Categories for Types

Hardback

Main Details

Title Categories for Types
Authors and Contributors      By (author) Roy L. Crole
Physical Properties
Format:Hardback
Pages:356
Dimensions(mm): Height 236,Width 156
Category/GenreAlgebra
Calculus and mathematical analysis
ISBN/Barcode 9780521450928
ClassificationsDewey:511
Audience
Professional & Vocational

Publishing Details

Publisher Cambridge University Press
Imprint Cambridge University Press
Publication Date 27 January 1994
Publication Country United Kingdom

Description

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.

Reviews

"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