This handbook with exercises reveals in formalisms, hitherto mainly used for hardware and software design and verification, unexpected mathematical beauty. The lambda calculus forms a prototype universal programming language, which in its untyped version is related to Lisp, and was treated in the first author's classic The Lambda Calculus (1984). The formalism has since been extended with types and used in functional programming (Haskell, Clean) and proof assistants (Coq, Isabelle, HOL), used in designing and verifying IT products and mathematical proofs. In this book, the authors focus on three classes of typing for lambda terms: simple types, recursive types and intersection types. It is in these three formalisms of terms and types that the unexpected mathematical beauty is revealed. The treatment is authoritative and comprehensive, complemented by an exhaustive bibliography, and numerous exercises are provided to deepen the readers' understanding and increase their confidence using types.

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

Well-respected text for computer science students provides an accessible introduction to functional programming. Cogent examples illuminate the central ideas, and numerous exercises offer reinforcement. Includes solutions. 1989 edition.

This is a textbook for final year undergraduates/first year graduates in computer science, as well as a useful introduction for research students seeking a solid introduction to more specialist literature. This text emphasises the role of calculus in programming language design and implementation, denotational semantics, and domain theory. Alternative books on the subject have been written by logicians, but this is the first to have been written from a computer science prespective, invaluable in emphasising the practical relevance of the key theortical ideas.

The book contains a completely new presentation of classical results in the field of Lambda Calculus, together with new results. The text is unique in that it presents a new calculus (Parametric Lambda Calculus) which can be instantiated to obtain already known lambda-calculi. Some properties, which in the literature have been proved separately for different calculi, can be proved once for the Parametric one. The lambda calculi are presented from a Computer Science point of view, with a particular emphasis on their semantics, both operational and denotational.

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 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.