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 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.

 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 emphasizes 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 three variants of the type-free [lambda]-calculus that have recently appeared in the research literature: the lazy [lambda]-calculus, the concurrent [gamma]-calculus and the [lambda][sigma]-calculus. The final chapter contains references and a guide to further reading. There are exercises throughout.

 The lambda calculus was developed in the 1930s by Alonzo Church. The calculus turned out to be an interesting model of computation and became theprototype for untyped functional programming languages. Operational and denotational semantics for the calculus served as examples for otherprogramming languages. In typed lambda calculi, lambda terms are classified according to their applicative behavior. In the 1960s it was discovered that the types of typed lambda calculi are in fact appearances of logical propositions. Thus there are two possible views of typed lambda calculi: - as models of computation, where terms are viewed as programs in a typed programming language; - as logical theories, where the types are viewed as propositions and the terms as proofs. The practical spin-off from these studies are: - functional programming languages which are mathematically more succinct than imperative programs; - systems for automated proof checking based on lambda caluli. This volume is the proceedings of TLCA '93, the first international conference on Typed Lambda Calculi and Applications,organized by the Department of Philosophy of Utrecht University. It includes29 papers selected from 51 submissions.

 This book constitutes the refereed proceedings of the 7th International Conference on Typed Lambda Calculi and Applications, TLCA 2005, held in Nara, Japan in April 2005. The 27 revised full papers presented together with 2 invited papers were carefully reviewed and selected from 61 submissions. The volume reports research results on all current aspects of typed lambda calculi, ranging from theoretical and methodological issues to applications in various contexts.

 The refereed proceedings of the 6th International Conference on Typed Lambda Calculi and Applications, TLCA 2003, held in Valencia, Spain in June 2003. The 21 revised full papers presented were carefully reviewed and selected from 40 submissions. The volume reports research results on all current aspects of typed lambda calculi, ranging from theoretical and methodological issues to the application of proof assistants.

 This book constitutes the refereed proceedings of the Third International Conference on Typed Lambda Calculi and Applications, TLCA '97, held in Nancy, France, in April 1997. The 24 revised full papers presented in the book were carefully selected from a total of 54 submissions. The book reports the main research advances achieved in the area of typed lambda calculi since the predecessor conference, held in 1995, and competently reflects the state of the art in the area.

 Graduate text on mathematical foundations of programming languages, and operational and denotational semantics.

 This book constitutes the joint refereed proceedings of the 17th International Workshop on Computer Science Logic, CSL 2003, held as the 12th Annual Conference of the EACSL and of the 8th Kurt Gödel Colloquium, KGC 2003 in Vienna, Austria, in August 2003. The 30 revised full papers presented together with abstracts of 9 invited presentations were carefully reviewed and selected from a total of 112 submissions. All current aspects of computer science logic are addressed ranging from mathematical logic and logical foundations to the application of logics in various computing aspects.

 This book constitutes the refereed proceedings of the 19th International Workshop on Computer Science Logic, CSL 2005, held as the 14th Annual Conference of the EACSL in Oxford, UK in August 2005. The 33 revised full papers presented together with 4 invited contributions were carefully reviewed and selected from 108 papers submitted. All current aspects of logic in computer science are addressed ranging from mathematical logic and logical foundations to methodological issues and applications of logics in various computing contexts. The volume is organized in topical sections on semantics and logics, type theory and lambda calculus, linear logic and ludics, constraints, finite models, decidability and complexity, verification and model checking, constructive reasoning and computational mathematics, and implicit computational complexity and rewriting.

 Content Description #Includes bibliographical references and index.

 This book constitutes the refereed proceedings of the 5th International Conference on Typed Lambda Calculi and Applications, TLCA 2001, held in Krakow, Poland in May 2001. The 28 revised full papers presented were carefully reviewed and selected from 55 submissions. The volume reports research results on all current aspects of typed lambda calculi. Among the topics addressed are type systems, subtypes, coalgebraic methods, pi-calculus, recursive games, various types of lambda calculi, reductions, substitutions, normalization, linear logic, cut-elimination, prelogical relations, and mu calculus.

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 For more than a decade, Foundations of Software Technology and Theoretical Computer Science Conferences have been providing an annual forum for the presentation of new research results in India and abroad. This year, 119 papers from 20 countries were submitted. Each paper was reviewed by at least three reviewers, and 33 papers were selected for presentation and included in this volume, grouped into parts on type theory, parallel algorithms, term rewriting, logic and constraint logic programming, computational geometry and complexity, software technology, concurrency, distributed algorithms, and algorithms and learning theory. Also included in the volume are the five invited papers presented at theconference.

 Logic is sometimes called the foundation of mathematics: the logician studies the kinds of reasoning used in the individual steps of a proof. Alonzo Church was a pioneer in the field of mathematical logic, whose contributions to number theory and the theories of algorithms and computability laid the theoretical foundations of computer science. His first Princeton book, The Calculi of Lambda-Conversion (1941), established an invaluable tool that computer scientists still use today. Even beyond the accomplishment of that book, however, his second Princeton book, Introduction to Mathematical Logic, defined its subject for a generation. Originally published in Princeton's Annals of Mathematics Studies series, this book was revised in 1956 and reprinted a third time, in 1996, in the Princeton Landmarks in Mathematics series. Although new results in mathematical logic have been developed and other textbooks have been published, it remains, sixty years later, a basic source for understanding formal logic. Church was one of the principal founders of the Association for Symbolic Logic; he founded the Journal of Symbolic Logic in 1936 and remained an editor until 1979 At his death in 1995, Church was still regarded as the greatest mathematical logician in the world.