An Introduction To Lambda Calculi For Computer Scientists

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.