This textbook explains the basic principles of categorical type theory and the techniques used to derive categorical semantics for specific type theories. It introduces the reader to ordered set theory, lattices and domains, and this material provides plenty of examples for an introduction to category theory. which covers categories, functors, ...
This volume presents the proceedings of the Second International Conference on Typed Lambda Calculi and Applications, held in Edinburgh, UK in April 1995. The book contains 29 full revised papers selected from 58 submissions and comprehensively reports the state of the art in the field. The following topics are addressed: proof theory of type ...
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. ...
This book describes the mathematical aspects of the semantics of programming languages. The main goals are to provide formal tools to assess the meaning of programming constructs in both a language-independent and a machine-independent way, and to prove properties about programs, such as whether they terminate, or whether their result is a ...
The lambda calculus was developed in the 1930s by AlonzoChurch. The calculus turned out to be an interesting modelof computation and became theprototype for untypedfunctional programming languages. Operational anddenotational semantics for the calculus served as examplesfor otherprogramming languages. In typed lambda calculi, lambda terms are ...
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 ...
This volume demonstrates the viability of mathematical research into the foundations of categorial grammar, a topic at the border between logic and linguistics. A new introduction to this paperback edition updates the open research problems and records relevant results through pointers to the literature. The author presents the categorial ...
This book constitutes the refereed proceedings of the 4th International Conference on Typed Lambda Calculi and Applications, TLCA'99, held in L'Aquila, Italy in April 1999. The 25 revised full papers presented were carefully reviewed and selected from a total of 50 submissions. Also included are two invited demonstrations. The volume reports ...
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 ...
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 ...
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 long-awaited new version is thoroughly revised and offers a fully ...
This monograph began life as a series of papers documenting five years of research into the logical foundations of Categorial Grammar, a grammatical paradigm which has close analogies with Lambda Calculus and Type Theory. The technical theory presented here stems from the interface between Logic and Linguistics and, in particular, the theory of ...
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 ...
Mathematics is about proofs, that is the derivation of correct statements; and calculations, that is the production of results according to well-defined sets of rules. The two notions are intimately related. Proofs can involve calculations, and the algorithm underlying a calculation should be proved correct. The aim of the author is to explore ...
This book constitutes the refereed proceedings of the 8th International Conference on Typed Lambda Calculi and Applications, TLCA 2007, held in Paris, France in June 2007 in conjunction with RTA 2007, the 18th International Conference on Rewriting Techniques and Applications as part of RDP 2007, the 4th International Conference on Rewriting, ...
Lambda calculus lies at the very foundation 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. This book is written from a systems perspective, emphasizing the practical relevance of many of the key ...
The application of logic to grammar is a fundamental issue in philosophy and has been investigated by such renowned philosophers as Leibniz, Bolzano, Frege, and Husserl. "Language and Grammar" examines categorial grammars and type-logical grammars, two linguistic theories that play a significant role in this area of study yet have been ...
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