Lambda-Calculus and Combinators: An Introduction

Description

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 up-to-date account of the subject, with the same authoritative exposition. The grammar and basic properties of both combinatory logic and lambda-calculus are discussed, followed by an introduction to type-theory. Typed and untyped versions of the systems, and their differences, are covered. Lambda-calculus models, which lie behind much of the semantics of programming languages, are also explained in depth. The treatment is as non-technical as possible, with the main ideas emphasized and illustrated by examples. Many exercises are included, from routine to advanced, with solutions to most at the end of the book.

CONTENTS:

Preface; 1. The ?-calculus; 2. Combinatory logic; 3. The power of ? and CL; 4. Computable functions; 5. Undecidability; 6. Formal theories; 7. Extensionality in ?-calculus; 8. Extensionality in CL; 9. Correspondence between ? and CL; 10. Simple typing, Church-style; 11. Simple typing, Curry-style in CL; 12. Simple typing, Curry-style in ?; 13. Generalizations of typing; 14. Models of CL; 15. Models of ? ; 16. Scott's D8 and other models; Appendix A1. a-conversion; Appendix A2. Confluence proofs; Appendix A3. Normalization proofs; Appendix A4. Care of your pet combinator; Appendix A5. Answers to starred exercises; Bibliography; Index.