Lambda-Calculus and Combinators An Introduction

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 version is thoroughly revised and offers an 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.

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 1. a-conversion; Appendix 2. Confluence proofs; Appendix 3. Normalization proofs; Appendix 4. Care of your pet combinator; Appendix 5. Answers to starred exercises; Bibliography; Index.

This much-anticipated new edition gives a thoroughly modern account of combinatory logic and lambda-calculus. The grammar and basic properties of both systems are discussed, followed by explanations of type-theory and lambda-calculus models. The treatment is as non-technical as possible with many examples and exercises.

J. Roger Hindley is an Honorary Research Fellow at Swansea University, Wales. His main research interests are Lambda-calculus and combinatory logic and he has taught at many international universities including Bristol University, Pennsylvania State University and Tokyo Institute of technology. This is his 7th book.
Jonathan P. Seldin is a Professor in the Department of Mathematics and Computer Science at the University of Lethbridge in Alberta, Canada.