Lambda Calculus with Types (Perspectives in Logic)

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. Features: --Presents three type disciplines using a unified framework --Reveals many mathematical gems through the simple definitions of terms and types --Introduces the reader to applications and includes almost 300 exercises. Henk Barendregt holds the chair on the Foundations of Mathematics and Computer Science at Radboud University, Nijmegen, The Netherlands. Wil Dekkers is an Associate Professor in the Institute of Information and Computing Sciences at Radboud University, Nijmegen, The Netherlands. Richard Statman is a Professor of Mathematics at Carnegie Mellon University, Pittsburgh, USA. Publisher's note Front Cover Abstract Perspective in Logic (series) Lambda Calculus with Types Copyright Contents Preface Contributors Our Founders Introduction Part I. SIMPLE TYPES 1 The Simply Typed Lambda Calculus 2 Properties 3 Tools 4 Definability, unification and matching 5 Extensions 6 Applications PArt II. RECURSIVE TYPES 7 The Systems 8 Properties of Recursive Types 9 Properties of Terms with Types 10 Models 11 Applications Part III. INTERSECTION TYPES 12 An Example System 13 Type Assignment Systems 14 Basic Properties of Intersection Type Assignment 15 Type and Lambda Structures 16 Filter Models 17 Advanced Properties and Applications References Index of terms Index of Citations Index of symbols This handbook with exercises reveals the mathematical beauty of formalisms hitherto mostly used for software and hardware design and verification