An Introduction to Lambda Calculi for Computer Scientists

by Chris Hankin

The lambda-calculus lies at the very foundations of computer science. Besides its historical role in computability theory it has had significant influence on programming language design and implementation, denotational semantics, and domain theory. The book emphasises the proof theory for the type-free lambda-calculus. The first six chapters concern this calculus and cover the basic theory, reduction, models, computability, and the relationship between the lambda-calculus and combinatory logic. Chapter 7 presents a variety of typed calculi; first the simply typed lambda-calculus, then Milner-style polymorphism and, finally, the polymorphic lambda-calculus. Chapter 8 concerns two variants of the type-free lambda-calculus that have appeared in the research literature: the lazy lambda-calculus, and the lambda sigma-calculus. The final chapter contains references and a guide to further reading. There are exercises throughout. In contrast to earlier books on these topics, which were written by logicians, this book is written from a computer science perspective and emphasises the practical relevance of many of the key theoretical ideas. The book is intended as a course text for final year undergraduates or first year graduate students in computer science. Research students should find it a useful introduction to more specialist literature.

Genres: Mathematics, Computer Science, Nonfiction, Computers

180 pages, Paperback

First published January 1, 1995

Reviews

[Ushan · Rating 4 out of 5]

This is a nice introduction to lambda calculus, combinatory logic and the like topics. It is based on Hankin's undergraduate course at Imperial College London. It is not self-contained; there are many references to the more comprehensive (and much more expensive) textbooks by Barendregt and by Hindley and Seldin. I wish I had read it in college.

[Jason Kowalski · Rating 5 out of 5]

This book brilliantly demystifies lambda calculus as a computational model, making complex concepts clear to me through practical examples.