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About this book
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.
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Table of contents
- Cover
- Half-title
- Title
- Copyright
- Contents
- Preface
- 1 The lambda-calculus
- 2 Combinatory logic
- 3 The power of lambda and combinators
- 4 Representing the computable functions
- 5 The undecidability theorem
- 6 The formal theories lamnda beta and CLw
- 7 Extensionality in lambda-calculus
- 8 Extensionality in combinatory logic
- 9 Correspondence between lambda and CL
- 10 Simple typing, Church-style
- 11 Simple typing, Curry-style in CL
- 12 Simple typing, Curry-style in lambda
- 13 Generalizations of typing
- 14 Models of CL
- 15 Models of lambda-calculus
- 16 Scott's D∞ and other models
- Appendix A1 Bound variables and alpha-conversion
- Appendix A2 Confluence proofs
- Appendix A3 Strong normalization proofs
- Appendix A4 Care of your pet combinator
- Appendix A5 Answers to starred exercises
- References
- List of symbols
- Index