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Book Review: Categories for Types by Roy L. Crole by Nandakumar Sankaran is a Computer Science article available to read on EtoBox.

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Crole explains the connections between type theory and category theory. Four type systems namely, Algebraic, Functional, Second order Polymorphic, and Higher Order Polymorphic type theories are formalized in detail and their intimate relations to particular kinds of category theories are shown. These relationships form the basis of Categorical Type Theory. The book does not assume that the reader is familiar with Category Theory; hence the first two chapters introduce the basic concepts of ordered sets, lattices, domains and categories. Chapter 2 of the book describes how various categories are related and reason about their properties based on ordered sets, functors, natural transformations, adjunctions, Yoneda Lemma, cartesian closed and indexed categories, limits and colimits. Although many examples illustrate the properties described, a reader unfamiliar with the fundamental concepts would find [1] and [3] very useful companions to Categories for Types. The beginner would also benefit from covering just those sections from Chapter 2 that are required for the specific type theories. Chapters 3 and 4 discuss Algebraic and Functional type theories and Chapters 5 and 6 discuss Seco

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Author

Nandakumar Sankaran

Publisher

ACM

Published

1995

Language

EN

Field

Computer Science (Physical Sciences)