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 An Introduction to Lambda Calculi for Computer Scientists
Chris Hankin
The λcalculus 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 typefree λcalculus.
The first six chapters concern this calculus and cover the basic theory, reduction, models, computability, and the relationship between the λcalculus and combinatory logic. Chapter 7 presents a variety of typed calculi; first the simply typed λcalculus, then Milnerstyle polymorphism and, finally, the polymorphic λcalculus. Chapter 8 concerns two variants of the typefree λcalculus that have appeared in the research literature: the lazy λcalculus, and the λσcalculus. 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.
180pp.
28th September 2004
ISBN 0954300653
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