Categories and Computer Science

Categories and Computer Science
Author: R. F. C. Walters
Publisher: Cambridge University Press
Total Pages: 180
Release: 1991
Genre: Computers
ISBN: 9780521422260
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Category theory has become increasingly important and popular in computer science, and many universities now have introductions to category theory as part of their courses for undergraduate computer scientists. The author is a respected category theorist and has based this textbook on a course given over the last few years at the University of Sydney. The theory is developed in a straightforward way, and is enriched with many examples from computer science. Thus this book meets the needs of undergradute computer scientists, and yet retains a level of mathematical correctness that will broaden its appeal to include students of mathematics new to category theory.

Basic Category Theory for Computer Scientists

Basic Category Theory for Computer Scientists
Author: Benjamin C. Pierce
Publisher: MIT Press
Total Pages: 117
Release: 1991-08-07
Genre: Computers
ISBN: 0262326450
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Basic Category Theory for Computer Scientists provides a straightforward presentation of the basic constructions and terminology of category theory, including limits, functors, natural transformations, adjoints, and cartesian closed categories. Category theory is a branch of pure mathematics that is becoming an increasingly important tool in theoretical computer science, especially in programming language semantics, domain theory, and concurrency, where it is already a standard language of discourse. Assuming a minimum of mathematical preparation, Basic Category Theory for Computer Scientists provides a straightforward presentation of the basic constructions and terminology of category theory, including limits, functors, natural transformations, adjoints, and cartesian closed categories. Four case studies illustrate applications of category theory to programming language design, semantics, and the solution of recursive domain equations. A brief literature survey offers suggestions for further study in more advanced texts. Contents Tutorial • Applications • Further Reading

Category Theory for Programmers (New Edition, Hardcover)

Category Theory for Programmers (New Edition, Hardcover)
Author: Bartosz Milewski
Publisher:
Total Pages:
Release: 2019-08-24
Genre:
ISBN: 9780464243878
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Category Theory is one of the most abstract branches of mathematics. It is usually taught to graduate students after they have mastered several other branches of mathematics, like algebra, topology, and group theory. It might, therefore, come as a shock that the basic concepts of category theory can be explained in relatively simple terms to anybody with some experience in programming.That's because, just like programming, category theory is about structure. Mathematicians discover structure in mathematical theories, programmers discover structure in computer programs. Well-structured programs are easier to understand and maintain and are less likely to contain bugs. Category theory provides the language to talk about structure and learning it will make you a better programmer.

Category Theory for Computing Science

Category Theory for Computing Science
Author: Michael Barr
Publisher:
Total Pages: 352
Release: 1995
Genre: Computers
ISBN:
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A wide coverage of topics in category theory and computer science is developed in this text, including introductory treatments of cartesian closed categories, sketches and elementary categorical model theory, and triples. Over 300 exercises are included.

Categories, Types, and Structures

Categories, Types, and Structures
Author: Andrea Asperti
Publisher: MIT Press (MA)
Total Pages: 330
Release: 1991
Genre: Computers
ISBN:
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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 programmes 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 in Computer Science and Logic

Categories in Computer Science and Logic
Author: John Walker Gray
Publisher: American Mathematical Soc.
Total Pages: 394
Release: 1989
Genre: Mathematics
ISBN: 0821851004
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Presents the proceedings of AMS-IMS-SIAM Summer Research Conference on Categories in Computer Science and Logic that was held at the University of Colorado in Boulder. This book discusses the use of category theory in formalizing aspects of computer programming and program design.

Theoretical Computer Science for the Working Category Theorist

Theoretical Computer Science for the Working Category Theorist
Author: Noson S. Yanofsky
Publisher: Cambridge University Press
Total Pages: 150
Release: 2022-03-03
Genre: Mathematics
ISBN: 9781108792745
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Using basic category theory, this Element describes all the central concepts and proves the main theorems of theoretical computer science. Category theory, which works with functions, processes, and structures, is uniquely qualified to present the fundamental results of theoretical computer science. In this Element, readers will meet some of the deepest ideas and theorems of modern computers and mathematics, such as Turing machines, unsolvable problems, the P=NP question, Kurt Gödel's incompleteness theorem, intractable problems, cryptographic protocols, Alan Turing's Halting problem, and much more. The concepts come alive with many examples and exercises.

Categories for Types

Categories for Types
Author: Roy L. Crole
Publisher: Cambridge University Press
Total Pages: 362
Release: 1993
Genre: Computers
ISBN: 9780521457019
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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.

Nominal Sets

Nominal Sets
Author: Andrew M. Pitts
Publisher: Cambridge University Press
Total Pages: 291
Release: 2013-05-30
Genre: Computers
ISBN: 1107244684
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Nominal sets provide a promising new mathematical analysis of names in formal languages based upon symmetry, with many applications to the syntax and semantics of programming language constructs that involve binding, or localising names. Part I provides an introduction to the basic theory of nominal sets. In Part II, the author surveys some of the applications that have developed in programming language semantics (both operational and denotational), functional programming and logic programming. As the first book to give a detailed account of the theory of nominal sets, it will be welcomed by researchers and graduate students in theoretical computer science.

Tool and Object

Tool and Object
Author: Ralph Krömer
Publisher: Springer Science & Business Media
Total Pages: 400
Release: 2007-06-25
Genre: Mathematics
ISBN: 3764375248
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Category theory is a general mathematical theory of structures and of structures of structures. It occupied a central position in contemporary mathematics as well as computer science. This book describes the history of category theory whereby illuminating its symbiotic relationship to algebraic topology, homological algebra, algebraic geometry and mathematical logic and elaboratively develops the connections with the epistemological significance.