logic- Theoretical foundations of computer-assisted reasoning · The Curry-Howard Isomorphism treated as the common theme.· Reader-friendly introduction to two complementary subjects: lambda-calculus and constructive logics · Thorough study of the connection between calculi and logics.· Elaborate study of classical logics and control operators.· Account of dialogue games for classical and intuitionistic logic.· Theoretical foundations of computer-assisted reasoning