Lambda-Calculus and Combinators

An Introduction

Inbunden, Engelska, 2008

1 169 kr

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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.

Produktinformation

Utgivningsdatum2008-07-24
Mått154 x 235 x 23 mm
Vikt610 g
FormatInbunden
SpråkEngelska
Antal sidor358
Upplaga2
FörlagCambridge University Press
ISBN9780521898850

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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.

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.

From reviews of the first edition: 'The book of R. Hindley and J. Seldin is a very good introduction to fundamental techniques and results in these fields ... the book is clear, pleasant to read, and it needs no previous knowledge in the domain, but only basic notions of mathematical logic ... Clearly, it was impossible to treat everything in detail; but even when a subject is only skimmed, the book always provides an incentive for going deeper, and furnishes the means to do it, owing to a substantial bibliography. Several chapters end with interesting and useful notes with history, comments, and indications for further reading ... In conclusion, this book is very interesting and well written, and is highly recommended to everyone who wants to approach combinatory logic and lambda-calculus (logicians or computer scientists). J. Symbolic Logic