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.
International Conference COSIT'99 Stade, Germany, August 25-29, 1999 Proceedings
Author: Christian Freksa,David M. Mark
The Conference on Spatial Information Theory – COSIT – grew out of a series of workshops / NATO Advanced Study Institutes / NSF specialist meetings concerned with cognitive and applied aspects of representing large-scale space, particularly geographic space. In these meetings, the need for a well-founded theory of spatial information processing was identified. The COSIT conference series was established in 1993 as a biennial interdisciplinary European conference on the representation and processing of information about large-scale space, after a successful international conference on the topic had been organized by Andrew Frank et al. in Pisa, Italy, in 1992 (frequently referred to as ‘COSIT zero’). After two successful European conferences with strong North-American participation (COSIT ’93, held on the Island of Elba, Italy; COSIT ’95, held in Semmering, Austria), the conference became a truly international enterprise when COSIT ’97 was held in the Laurel Highlands, Pennsylvania, USA. COSIT ’99 will take place in Stade, Germany. All aspects of large-scale space, i. e. spaces too large to be seen from a single vantage point, are addressed in the COSIT conferences. These include spaces of geographic scale, as well as smaller spaces in which humans, animals, or autonomous robots have to find their way around. Spatial information theory also deals with the description of objects, processes, or events in spatial environments and it forms the foundation for the construction of Geographic Information Systems (GIS) and for spatial information and communication system design in general.
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.
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.
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.
Functional programming (Computer science) by Tetsuo Ida,Atsushi Ohori,Masato Takeichi
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.
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.
Eine Informatik-einfhrung/ a Computer Science Introduction
Author: Harold Abelson,Julie Sussman,Gerald Jay Sussman
Die Übersetzung der bewährten Einführung in die Informatik, entstanden am Massachusetts Institute of Technology (MIT), wird seit Jahren erfolgreich in der Lehre eingesetzt. Schritt für Schritt werden Konstruktion und Abstraktion von Daten und Prozeduren dargestellt. Von der Modularisierung bis zum Problemlösen mit Registermaschinen werden verschiedene Programmierparadigmen entwickelt und die effektive Handhabung von Komplexität gezeigt. Als Programmiersprache wird SCHEME verwendet, ein Dialekt von LISP. Alle Programme laufen in jeder dem IEEE-Standard entsprechenden SCHEME-Implementierung.
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.
Mathematics by F. William Lawvere,Stephen Hoel Schanuel
This is an introduction to thinking about elementary mathematics from a categorial point of view. The goal is to explore the consequences of a new and fundamental insight about the nature of mathematics.
Business & Economics by Geoffrey G. Parker,Marshall W. Van Alstyne,Sangeet Paul Choudary