Lambda-Calculus and Combinators: An Introduction
Cambridge University Press
Edition: 2, 7/24/2008
EAN 9780521898850, ISBN10: 0521898854
Hardcover, 358 pages, 23.6 x 15.5 x 2.3 cm
Language: English
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 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