Lambda-Calculus and Combinators: An Introduction [Hardcover]

J. Roger Hindley (Author), Jonathan P. Seldin (Author)

Book Description

ISBN-10: 0521898854 | ISBN-13: 978-0521898850 | Publication Date: August 11, 2008 | Edition: 2

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.

Editorial Reviews

Review

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

'The best general book on lambda-calculus (typed or untyped) and the theory of combinators.' Gérard Huet, INRIA

'... for teaching and for research or self-study the book is an outstanding source with its own clear merits. I think this second edition of this classical book is a beautiful asset for the literature on λ-calculus and CL.' Theory and Practice of Logic Programming

'... well written and offers a broad coverage backed by an extensive list of references. It could serve as an excellent study material for classes on λ-calculus and CL as well as a reference for logicians and computer scientists interested in the formal background for functional programming and related areas.' EMS Newsletter

'Without doubt this is a valuable treatment of a venerable topic that rewards those who understand it. The authors successfully promulgate their tradition, and that is certainly more important than providing full proofs for every result.' The Journal of JFP

Book Description

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.

See all Editorial Reviews

Product Details

• Hardcover: 360 pages
• Publisher: Cambridge University Press; 2 edition (August 11, 2008)
• Language: English
• ISBN-10: 0521898854
• ISBN-13: 978-0521898850
• Product Dimensions: 9 x 6 x 0.9 inches
• Shipping Weight: 1.4 pounds (View shipping rates and policies)
• Average Customer Review: 4.0 out of 5 stars  See all reviews (1 customer review)
• Amazon Best Sellers Rank: #1,040,124 in Books (See Top 100 in Books)

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3 of 4 people found the following review helpful:

4.0 out of 5 stars A very good undergraduate textbook, May 17, 2011

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Scott (Dubuque, IA) - See all my reviews

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This review is from: Lambda-Calculus and Combinators: An Introduction (Hardcover)

This text by Hindley and Seldin is a thorough introduction to Alonzo Church's lambda calculus, to Haskell Curry's combinatory logic, and to their interesting interrelationships. Also covers several of the ways that type theories can influence these logics, plus model theories for them. This book is a nice expansion related to a long paper by Felice Cardone and Roger Hindley on the histories of lambda calculus and combinatory logic and their type theories that I read recently, and that good paper influenced me to buy this book. Therefore, I hope to have time to start reading this textbook rather soon.

I did start reading this textbook on Tue 11Oct11, and thru the first 3 short chapters at least, this book is an undergraduate gem! That gets us small exposure to lambda in Chap 1 and to combinatory (CL) in Chap 2, interestingly combining them in Chap 3. Chap 4 is about computable functions in both lambda and CL and mostly contains some definitions and long proofs of several representation theorems. That was a bit tedious.

Most chapters, especially good Chap 5 on undecidability and excellent Chap 6 on formal theories of lambda and CL, are rather short, with Chap 11 at about 40 pages and Chap 13 at about 37 pages being by far the longest. Chapter 7 is about what is called extensionality in lambda, while chapter 8 is about the same for CL. I am not really sure how extensionality is significant, and skipped chapter 8 to successfully read chapter 9 which almost fully combines lambda and CL into one 'thing'.

Chapter 10 is an interesting first look at Church-style type theory for both lambda and CL, and I decided to stop reading this book at end of section 10B and p. 115 on Mon 7Nov11. The type theoretical chapters 10-13 get more intensely difficult, and for me also less interesting. Plus, I am much more interested in lambda than in CL, and so started to feel obligated to skip the CL-related writing in the later chapters.

This is still a very good textbook on its subjects and the one to read if you are truly interested in both lambda calculus and combinatory logic, as those two subjects are treated quite equally in this book.