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【实例简介】
Categories and Computer Science -Cambridge Computer Science Texts)R. F. C. Walters.pdf
28 Cambridge Computer Science Texts Categories and computer Science RF C. Walters Department of Computer Science, University of Sydney SE CAMBRIDGE UNIVERSITY PRESS CAMBRIDGE UNIVERSITY PRESS Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, Sao Paulo Cambridge University Press The Edinburgh Building, Cambridge CB2 2RU, UK Published in the United States of America by Cambridge University Press, New York www.cambridge.org Informationonthistitlewww.cambridge.org/9780521419970 c Carslaw publications 199 1 First published by Carslaw Publications 1991 First Cambridge university Press edition 1992 A catalogue record for this publication is available from the british library ISBN-13978-0-521-41997-0 hardback ISBN-10 0-521-41997-2 hardback ISBN-13978-0-521-42226-0 paperback ISBN-10 0-521-42226-4 paperback Transferred to digital printing 2006 In memory of my father Lynn David Walters Preface This book has its origins in an undergraduate course i have given on categories and Computer Science over the past three years to a total of approximately 200 students at the University of Sydney. The course is a gentle introduction to category theory with motivating examples taken from computer science, and was developed through interaction with the students Although this book is an undergraduate text, it contains quite a deal of origi nal material, further details of which may be found in my reports and papers listed with the references. In particular, much of the discussion of distributive categories, data types, and imperative programs is new, and Chapter 7, $2 con- tains a description of a generalization of the Todd-Coxeter algorithm suitable for computing left Kan extensions developed with Sean Carmody; this section was written together with Sean The idea for the course came from discussions with Bill Lawvere while he was in Sydney in 1988. Since then we have held in Sydney, in addition to the Sydney Categor Seminar(now 21 years old, chaired by Max Kelly), a further seminar The Sydney Categories in Computer Science Seminar. I have learnt much from the members of this seminar, visitors to the seminar, and from my graduate students, fourth-year students, and vacation scholars. My thanks go to David Benson, Aurelio Carboni, Sean Carmody, Robin Cockett, Robbie Gates, Diana Gibson, Mike Johnson, Lesley Johnston, Giulio Katis, Wafaa. Khalil, Stephen Lack, Mark Lauer, Phil Lavers, Mark Leeming, Stephen Ma, gordon Monro Wesley Phoa, Steve Schanuel, Usha Sridhar, Sun Shu-Hao, Andrew Solomon Margaret Thiel, Phil Wadler, and Bill Unger. The research and visitors have been supported by an australian Research Council Program grant, and an Aus tralian Research Council Small Grant The main assistance in actually producing the book has come from Sean Car mody Wafaa Khalil, and Karl Wehrhahn. Their help has been invaluable. Ad ditional assistance has been received from Mike Johnson, Stephen Lack, and Wesley Phoa. A further important debt is to my friend and collaborator in Mi lan, Stefano Kasangian, who first introduced me to the community of computer scientists interested in category theory R. F.C. Walters walters_bomaths su oz au 31May1991 v11 Contents Introduction 1 2. Examples 58 3. Imperative Programs 62 1 The Algebra of Functions 3 Problems 68 1. Categories 3 4 Data Types 2. General Examples 8 3. Free Categories 1. Arithmetic 71 Generators and relations 10 2. Stacks 74 4. Some Large Categories 14 3. Arrays 80 5. The Dual of a Category 16 4. Binary Trees 81 Problems 20 5. Queues 83 6. Pointers 86 2 Products and sums 25 7. Turing Machines 87 1. Initial and Terminal ob jects 25 Problems 90 2. Products 27 5 Categories of Functors 93 3. Categories with Products circuits 32 1. Functors 93 4. Products of Families 39 2. Functor Categories 99 5. Sums 42 3. Directed Graphs 6. Categories with Sums; and Regular grammars 102 Flow Charts 45 4. Automata and Im tive Problems 52 Programs with Ir nput 112 3 Distributive Categories 55 5. The Specification of functions 116 1. The Distributive law 55 6. What does free mean 120 CoNTENTS 7. Adjoint Functors 123 7 Computational Problems 126 Category Theory 143 6 More About Products 129 1. The Knuth-Bendix Procedure 143 1. The Free Category 2. Computing Left Kan Extensions 147 with Products 129 Problems 159 2. Functional Specification with Products 133 References 161 3. Context-free Languages 137 4. Natural Numbers and Cartesian Closed Categories 138 Index 163 Problems 141 【实例截图】
【核心代码】
Categories and Computer Science -Cambridge Computer Science Texts)R. F. C. Walters.pdf
28 Cambridge Computer Science Texts Categories and computer Science RF C. Walters Department of Computer Science, University of Sydney SE CAMBRIDGE UNIVERSITY PRESS CAMBRIDGE UNIVERSITY PRESS Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, Sao Paulo Cambridge University Press The Edinburgh Building, Cambridge CB2 2RU, UK Published in the United States of America by Cambridge University Press, New York www.cambridge.org Informationonthistitlewww.cambridge.org/9780521419970 c Carslaw publications 199 1 First published by Carslaw Publications 1991 First Cambridge university Press edition 1992 A catalogue record for this publication is available from the british library ISBN-13978-0-521-41997-0 hardback ISBN-10 0-521-41997-2 hardback ISBN-13978-0-521-42226-0 paperback ISBN-10 0-521-42226-4 paperback Transferred to digital printing 2006 In memory of my father Lynn David Walters Preface This book has its origins in an undergraduate course i have given on categories and Computer Science over the past three years to a total of approximately 200 students at the University of Sydney. The course is a gentle introduction to category theory with motivating examples taken from computer science, and was developed through interaction with the students Although this book is an undergraduate text, it contains quite a deal of origi nal material, further details of which may be found in my reports and papers listed with the references. In particular, much of the discussion of distributive categories, data types, and imperative programs is new, and Chapter 7, $2 con- tains a description of a generalization of the Todd-Coxeter algorithm suitable for computing left Kan extensions developed with Sean Carmody; this section was written together with Sean The idea for the course came from discussions with Bill Lawvere while he was in Sydney in 1988. Since then we have held in Sydney, in addition to the Sydney Categor Seminar(now 21 years old, chaired by Max Kelly), a further seminar The Sydney Categories in Computer Science Seminar. I have learnt much from the members of this seminar, visitors to the seminar, and from my graduate students, fourth-year students, and vacation scholars. My thanks go to David Benson, Aurelio Carboni, Sean Carmody, Robin Cockett, Robbie Gates, Diana Gibson, Mike Johnson, Lesley Johnston, Giulio Katis, Wafaa. Khalil, Stephen Lack, Mark Lauer, Phil Lavers, Mark Leeming, Stephen Ma, gordon Monro Wesley Phoa, Steve Schanuel, Usha Sridhar, Sun Shu-Hao, Andrew Solomon Margaret Thiel, Phil Wadler, and Bill Unger. The research and visitors have been supported by an australian Research Council Program grant, and an Aus tralian Research Council Small Grant The main assistance in actually producing the book has come from Sean Car mody Wafaa Khalil, and Karl Wehrhahn. Their help has been invaluable. Ad ditional assistance has been received from Mike Johnson, Stephen Lack, and Wesley Phoa. A further important debt is to my friend and collaborator in Mi lan, Stefano Kasangian, who first introduced me to the community of computer scientists interested in category theory R. F.C. Walters walters_bomaths su oz au 31May1991 v11 Contents Introduction 1 2. Examples 58 3. Imperative Programs 62 1 The Algebra of Functions 3 Problems 68 1. Categories 3 4 Data Types 2. General Examples 8 3. Free Categories 1. Arithmetic 71 Generators and relations 10 2. Stacks 74 4. Some Large Categories 14 3. Arrays 80 5. The Dual of a Category 16 4. Binary Trees 81 Problems 20 5. Queues 83 6. Pointers 86 2 Products and sums 25 7. Turing Machines 87 1. Initial and Terminal ob jects 25 Problems 90 2. Products 27 5 Categories of Functors 93 3. Categories with Products circuits 32 1. Functors 93 4. Products of Families 39 2. Functor Categories 99 5. Sums 42 3. Directed Graphs 6. Categories with Sums; and Regular grammars 102 Flow Charts 45 4. Automata and Im tive Problems 52 Programs with Ir nput 112 3 Distributive Categories 55 5. The Specification of functions 116 1. The Distributive law 55 6. What does free mean 120 CoNTENTS 7. Adjoint Functors 123 7 Computational Problems 126 Category Theory 143 6 More About Products 129 1. The Knuth-Bendix Procedure 143 1. The Free Category 2. Computing Left Kan Extensions 147 with Products 129 Problems 159 2. Functional Specification with Products 133 References 161 3. Context-free Languages 137 4. Natural Numbers and Cartesian Closed Categories 138 Index 163 Problems 141 【实例截图】
【核心代码】
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