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Categories for Types : Cambridge Mathematical Textbooks - Roy L. Crole

Categories for Types

Cambridge Mathematical Textbooks

Paperback

Published: 28th March 1994
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This textbook explains the basic principles of categorical type theory and the techniques used to derive categorical semantics for specific type theories. It introduces the reader to ordered set theory, lattices and domains, and this material provides plenty of examples for an introduction to category theory, which covers categories, functors, natural transformations, the Yoneda lemma, cartesian closed categories, limits, adjunctions and indexed categories. Four kinds of formal system are considered in detail, namely algebraic, functional, polymorphic functional, and higher order polymorphic functional type theory. For each of these the categorical semantics are derived and results about the type systems are proved categorically. Issues of soundness and completeness are also considered. Aimed at advanced undergraduates and beginning graduates, this book will be of interest to theoretical computer scientists, logicians and mathematicians specializing in category theory.

"A well-organized introduction to categorical methods of lambda calculus...The individual topics are treated in a uniform, balanced style from introduction, syntax, to categorical models and categorical-type theory correspondence." Jiri Adamek, Mathematical Reviews

Order, lattices and domains
Basic category theory
Algebraic type theory
Functional type theory
Polymorphic functional type theory
Higher order polymorphism
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780521457019
ISBN-10: 0521457017
Series: Cambridge Mathematical Textbooks
Audience: Professional
Format: Paperback
Language: English
Number Of Pages: 356
Published: 28th March 1994
Publisher: CAMBRIDGE UNIV PR
Country of Publication: GB
Dimensions (cm): 22.73 x 15.16  x 2.29
Weight (kg): 0.5