Monograph: "...Category Theory for the Working Computer Scientist"
Date: Mon, 21 Oct 91 12:55:32 +0100
Categories, Types, and Structures
An Introduction to Category Theory for the Working
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
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
55 Hayward ST.
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