Map Framework A Formal Model of Maps as a Fundamental Data Type in I
This book explores the concept of a map as a fundamental data type. It defines maps at three levels. The first is an abstract level, in which mathematic concepts are leveraged to precisely explain maps and operational semantics. The second is at a discret
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p Framework A Formal Model of Maps as a Fundamental Data Type in Information Systems
Map Framework
Mark McKenney Markus Schneider •
Map Framework A Formal Model of Maps as a Fundamental Data Type in Information Systems
123
Markus Schneider University of Florida Gainesville, FL USA
Mark McKenney Southern Illinois University Edwardsville, IL USA
ISBN 978-3-319-46764-1 DOI 10.1007/978-3-319-46766-5
ISBN 978-3-319-46766-5
(eBook)
Library of Congress Control Number: 2016952010 © Springer International Publishing AG 2016 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. Printed on acid-free paper This Springer imprint is published by Springer Nature The registered company is Springer International Publishing AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland
To my family, Elizabeth, Samantha, and Evelyn, for their support and understanding through the hours of research and writing that went into it. And to my parents, Scott and Joan, for their never-ending support and encouragement. —Mark McKenney To my family, Annette, Florian, and Tim, as well as my parents Hans and Christel Schneider, for their never-ending love, support, and encouragement. —Markus Schneider
Contents
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1 3 3 4 5 7 8 9 10 12 13
2 A Formal Model of Maps as a Fundamental Type . . . . . . 2.1 Spatial Data Models . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Topological Relationships . . . . . . . . . . . . . . . . . . . . . . . 2.3 An Informal Overview of Spatial Partitions . . . . . . . . . 2.4 Spatial Partitions: A Mathematical Model of Maps . . . 2.4.1 Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4.2 Spatial Partitions . . . . . . . . . . . . . . . . . . . . . . . . 2.5 Summary . . . . . . . . . . . . . . . . .
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