Categories Allegories

Author: P.J. Freyd
Publisher: Elsevier
ISBN: 9780080887012
Size: 52.55 MB
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General concepts and methods that occur throughout mathematics – and now also in theoretical computer science – are the subject of this book. It is a thorough introduction to Categories, emphasizing the geometric nature of the subject and explaining its connections to mathematical logic. The book should appeal to the inquisitive reader who has seen some basic topology and algebra and would like to learn and explore further. The first part contains a detailed treatment of the fundamentals of Geometric Logic, which combines four central ideas: natural transformations, sheaves, adjoint functors, and topoi. A special feature of the work is a general calculus of relations presented in the second part. This calculus offers another, often more amenable framework for concepts and methods discussed in part one. Some aspects of this approach find their origin in the relational calculi of Peirce and Schroeder from the last century, and in the 1940's in the work of Tarski and others on relational algebras. The representation theorems discussed are an original feature of this approach.

Relational And Algebraic Methods In Computer Science

Author: Wolfram Kahl
Publisher: Springer
ISBN: 3319247042
Size: 18.79 MB
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This book constitutes the proceedings of the 15th International Conference on Relational and Algebraic Methods in Computer Science, RAMiCS 2015, held in Braga, Portugal, in September/October 2015. The 20 revised full papers and 3 invited papers presented were carefully selected from 25 submissions. The papers deal with the theory of relation algebras and Kleene algebras, process algebras; fixed point calculi; idempotent semirings; quantales, allegories, and dynamic algebras; cylindric algebras, and about their application in areas such as verification, analysis and development of programs and algorithms, algebraic approaches to logics of programs, modal and dynamic logics, interval and temporal logics.

Category Theory In Context

Author: Emily Riehl
Publisher: Courier Dover Publications
ISBN: 0486820807
Size: 20.95 MB
Format: PDF
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Introduction to concepts of category theory — categories, functors, natural transformations, the Yoneda lemma, limits and colimits, adjunctions, monads — revisits a broad range of mathematical examples from the categorical perspective. 2016 edition.

Relations And Kleene Algebra In Computer Science

Author: Rudolf Berghammer
Publisher: Springer Science & Business Media
ISBN: 364204638X
Size: 70.25 MB
Format: PDF
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The book constitutes the joint refereed proceedings of the 11th International Conference on Relational Methods in Computer Science, RelMiCS 2009, and the 6th International Conference on Applications of Kleene Algebras, AKA 2009, held in Doha, Qatar in November 2009. The 22 revised full papers presented together with 2 invited papers were carefully reviewed and selected from numerous submissions. The papers describe the calculus of relations and similar algebraic formalisms as methodological and conceptual tools with special focus on formal methods for software engineering, logics of programs and links to neighbouring disciplines. Their scope comprises relation relation algebras and Kleene algebras, related formalisms such as process algebras, fixed point calculi, idempotent semirings, quantales, allegories, dynamic algebras, cylindric algebras and their applications in areas such as verification, analysis and development of programs and algorithms relational formal methods such as B or Z, tabular methods, algebraic approaches to logics of programs, modal and dynamic logics, interval and temporal logics, algebraic semantics of programming languages , graph theory and combinatorial optimization, games, automata and language theory, mechanised and automated reasoning, decision procedures, spatio-temporal reasoning, knowledge acquisition, preference and scaling methods or information systems.

Category Theory And Computer Science

Author: David Pitt
Publisher: Springer
ISBN:
Size: 10.22 MB
Format: PDF, ePub
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This book presents the proceedings of the Sixth International Conference on Category Theory and Computer Science, CTCS '95, held in Cambridge, UK in August 1995. The 15 revised full papers included in the volume document the exploitation of links between logic and category theory leading to a solid basis for much of the understanding of the semantics of computation. Notable amongst other advances is the introduction of linear logic and other substructural logics, providing a new approach to proof theory. Further aspects covered are semantics of lambda calculi and type theories, program specification and development, and domain theory.

Mathematical Foundations Of Programming Semantics

Author: Stephen D. Brookes
Publisher: Springer Verlag
ISBN:
Size: 72.70 MB
Format: PDF, Docs
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In translating the second edition of his book on high voltage measurement techniques from the original German, published also in English, Russian and Chinese, the author has added a number of revisions and late developments inthe fields of high-voltage technology, electric energy systems and pulsepower. A survey of measurement techniques for nonsinusoidal, rapidly changing high voltages and high currents seemed particularly desireable, since power pulses are employed more frequently outside the normal electronics. Special attention has been given to high-voltage probes, high-current shunts, fast electrical and optical diagnostic principles, transient recorders, electromagnetic compatibility in high-voltage laboratories etc.

A Classical Mind

Author: A. W. Roscoe
Publisher: Prentice Hall PTR
ISBN: 9780132948449
Size: 13.73 MB
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To celebrate the 60th birthday and the achievement of C.A.R. Hoare, a rich assembly of contributors have pulled together to provide a volume of essays which are dedicated to Tony Hoare and his approach to Computer Science. Recognizing the huge difference that Tony has made to the way that computing is perceived each contributor has a very personal way of expressing their respect for his commitment and enterprise. To be included with the Hoare Computer Science Series. Reads like a who's who of computing, each paper written by a key person in the field. Niche market, but has the ability to appeal to a wide range of lecturers, students, librarians.