Representing Functions
In order to represent a numerical function with respect to an evaluation relation O, it is necessary to exhibit a term mimicking the behaviour of the function itself. More precisely the reduction machine, taken as input this term applied to a sequence of
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Advisory Board: G. Ausiello M. Broy C. S. Calude S. Even J. Hartmanis J. Hromkovic N. Jones T. Leighton M. Nivat C. Papadimitriou D. Scott
Springer-Verlag Berlin Heidelberg GmbH
Simona Ronchi DeHa Rocca Luca Paolini
The Parametric lambda Calculus A Metamodel for Computation
Springer
Authors
Series Editors
Prof. Simona Ronchi Delia Rocca Universita di Torino Dipartimento di Informatica corso Svizzera 185 10149 Torino, Italy [email protected] www.di.unito.iU-ronchi
Prof. Dr. Wilfried Brauer Institut rur Informatik der TUM Boltzmannstr. 3, 85748 Garching, Germany [email protected]
Dr. Luca Paolini Universita di Torino Dipartimento di Informatica corso Svizzera 185 10149 Torino, Italy [email protected] www.di.unito.it/-paolini
Prof. Dr. Grzegorz Rozenberg Leiden Institute of Advanced Computer Science University of Leiden Niels Bohrweg 1,2333 CA Leiden, The Netherlands [email protected] Prof. Dr. Arto Salomaa Turku Centre for Computer Science Lemminkiiisenkatu 14 A, 20520 Turku, Finland [email protected]
Library of Congress Cataloging-in-Publication Data Ronchi Della Rocca, S. (Simona) The parametric lambda calculus : A metamodel for computation / Simona Ronchi Della Rocca, Luca Paolini. p. cm. - (Texts in theoretical computer science) Includes bibliographical references and index. ISBN 978-3-642-05746-5 ISBN 978-3-662-10394-4 (eBook) DOI 10.1007/978-3-662-10394-4 1. Lambda calculus. 1. Paolini, Luca, 1970- II. Title. III. Series. QA9.5.R66 2004 511.3'5-dc22 2003069100
ACM Computing Classification (1998): FA, F,3, 1.2.3, D.2 ISBN 978-3-642-05746-5 This work is subject to copyright. AlI rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springet-Verlag Berlin Heidelberg GmbH . Violations are liable for prosecution under the German Copyright Law. springeronline.com © Springer-Verlag Berlin Heidelberg 2004 Originally published by Springet:-Verlag Berlin Heidelberg New York in 2004 Softcover reprint of the hardcover 1st edition 2004 The use of general descriptive names, trademarks, 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 therefore free for general use. Cover Design: KiinkelLopka, Heidelberg 1)1pesetting: Camera-ready by the authors Printed on acid-free paper 45/3142/GF - 5432 1 O
To Corrado Băhm, fram which Simona and by transitivity - Luca leamed the pleasure of research and the interest in A-calculus
Preface
The A-calculus was invented by Church in the 1930s with the purpose of supplying a logical foundation for logic and mathematics [25]. Its use by Kleene as a coding
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