Categories, Types, and Structures : An Introduction to Category Theory for the Working Computer Scientist

Category theory is a mathematical subject whose importance in several areas of computer science, most notably the semantics of programming languages and the design of programs using abstract data types, is widely acknowledged. This book introduces category theory at a level appropriate for computer scientists and provides practical examples in the context of programming language design. "Categories, Types, and Structures provides a self-contained introduction to general category theory and explains the mathematical structures that have been the foundation of language design for the past two decades. The authors observe that the language of categories could provide a powerful means of standardizing of methods and language, and offer examples ranging from the early dialects of LISP, to Edinburgh ML, to current work in polymorphisms and modularity. The book familiarizes readers with categorical concepts through examples based on elementary mathematical notions such as monoids, groups, and topological spaces, as well as elementary notions from programming language semantics such as partial orders and categories of domains in denotational semantics. It then pursues the more complex mathematical semantics of data types and programs as objects and morphisms of categories. Both authors are on the faculty of the Instituto di Scienze dell'Informazione at the Universita di Pisa. "Categories, Types, and Structures is included inAsperti, Andrea is the author of 'Categories, Types, and Structures : An Introduction to Category Theory for the Working Computer Scientist', published 1990 under ISBN 9780262121453 and ISBN 026212145X.