Categories, Types, and Structures An Introduction to Category Theory for the Working Computer Scientist by Andrea Asperti and Giuseppe Longo Categories, Types, and Structures provides a self-contained introduction to general category theory and explains the mathematical structures that have been the foundation of programming language design for the past two decades. The authors observe that the language of categories could provide a powerful means for standardizing methods and language, and they offer examples including recursion theory, the early dialect of LISP, Edingurg ML, and current work in polymorphism and modularity. In Part 1, 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. Part 2 pursues the more complex mathematical semantics of data types and programs as objects and morphisms of categories. In particular, the semantics of type-free lambda calculus and of its more recent higher-order versions is closely discussed. The basis for a theory of internal category theory is also developed as a tool for the categorical understanding of polymorphism in functional programming. Andrea Asperti is Charg de Recherche at INRIA-Rocquencourt. Giuseppe Longo is Directeur de Recherches CNRS at the Departement de Mathematiques et Informatique, Ecole Normale Superieure, Paris, and is former Professor Computer Science at the University of Pisa. The first draft of the book was written while Longo was teaching a course on the topic at Carnegie Mellon University, in 1987/88, and Asperti was visiting there as a graduate student. September 1991 307 pages ISBN 0-262-01125 #29.25/$43.95 MIT PRESS 55 Hayward ST. Cambridge Mass 02142 USA EUROPE: 14 Bloomsbury Square London WC1A 2LP U.K. Facsimile: 071-404-0601 ====================================