Introduction to Combinators and (lambda) Calculus (London Mathematical Society Student Texts) [Paperback]

J. R. Hindley (Author), J. P. Seldin (Author)

Book Description

Publication Date: May 31, 1986 | Series: London Mathematical Society Student Texts (Book 1)

Combinatory logic and lambda-conversion were originally devised in the 1920s for investigating the foundations of mathematics using the basic concept of 'operation' instead of 'set'. They have now developed into linguistic tools, useful in several branches of logic and computer science, especially in the study of programming languages. These notes form a simple introduction to the two topics, suitable for a reader who has no previous knowledge of combinatory logic, but has taken an undergraduate course in predicate calculus and recursive functions. The key ideas and basic results are presented, as well as a number of more specialised topics, and man), exercises are included to provide manipulative practice.

Product Details

• Paperback: 368 pages
• Publisher: Cambridge University Press (May 31, 1986)
• Language: English
• ISBN-10: 0521318394
• ISBN-13: 978-0521318396
• Product Dimensions: 8.9 x 5.9 x 0.9 inches
• Shipping Weight: 1 pounds
• Average Customer Review: 5.0 out of 5 stars  See all reviews (1 customer review)
• Amazon Best Sellers Rank: #2,514,450 in Books (See Top 100 in Books)

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Most Helpful Customer Reviews

9 of 9 people found the following review helpful:

5.0 out of 5 stars A MUST for programmers using Haskell and/or ML!, January 9, 2002

By 

Hidetaka Kondoh (Kawasaki, Kanagawa Japan) - See all my reviews
(REAL NAME)   

This review is from: Introduction to Combinators and (lambda) Calculus (London Mathematical Society Student Texts) (Hardcover)

This book is a very well-written introductory textbook on combinatory logic and lambda-calculus, both of which are the most essntial core of modern functional programming languages such as Haskell, Standard ML, CAML, etc.

This book covers typed lambda-calculi/combinatory logic as well as type-free ones.

Many useful and understandable examples/counter-examples are given when theorems or definitions of notions must be rather abstract and general.

Those (especially counter-)examples avoid readers from falling into pitfalls of abstract notions for novices of math logic.

It is often the case that several distinct notions seem to be equivalent for novices. This is a typical pitfall of abstractness, but clear counter-examples are carefully given just at such pitfalls so that novices of lambda-calculus/combinatory logic can prevent to fall down into confusion.

Proofs in this charming textbook are very easily followable.

Owing to various helpful examples and/or counter-examples, readers will not lose their intuition even in front of such logical exactness and/or very dry abstractness.

Needless to say, this book is imperative for students of lambda-calculus, combinatory logic, type theory, or constructive math (all of these are fields of math logic), because this book gives very self-contained accounts on core parts of those fields.

The value of this beautiful book is not limitted within such purely academic math logic fields, though.

This beautiful book is also a must for practical programmers of functional languages as listed above, because this book very well tells practitioners about the scientific theory behind their working tools, i.e. functional programming languages.

Then, programmers can become to believe that science is really useful in software development, which is often regarded as an engineering field where academic pure science does not give any help.

If you are a functional programmer, you should have a copy!

(If you are a students on topics of this book, you MUST, too, of course!)