Programming In Martin L F S Type Theory

In recent years, several formalisms for program construction have appeared. One such formalism is the type theory developed by Per Martin-Löf. Well suited as a theory for program construction, it makes possible the expression of both specifications and programs within the same formalism. Furthermore, the proof rules can be used to derive a correct program from a specification as well as to verify that a given program has a certain property. This book contains a thorough introduction to type theory, with information on polymorphic sets, subsets, monomorphic sets, and a full set of helpful examples.

Extensional Constructs in Intensional Type Theory presents a novel approach to the treatment of equality in Martin-Loef type theory (a basis for important work in mechanised mathematics and program verification). Martin Hofmann attempts to reconcile the two different ways that type theories deal with identity types. The book will be of interest particularly to researchers with mainly theoretical interests and implementors of type theory based proof assistants, and also fourth year undergraduates who will find it useful as part of an advanced course on type theory.

This book explores the role of Martin-Lof s constructive type theory in computer programming. The main focus of the book is how the theory can be successfully applied in practice. Introductory sections provide the necessary background in logic, lambda calculus and constructive mathematics, and exercises and chapter summaries are included to reinforce understanding.

Handbook of Automated Reasoning.

In Logical Frameworks, first published in 1991, Huet and Plotkin gathered contributions from the first International Workshop on Logical Frameworks. The contributions are of the highest calibre. Four main themes are covered: the general problem of representing formal systems in logical frameworks, basic algorithms of general use in proof assistants, logical issues, and large-scale experiments with proof assistants.

The second edition of The Handbook of Contemporary Semantic Theory presents a comprehensive introduction to cutting-edge research in contemporary theoretical and computational semantics. Features completely new content from the first edition of The Handbook of Contemporary Semantic Theory Features contributions by leading semanticists, who introduce core areas of contemporary semantic research, while discussing current research Suitable for graduate students for courses in semantic theory and for advanced researchers as an introduction to current theoretical work

This book develops a theory of enriched meanings for natural language interpretation that uses the concept of monads and related ideas from category theory, a branch of mathematics that has been influential in theoretical computer science and elsewhere. Certain expressions that exhibit complex effects at the semantics/pragmatics boundary live in an enriched meaning space, while others live in a more basic meaning space. These basic meanings are mapped to enriched meanings only when required compositionally, which avoids generalizing meanings to the worst case. Ash Asudeh and Gianluca Giorgolo show that the monadic theory of enriched meanings offers a formally and computationally well-defined way to tackle important challenges at the semantics/pragmatics boundary. In particular, they develop innovative monadic analyses of three phenomena - conventional implicature, substitution puzzles, and conjunction fallacies - and demonstrate that the compositional properties of monads model linguistic intuitions about these cases particularly well. The analyses are accompanied by exercises to aid understanding, and the computational tools used are available on the book's companion website. The book also contains background chapters on enriched meanings and category theory. The volume is interdisciplinary in nature, with insights from semantics, pragmatics, philosophy of language, psychology, and computer science, and will appeal to graduate students and researchers from a wide range of disciplines with an interest in natural language understanding and representation.

This volume is the first comprehensive overview of the syntax and semantics of wh-scope marking. Wh-scope marking constructions have recently received a lot of attention; their very existence and their intricate properties have important consequences for syntax, semantics, and the syntax–semantics interface (e.g., with respect to the wh-criterion, the wh-movement parameter, feature checking, the theory of locality, the interpretation of wh-phrases and why-chains, and the nature of LF). The fifteen contributions share the basic assumptions of the Chomskyan approach to syntax and the model-theoretic approach to semantics; they address a variety of languages (among them German, Hindi, Hungarian, English, Frisian, Kikuyu, and Malay). A recurrent theme in all articles is whether wh-scope marking should be analyzed in terms of a direct, indirect, or mixed dependency. The wealth of cross-linguistic empirical evidence and the theory-independent relevance of the conclusions should make this book the ultimate source of information on wh-scope marking for years to come.