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Lambda-Calculus and Combinators
An Introduction

2nd Edition

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About the Authors
  • Combinatory logic and lambda-calculus, originally devised in the 1920’s, 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.

    • The authors' 1986 version of this book is widely recognised as the best introduction to these topics for the reader with some previous experience of logic; this version builds and updates that framework
    • Accessible and clear: a non-technical treatment of the subject with the main ideas emphasized and illustrated by examples
    • Exercises are designed to give practice to beginners and range from elementary to advanced, with solutions to most found at the end of the book
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    Product details

    • Edition: 2nd Edition
    • Date Published: August 2008
    • format: Adobe eBook Reader
    • isbn: 9780511410963
    • contains: 10 b/w illus. 1 table 55 exercises
    • availability: Adobe Reader ebooks available from eBooks.com
  • Table of Contents

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

  • Resources for

    Lambda-Calculus and Combinators

    J. Roger Hindley, Jonathan P. Seldin

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  • Authors

    J. Roger Hindley, University of Wales, Swansea
    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, University of Lethbridge, Alberta
    Jonathan P. Seldin is a Professor in the Department of Mathematics and Computer Science at the University of Lethbridge in Alberta, Canada.

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