categories for types cambridge mathematical textbooks

Download Book Categories For Types Cambridge Mathematical Textbooks in PDF format. You can Read Online Categories For Types Cambridge Mathematical Textbooks here in PDF, EPUB, Mobi or Docx formats.

Categories For Types

Author : Roy L. Crole
ISBN : 0521457017
Genre : Computers
File Size : 58. 96 MB
Format : PDF, ePub, Mobi
Download : 507
Read : 846

Download Now


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.

Practical Foundations Of Mathematics

Author : Paul Taylor
ISBN : 0521631076
Genre : Mathematics
File Size : 90. 62 MB
Format : PDF
Download : 948
Read : 331

Download Now


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.

Categories And Computer Science

Author : R. F. C. Walters
ISBN : 0521422264
Genre : Computers
File Size : 21. 31 MB
Format : PDF
Download : 922
Read : 985

Download Now


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.

Introduction To Higher Order Categorical Logic

Author : J. Lambek
ISBN : 0521356539
Genre : Mathematics
File Size : 55. 80 MB
Format : PDF, Kindle
Download : 902
Read : 830

Download Now


Part I indicates that typed-calculi are a formulation of higher-order logic, and cartesian closed categories are essentially the same. Part II demonstrates that another formulation of higher-order logic is closely related to topos theory.

Topology Via Logic

Author : Steven Vickers
ISBN : 0521576512
Genre : Computers
File Size : 62. 51 MB
Format : PDF, ePub, Docs
Download : 676
Read : 1145

Download Now


This is an advanced textbook on topology for computer scientists. It is based on a course given by the author to postgraduate students of computer science at Imperial College.

Categorical Logic And Type Theory

Author : Bart Jacobs
ISBN : 0444508538
Genre : Mathematics
File Size : 27. 79 MB
Format : PDF, ePub, Mobi
Download : 761
Read : 395

Download Now


This book is an attempt to give a systematic presentation of both logic and type theory from a categorical perspective, using the unifying concept of fibred category. Its intended audience consists of logicians, type theorists, category theorists and (theoretical) computer scientists.

Algebraic And Coalgebraic Methods In The Mathematics Of Program Construction

Author : Roland Backhouse
ISBN : 9783540477976
Genre : Computers
File Size : 55. 65 MB
Format : PDF, ePub, Docs
Download : 510
Read : 1113

Download Now


Program construction is about turning specifications of computer software into implementations. Recent research aimed at improving the process of program construction exploits insights from abstract algebraic tools such as lattice theory, fixpoint calculus, universal algebra, category theory, and allegory theory. This textbook-like tutorial presents, besides an introduction, eight coherently written chapters by leading authorities on ordered sets and complete lattices, algebras and coalgebras, Galois connections and fixed point calculus, calculating functional programs, algebra of program termination, exercises in coalgebraic specification, algebraic methods for optimization problems, and temporal algebra.

Theorem Proving In Higher Order Logics

Author : Richard J. Boulton
ISBN : 9783540447559
Genre : Computers
File Size : 66. 89 MB
Format : PDF
Download : 601
Read : 258

Download Now


This volume constitutes the proceedings of the 14th International Conference on Theorem Proving in Higher Order Logics (TPHOLs 2001) held 3–6 September 2001 in Edinburgh, Scotland. TPHOLs covers all aspects of theorem proving in higher order logics, as well as related topics in theorem proving and veri?cation. TPHOLs 2001 was collocated with the 11th Advanced Research Working Conference on Correct Hardware Design and Veri?cation Methods (CHARME 2001). This was held 4–7 September 2001 in nearby Livingston, Scotland at the Institute for System Level Integration, and a joint half-day session of talks was arranged for the 5th September in Edinburgh. An excursion to Traquair House and a banquet in the Playfair Library of Old College, University of Edinburgh were also jointly organized. The proceedings of CHARME 2001 have been p- lished as volume 2144 of Springer-Verlag’s Lecture Notes in Computer Science series, with Tiziana Margaria and Tom Melham as editors. Each of the 47 papers submitted in the full research category was refereed by at least 3 reviewers who were selected by the Program Committee. Of these submissions, 23 were accepted for presentation at the conference and publication in this volume. In keeping with tradition, TPHOLs 2001 also o?ered a venue for the presentation of work in progress, where researchers invite discussion by means of a brief preliminary talk and then discuss their work at a poster session. A supplementary proceedings containing associated papers for work in progress was published by the Division of Informatics at the University of Edinburgh.

Generic Programming

Author : Roland Backhouse
ISBN : 9783540201946
Genre : Computers
File Size : 23. 72 MB
Format : PDF
Download : 359
Read : 842

Download Now


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

Basic Category Theory

Author : Tom Leinster
ISBN : 9781107044241
Genre : Mathematics
File Size : 37. 3 MB
Format : PDF
Download : 883
Read : 396

Download Now


A short introduction ideal for students learning category theory for the first time.

Top Download:

Best Books