Lambda-Calculus and Combinators: An Introduction 2nd Edition by J. Roger Hindley (PDF)

Description

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.

User’s Reviews

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 book gives an account of combinatory logic and lambda-calculus models. About the Author 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. Read more

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐I found Hindley and Seldin’s book to be a reasonably good fit for my expectations, and I think it’s just the right expectations that really matter when you’re deciding whether to take it on or not.Firstly, I should note that in my opinion this book is really written from a logician’s or mathematician’s perspective rather than a computer scientist’s one. Of course, the boundary between logic and foundational parts of theoretical computer science is thin at best, but I feel that the approach taken here, the parts of the subject chosen for study and the general tone of the text reflect a more abstract perspective than that I’d expect from a “model” CS book. In particular, I found the sections covering equality and modelling of lambda calculus to be rather boring and ill-motivated — not because of any inherent qualities of those chapters, but simply because I presently have little interest in those specific subjects, and so far I fail to see why would they be important for me as a student of PLT and FP.That said, if you’re interested in stuff somewhat closer to the proverbial metal, the book still offers plenty of juicy stuff for you to ponder. The introduction to untyped lambda calculus, combinatory logic and simply typed lambda calculus provides a very principled coverage of those topics, discussing the subtle differences between the calculi in much gory detail, and being richly adorned with many lemmas one would take for granted, but which are discussed here in full formal glory instead, allowing the reader to develop — if one so desires — a fairly nuanced feel for the fundamentals.The discussion of Barendregt’s Lambda cube was thoroughly fascinating and in many ways eye-opening to me, even though — along with many of the later chapters — it made me feel in sore need of waders, and, occasionally, a snorkel. The math is dense, and working through all of it would likely require expending much more time than I’m willing to invest into it right now.Lastly, I cannot properly judge just how broad the coverage of modern state of the art in lambda calculus this book provides, as this very book itself is about the most thorough exposure to these topics I had to date, but it leaves the impression of being a fairly thorough survey of the basics, including touching on some recent results in the field (which, of course, is quite new of itself). The books omits many of the meatier proofs, but I found this to be perfectly understandable as the bloat would be unimaginable otherwise, and of course there are always proper references to follow for those interested in the full treatment.On a side note not directly relevant to the book as such, but more to how the Kindle edition was done, one thing I would wish for would be something more comfortable for dealing with exercise solutions. Making them available at a touch of a finger is certainly technically possible, so it’s a pity this requires juggling the bookmarks instead in this version.If you’re looking for something theoretical, rigorous and full of math, *Lambda-Calculus* is definitely a good choice, especially if you’re prepared to put a fair deal of effort into following the text, and, perhaps, skip or skim the parts not directly relevant to your interests. For a much lighter introduction into lambda calculus — and much closer to a working programmer’s perspective — Michaelson’s *Intro to FP through Lambda Calculus* still remains the best choice. (And you can always come back here for more.)

⭐I’ve been learning Standard ML, Scheme and Lisp, and I’ve been writing small programs with these languages.However I was only able to know how, rather than why of these languages, which are deeply rooted in Lambda calculus.I knew how lambda and combinators work, but I had no idea why they were invented in the first place.When reading this book, I started to get the idea behind these languages. And I now can understand why these languages were invented, and from where those concepts were innovated.This book answers all my questions of “why”, gives a thorough and clear background from a historical point of view, and suggests a long list of other books as reference.The examples and exercises are well organized which help a lot in understanding the newly introduced concepts. Most of the exercises have answers, except very trivial ones.Though there are tons of documents of Lambda and combinators online, I believe this is the best book as an introduction to Lambda and combinators. Strongly recommended to all that want to understand the why of Lambda and combnators.

⭐lambda loved.loved

⭐Good introduction by an expert in the field.

⭐This book introduces rigorously several variants of lambda calculus and combinatory logic. The book assumes a solid background in mathematical logic. The book assumes a level of familiarity with formal languages and natural deduction systems. If you are interested in a mathematical understanding of lambda calculus, this reference will get you there.

⭐Content:- excellent presentation of the theory- great examples and exercises (with solutions)Printing quality (Lightning source UK Ltd.):- a nightmare; I will return the book immediately, since reading pages of such a low of quality is absolutely unacceptable and definitely no fun!- a library copy I have in front of me (“Printed in the United Kingdom at the University Press, Cambridge) has an excellent printing quality as the books from Cambridge University Press used to have.Advice:- Get the e-book, preferably in pdf-format. Make a book from the pdf-file in a quality you find acceptable. This will definitely be worth the trouble.

⭐和書無し。英語は平均的な数学の本程度。つまりそれほど難しくはない。ただし専門用語が定義と共に導入されていくので、日本語との対応関係は読者が調べるしかない。’入門書’となっているが要は証明を他の論文の紹介にしていることであるが、この方針は定理を順に確認していくのを簡単にしているので成功だと思われる。内容の量は十分多く、その上すべての証明を載せたとすれば、気軽に買える値段には出来ないと思う。専門の人には、論文を追かける小事典として使えると思うが、この本だけ持っていても、練習問題もありその答えもあるので楽しめる本だと思う。授業で、必要だったので、中古で購入しました。安く購入できて助かりました。

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