Category Theory has, in recent years, become increasingly important and popular in computer science, and many universities now introduce Category Theory as part of the curriculum for undergraduate computer science students. Here, the theory is developed in a straightforward way, and is enriched with many examples from computer science.
Mathematics by London Mathematical Society. Symposium
Proceedings of the London Mathematical Society Symposium, Durham 1991
Author: London Mathematical Society. Symposium
Publisher: Cambridge University Press
Category theory and related topics of mathematics have been increasingly applied to computer science in recent years. This book contains selected papers from the London Mathematical Society Symposium on the subject which was held at the University of Durham. Participants at the conference were leading computer scientists and mathematicians working in the area and this volume reflects the excitement and importance of the meeting. All the papers have been refereed and represent some of the most important and current ideas. Hence this book will be essential to mathematicians and computer scientists working in the applications of category theory.
Generic programming attempts to make programming more efficient by making it more general. This book is devoted to a novel form of genericity in programs, based on parameterizing programs by the structure of the data they manipulate. The book presents the following four revised and extended chapters first given as lectures at the Generic Programming Summer School held at the University of Oxford, UK in August 2002: - Generic Haskell: Practice and Theory - Generic Haskell: Applications - Generic Properties of Datatypes - Basic Category Theory for Models of Syntax
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.
Geographic information systems by Christian Freksa,David M. Mark
International Conference COSIT'99 Stade, Germany, August 25-29, 1999 Proceedings
Author: Christian Freksa,David M. Mark
Category: Geographic information systems
This book constitutes the refereed proceedings of the International Conference on Spatial Information Theory, COSIT '99, held in Stade, Germany, in August 1999. The 30 revised full papers presented were carefully reviewed and selected from 70 submissions. The book is divided into topical sections on landmarks and navigation, route directions, abstraction and spatial hierarchies, spatial reasoning calculi, ontology of space, visual representation and reasoning, maps and routes, and granularity and qualitative abstraction.
Practical Foundations collects the methods of construction of the objects of twentieth-century mathematics. Although it is mainly concerned with a framework essentially equivalent to intuitionistic Zermelo-Fraenkel logic, the book looks forward to more subtle bases in categorical type theory and the machine representation of mathematics. Each idea is illustrated by wide-ranging examples, and followed critically along its natural path, transcending disciplinary boundaries between universal algebra, type theory, category theory, set theory, sheaf theory, topology and programming. Students and teachers of computing, mathematics and philosophy will find this book both readable and of lasting value as a reference work.
To clarify the understanding of reasoning systems that underpin much computing theory, this text criticizes and challenges the results of formalization with the language of PROLOG. It analyzes the process of formalization, setting out to explain proof and reasoning.
Describes an algebraic approach to programming that permits the calculation of programs. Introduces the fundamentals of algebra for programming. Presents paradigms and strategies of program construction that form the core of Algorithm Design. Discusses functions and categories; applications; relations and allegories; datatypes; recursive programs, optimization issues, thinning algorithms, dynamic programming and greedy algorithms. Appropriate for all programmers.
Category theory provides a general conceptual framework that has proved fruitful in subjects as diverse as geometry, topology, theoretical computer science and foundational mathematics. Here is a friendly, easy-to-read textbook that explains the fundamentals at a level suitable for newcomers to the subject. Beginning postgraduate mathematicians will find this book an excellent introduction to all of the basics of category theory. It gives the basic definitions; goes through the various associated gadgetry, such as functors, natural transformations, limits and colimits; and then explains adjunctions. The material is slowly developed using many examples and illustrations to illuminate the concepts explained. Over 200 exercises, with solutions available online, help the reader to access the subject and make the book ideal for self-study. It can also be used as a recommended text for a taught introductory course.
First the concepts of [lambda]-presentable objects, locally [lambda]-presentable categories, and [lambda]-accessible categories are discussed in detail. The authors go on to prove that Freyd's essentially algebraic categories are precisely the locally presentable categories. In the final chapter they treat some advanced topics in model theory. For researchers in category theory, algebra, computer science, and model theory, this book will be a necessary purchase.