DOCSLIB.ORG

Nondeterminism in Algebraic Specifications and Algebraic Programs

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Nondeterminism in Algebraic Specifications and Algebraic Programs Progress in Theoretical Computer Science Editor Ronald V. Book, University of California Editorial Board Erwin Engeler, ΕΤΗ Zentrum, Zurich, Switzerland G6rard Huet, INRIA, Le Chesnay, France Jean-Pierre Jouannaud, Universit6 de Paris-Sud, Orsay, France Robin Milner, University of Edinburgh, Edinburgh, Scotland Maurice Nivat, Universite de Paris VII, Paris, France Martin Wirsing, Universität Passau, Passau, Germany Heinrich Hussmann Nondeterminism in Algebraic Specifications and Algebraic Programs Birkhäuser Boston · Basel · Berlin Heinrich Hussmann Technische Universität München Institut für Informatik D-8000 München 2 Germany Library of Congress Cataloging-in-Publication Data Hussmann, Heinrich, 1959- Nondeterminism in algebraic specification and algebraic programs / Heinrich Hussmann. p. cm. -- (Progress in theoretical computer science) Includes bibliographical references, ISBN 0-8176-3700-1 (alk. paper) 1. Computer science—Mathematics. I. Title. II. Series. QA76.9.M35H87 1993 93-9340 005.13'l~dc20 CIP Printed on acid-free paper. © Birkhäuser Boston 1993. Copyright is not claimed for works of U.S. Government employees. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photo• copying, recording, or otherwise, without prior permission of the copyright owner. Permission to photocopy for internal or personal use of specific clients is granted by Birkhäuser Boston for libraries and other users registered with the Copyright Clearance Center (CCC), provided that the base fee of $6.00 per copy, plus $0.20 per page is paid directly to CCC, 21 Congress Street, Salem, MA 01970, U.S.A. Special requests should be addressed directly to Birkhäuser Boston, 675 Massachusetts Avenue, Cambridge, MA 02139, U.S.A. ISBN 0-8176-3700-1 ISBN 3-7643-3700-1 Typset copy prepared by the Author. Printed and bound by Quinn-Woodbine, Woodbine, NJ. Printed in the U.S.A. 987654321 Table of Contents Chapter 0: Introduction 1 0.1 Preview 3 0.2 Historical Background 9 0.3 Basic Notions 10 Chapter 1: Nondeterministic Algebraic Specifications 17 1.1 Nondeterministic Algebras 17 1.1.1 A Discussion of Alternative Approaches 18 1.1.2 The Principle of Extensionality 22 1.1.3 The Notion of an Algebra 24 1.2 Inclusion Rules as a Specification Language 28 1.2.1 Axioms and their Semantics 28 1.2.2 The Calculus of Term Rewriting 31 1.2.3 Soundness: A Negative Result 34 1.2.4 Right-Linearity: A Special Case 38 Chapter 2: Specifications with a Deterministic Basis 43 2.1 Deterministic Basis 44 2.1.1 Soundness and Deterministic Basis 45 2.1.2 Determinacy Predicate 46 2.1.3 Completeness: A Negative Result 49 2.2 Additive Specifications 53 2.2.1 DET-Completeness and DET-Additi vity 54 2.2.2 Term Models and Completeness 57 2.3 Junk-Free Models 60 2.3.1 "Junk" in Nondeterministic Models 60 2.3.2 Breadth Induction 63 2.3.4 DET-Generated Models 66 2.3.5 Term-Generated Models 67 2.4 Hierarchical Specifications 71 Chapter 3: Structure of the Model Classes 75 3.1 Homomorphisms and Extremal Algebras 76 3.2 Initial Models 80 3.3 Initial Models with Deterministic Basis 83 Chapter 4: Nondeterministic Specifications as a General Framework 89 4.1 Equational Logic 89 4.2 Term Rewriting 91 vi CONTENTS 4.3 Conditional Axioms 93 4.4 Algebraic Programming 99 4.4.1 Constructor-Based Specifications 99 4.4.2. Narrowing without Confluence 107 4.5 Logic Programming 113 4.5.1. Narrowing Simulates Logic Programming 114 4.5.2. Logic Programming Simulates Narrowing 119 Chapter 5: Implementation and Examples 125 5.1 Term Rewriting 125 5.1.1 Innermost Rewriting 126 5.1.2 Search Strategies 131 5.1.3 Optimizations 132 5.2 Graph Rewriting 136 5.2.1 Representation of Terms by Graphs 137 5.2.2 Rewriting of Term Graphs 139 5.2.3 Soundness and Completeness 142 5.3 Examples 147 5.3.1 Nondeterministic Finite State Automata 147 5.3.2 Petri Nets 150 5.3.3 The Eight Queens Problem 152 5.3.4 The Monkey-Banana Problem 154 5.3.5 Printer Scheduling 156 Chapter 6: Partial Nondeterministic Specifications 161 6.1 Partial Operations 161 6.1.1 Undefined "Values" 161 6.1.2 Partial Multi-Algebras 164 6.2 Partiality and Term Rewriting 167 6.2.1 A Calculus for Partial Specifications 168 6.2.2 Partial DET-Completeness and DET-Additivity 170 6.3 Partial Specifications with Constructor Basis 172 6.4 Structure of the Model Classes 176 6.4.1 Homomorphisms 176 6.4.2 Initial Algebras 178 6.4.3 Terminal Algebras 183 CONTENTS vii Chapter 7: Communicating Processes: An Example 187 7.1. Communicating Processes (CP) 187 7.2. Semantics of CP 189 7.2.1. Transition Semantics 190 7.2.2. Trace Semantics 195 7.2.3. Refusal Semantics 197 7.3. Improvements and Applications 200 Chapter 8: Concluding Remarks 201 8.1. Summary and Evaluation 201 8.2. Future Work 202 References 205 Appendix A: Proofs 215 Appendix B: Experiments with RAP 243 Preface Algebraic specification, nondeterminism and term rewriting are three active research areas aiming at concepts for the abstract description of software systems: Algebraic specifications are well-suited for describing data structures and sequential software systems in an abstract way. Term rewriting methods are used in many prototyping systems and form the basis for executing specifi• cations. Nondeterminism plays a major role in formal language theory; in programming it serves for delaying design decisions in program development and occurs in a "natural" way in formalisations of distributed processes. Heinrich Hussmann presents an elegant extension of equational specification and term rewriting to include nondeterminism. Based on a clean modeltheoretic semantics he considers term rewriting systems without confluence restrictions as a specification language and shows that fundamental properties such as the existence of initial models or the soundness and completeness of narrowing, the basic mechanism for executing equational specifications, can be extended to nondeterministic computations. The work of Heinrich Hussmann is an excellent contribution to Algebraic Programming; it gives a framework that admits a direct approach to program verification, is suitable for describing concurrent and distributed processes, and it can be executed as fast as Prolog. Munich, January 1993 Martin Wirsing Preface by the Author This monograph is based on a Ph. D. thesis with the title „Nichtdetermini• stische Algebraische Spezifikationen" (in German), which was accepted by the University of Passau in the winter term 1988/1989. The text has been thoroughly revised and substantially extended in the meantime. The original thesis was primarily aimed at the "core" theme of generalizing algebraic specifications to nondeterminism. The monograph version now contains a comparison with the established field of logic programming, a new chapter on narrowing for nondeterministic specifications and a more detailed treatment of graph rewriting techniques. I hope that the revision will extend the readership of this book from specialists in algebraic specification to everybody who is interested in the relationship between logic programming, term rewriting and formal specification. I would like to thank Prof. Broy for finding the topic of the thesis and for his manyfold support, in particular for many fruitful discussions and for reading a preliminary version. Many thanks also to Prof. Wirsing, for reading a draft, for valuable remarks and for proposing the publication within this series of books. The anonymous referee has given very helpful suggestions for the revision of the manuscript, many thanks also to him or her. Many collegues have contributed to this work by discussions and remarks; for their particular interest I would like to thank Thomas Beizner, Alfons Geser, Jürgen Knopp, Bernhard Möller, Peter Mosses, Tobias Nipkow, Gert Smolka and Michal Walicki. Gabi Kohlmaier, now Gabi Hussmann, is entitled to special warm thanks for moral support. Finally, I would like to thank the staff of Birkhäuser for their excellent support in the technical production of the book. Munich, December 22, 1992 Heinrich Hussmann Chapter Ο Introduction This monograph presents a generalization of the theory of equational algebraic specifications, where the equational axioms are replaced by directed rewrite rules. A model-theoretic semantics for such specifications is given, which provides a rather general framework for studying • the integration of nondeterminism into algebraic specifications, and • model-oriented semantics for general (non-confluent) term rewriting. The study of this central topic leads to interesting side results in the fields of • relationships between algebraic and logic programming, and • relationships between term rewriting and graph rewriting. The starting point for this work is the observation that the available formal specification languages for software are very much influenced by the concepts of traditional mathematical logic. In particular, the notion of equality (which is a symmetric operation) plays a central role in algebraic specifications. This emphasis on symmetry does not correspond well to the fact that software belongs to a computational paradigm, which is always directed. Every execution of an algorithm consists in a directed evaluation of its formal descripton (therefore leading to such problems as the question of termination). This kind of directed evaluation transforms syntactical objects into semantically equal ones. Classical (deterministic) evaluation gives a close connection between a non- symmetric
Load more

Recommended publications
  • Thomas Ströhlein's Endgame Tables: a 50Th Anniversary
    Thomas Ströhlein's Endgame Tables: a 50th Anniversary Article Supplemental Material The Festschrift on the 40th Anniversary of the Munich Faculty of Informatics Haworth, G. (2020) Thomas Ströhlein's Endgame Tables: a 50th Anniversary. ICGA Journal, 42 (2-3). pp. 165-170. ISSN 1389-6911 doi: https://doi.org/10.3233/ICG-200151 Available at http://centaur.reading.ac.uk/90000/ It is advisable to refer to the publisher’s version if you intend to cite from the work. See Guidance on citing . Published version at: https://content.iospress.com/articles/icga-journal/icg200151 To link to this article DOI: http://dx.doi.org/10.3233/ICG-200151 Publisher: The International Computer Games Association All outputs in CentAUR are protected by Intellectual Property Rights law, including copyright law. Copyright and IPR is retained by the creators or other copyright holders. Terms and conditions for use of this material are defined in the End User Agreement . www.reading.ac.uk/centaur CentAUR Central Archive at the University of Reading Reading’s research outputs online 40 Jahre Informatik in Munchen:¨ 1967 – 2007 Festschrift Herausgegeben von Friedrich L. Bauer unter Mitwirkung von Helmut Angstl, Uwe Baumgarten, Rudolf Bayer, Hedwig Berghofer, Arndt Bode, Wilfried Brauer, Stephan Braun, Manfred Broy, Roland Bulirsch, Hans-Joachim Bungartz, Herbert Ehler, Jurgen¨ Eickel, Ursula Eschbach, Anton Gerold, Rupert Gnatz, Ulrich Guntzer,¨ Hellmuth Haag, Winfried Hahn (†), Heinz-Gerd Hegering, Ursula Hill-Samelson, Peter Hubwieser, Eike Jessen, Fred Kroger,¨ Hans Kuß, Klaus Lagally, Hans Langmaack, Heinrich Mayer, Ernst Mayr, Gerhard Muller,¨ Heinrich Noth,¨ Manfred Paul, Ulrich Peters, Hartmut Petzold, Walter Proebster, Bernd Radig, Angelika Reiser, Werner Rub,¨ Gerd Sapper, Gunther Schmidt, Fred B.
    [Show full text]
  • R ˘Azvan Diaconescu
    RA˘ ZVAN DIACONESCU list of publications MONOGRAPHS AND TEXTBOOKS [1-B] Institution-independent Model Theory. volume of Studies in Universal Logic series. Birkhauser¨ Basel, 2008. (386 pages). [2-B] (with K. Futatsugi) CafeOBJ Report: the language, proof techniques, and methodologies for object-oriented algebraic specification, volume 6 of AMAST Series in Computing. World Scientific Singapore, 1998. (174 pages) [3-B] Category-based Semantics for Equational and Constraint Logic Programming. D.Phil thesis, University of Oxford, 1994. (published as OUCL Monograph PRG-116, 120 pages) JOURNAL ARTICLES [4-J] Borrowing interpolation. Journal of Logic and Computation, Oxford Univ. Press. DOI:10.1093/logcom/exr007 [5-J] An axiomatic approach to structuring specifications. Theoretical Computer Science, 433:20–42, Elsevier, 2012. [6-J] Interpolation for predefined types. Mathematical Structures in Computer Science, 22(1):1–24, Cambridge Univ. Press, 2012. [7-J] Grothendieck inclusion systems. Applied Categorical Structures, 19(5):783–802, Springer, 2011. [8-J] Structural Induction in Institutions. Information and Computation, 209(9):1197–1222, Elsevier, 2011. [9-J] (with I. T¸ut¸u) On the Algebra of Structured Specifications. Theoretical Computer Science, 412(28):3145–3174, Elsevier, 2011. [10-J] On quasi-varieties of multiple valued logic models. Mathematical Logic Quarterly, 57(2):194–203, Wiley, 2011. [11-J] Coinduction for preordered algebras. Information and Computation, 209(2):108–117, Elsevier, 2011. [12-J] (with M. Petria) Saturated models in institutions. Archive for Mathematical Logic, 49(6):693–723, Springer, 2010. [13-J] Quasi-Boolean encodings and conditionals in algebraic specification. Journal of Logic and Algebraic Programming, 79(2):174–188, Elsevier, 2010.
    [Show full text]
  • Lecture Notes in Computer Science 1378 Edited by G
    Lecture Notes in Computer Science 1378 Edited by G. Goos, J. Hartmanis and J. van Leeuwen Maurice Nivat (Ed.) Foundations of Software Science and Computation Structures First International Conference, FoSSaCS'98 Held as Part of the Joint European Conferences on Theory and Practice of Software, ETAPS' 98 Lisbon, Portugal, March 28 - April 4, 1998 Proceedings ~ Springer Series Editors Gerhard Goos, Karlsruhe University, Germany Juris Hartmanis, Cornell University, NY, USA Jan van Leeuwen, Utrecht University, The Netherlands Volume Editor Maurice Nivat LITP, Universit6 Paris 7 2, Place Jussieu, F-75251 Paris Cedex 05, France E-mail: Maurice.Nivat @litp.liafa.jussieu.fr Cataloging-in-Publication data applied for Die Deutsche Bibliothek - CIP-Einheitsaufnahme Foundations of software science and computation structures : first international conference ; proceedings / FoSSaCS '98, held as part of the Joint European Conferences on Theory and Practice of Software, ETAPS '98, Lisbon, Portugal, March 28 - April 4, 1998. Maurice Nivat (ed.). - Berlin ; Heidelberg ; New York ; Barcelona ; Budapest ; Hong Kong ; London Milan ; Paris ; Santa Clara ; Singapore ; Tokyo : Springer, 1998 (Lecture notes in computer science ; Vol. 1378) ISBN 3-540-64300-1 CR Subject Classification (1991):F.3. F.4.2, El.I, D.3.3-4, D.2.1 ISSN 0302-9743 ISBN 3-540-64300-1 Springer-Verlag Berlin Heidelberg New York This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, re-use of illustrations, recitation, broadcasting, reproduction on microfilms 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 Springer -Verlag.
    [Show full text]
  • Kolmogorov Complexity in Perspective. Part II: Classification, Information Processing and Duality Marie Ferbus-Zanda
    Kolmogorov Complexity in perspective. Part II: Classification, Information Processing and Duality Marie Ferbus-Zanda To cite this version: Marie Ferbus-Zanda. Kolmogorov Complexity in perspective. Part II: Classification, Information Processing and Duality. Synthese, Springer Verlag (Germany), 2010, pp.00. hal-00525505 HAL Id: hal-00525505 https://hal.archives-ouvertes.fr/hal-00525505 Submitted on 13 Oct 2010 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Kolmogorov Complexity in perspective Part II: Classification, Information Processing and Duality∗ Marie Ferbus-Zanda LIAFA, CNRS & Universit´eParis Diderot - Paris 7 Case 7014 75205 Paris Cedex 13 France [email protected] Abstract We survey diverse approaches to the notion of information: from Shan- non entropy to Kolmogorov complexity. Two of the main applications of Kolmogorov complexity are presented: randomness and classification. The survey is divided in two parts published in a same volume. Part II is dedicated to the relation between logic and information sys- tem, within the scope of Kolmogorov algorithmic information theory. We present a recent application of Kolmogorov complexity: classification us- ing compression, an idea with provocative implementation by authors such as Bennett, Vit´anyi and Cilibrasi.
    [Show full text]
  • A Rational Deconstruction of Landin's J Operator
    BRICS RS-06-4 Danvy & Millikin: A Rational Deconstruction of Landin’s J Operator BRICS Basic Research in Computer Science A Rational Deconstruction of Landin’s J Operator Olivier Danvy Kevin Millikin BRICS Report Series RS-06-4 ISSN 0909-0878 February 2006 Copyright c 2006, Olivier Danvy & Kevin Millikin. BRICS, Department of Computer Science University of Aarhus. All rights reserved. Reproduction of all or part of this work is permitted for educational or research use on condition that this copyright notice is included in any copy. See back inner page for a list of recent BRICS Report Series publications. Copies may be obtained by contacting: BRICS Department of Computer Science University of Aarhus IT-parken, Aabogade 34 DK–8200 Aarhus N Denmark Telephone: +45 8942 9300 Telefax: +45 8942 5601 Internet: [email protected] BRICS publications are in general accessible through the World Wide Web and anonymous FTP through these URLs: http://www.brics.dk ftp://ftp.brics.dk This document in subdirectory RS/06/4/ A Rational Deconstruction of Landin’s J Operator∗ Olivier Danvy and Kevin Millikin BRICS† Department of Computer Science University of Aarhus‡ February 28, 2006 Abstract Landin’s J operator was the first control operator for functional languages, and was specified with an extension of the SECD machine. Through a se- ries of meaning-preserving transformations (transformation into continu- ation-passing style (CPS) and defunctionalization) and their left inverses (transformation into direct style and refunctionalization), we present a compositional evaluation function corresponding to this extension of the SECD machine. We then characterize the J operator in terms of CPS and in terms of delimited-control operators in the CPS hierarchy.
    [Show full text]
  • Introduction to the Literature on Programming Language Design Gary T
    Computer Science Technical Reports Computer Science 7-1999 Introduction to the Literature On Programming Language Design Gary T. Leavens Iowa State University Follow this and additional works at: http://lib.dr.iastate.edu/cs_techreports Part of the Programming Languages and Compilers Commons Recommended Citation Leavens, Gary T., "Introduction to the Literature On Programming Language Design" (1999). Computer Science Technical Reports. 59. http://lib.dr.iastate.edu/cs_techreports/59 This Article is brought to you for free and open access by the Computer Science at Iowa State University Digital Repository. It has been accepted for inclusion in Computer Science Technical Reports by an authorized administrator of Iowa State University Digital Repository. For more information, please contact [email protected]. Introduction to the Literature On Programming Language Design Abstract This is an introduction to the literature on programming language design and related topics. It is intended to cite the most important work, and to provide a place for students to start a literature search. Keywords programming languages, semantics, type systems, polymorphism, type theory, data abstraction, functional programming, object-oriented programming, logic programming, declarative programming, parallel and distributed programming languages Disciplines Programming Languages and Compilers This article is available at Iowa State University Digital Repository: http://lib.dr.iastate.edu/cs_techreports/59 Intro duction to the Literature On Programming Language Design Gary T. Leavens TR 93-01c Jan. 1993, revised Jan. 1994, Feb. 1996, and July 1999 Keywords: programming languages, semantics, typ e systems, p olymorphism, typ e theory, data abstrac- tion, functional programming, ob ject-oriented programming, logic programming, declarative programming, parallel and distributed programming languages.
    [Show full text]
  • A Verified Prover Based on Ordered Resolution Anders Schlichtkrull, Jasmin Christian Blanchette, Dmitriy Traytel
    A Verified Prover Based on Ordered Resolution Anders Schlichtkrull, Jasmin Christian Blanchette, Dmitriy Traytel To cite this version: Anders Schlichtkrull, Jasmin Christian Blanchette, Dmitriy Traytel. A Verified Prover Based on Ordered Resolution. CPP 2019 - The 8th ACM SIGPLAN International Conference on Certified Programs and Proofs, Jan 2019, Cascais, Portugal. 10.1145/3293880.3294100. hal-01937141 HAL Id: hal-01937141 https://hal.archives-ouvertes.fr/hal-01937141 Submitted on 27 Nov 2018 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. A Verified Prover Based on Ordered Resolution Anders Schlichtkrull Jasmin Christian Blanchette Dmitriy Traytel DTU Compute Department of Computer Science Department of Computer Science Technical University of Denmark Vrije Universiteit Amsterdam ETH Zürich Kongens Lyngby, Denmark Amsterdam, the Netherlands Zürich, Switzerland [email protected] [email protected] [email protected] Abstract interpreted universally. Each literal is either an atom A or The superposition calculus, which underlies first-order the- its negation :A. An atom is a symbol applied to a tuple of orem provers such as E, SPASS, and Vampire, combines or- terms—e.g., prime¹nº. The empty clause is denoted by ?.
    [Show full text]
  • MAURICE NIVAT, UNE GRANDE FIGURE 89 ◦◦◦◦••◦◦ Une Brève Biographie Scientifique De Maurice Nivat 2
    HOMMAGE Maurice Nivat, une grande gure Pierre-Louis Curien 1 Le texte qui suit a été rédigé en 2001, pour le volume intitulé « Merci, Maurice : a mosaic in honour of Maurice Nivat », paru comme numéro spécial de la revue Theoretical Com- puter Science, que Maurice Nivat avait fon- dée. En écrivant ce texte, je me réjouissais par avance des travaux scientifiques que Maurice continuerait de poursuivre, des combats qu’il continuerait à livrer pour la pleine reconnais- sance de notre discipline et pour son enseigne- ment « de première classe », et de la liberté qu’il aurait, sa retraite prise, pour assouvir à loisir d’autres passions : celles pour le patri- moine, pour l’ethnographie, pour le théâtre, pour les voyages... Et, en effet, Maurice a poursuivi pendant plusieurs années ses travaux en tomographie discrète. Accompagné par son épouse Paule, il a parcouru le monde en long et en large, à six reprises. Il a mené un combat acharné pour l’introduction de l’informatique dans les programmes de l’enseignement secon- daire. Maurice nous a quittés au terme d’une maladie qu’il a combattue avec un im- mense courage, continuant à lire, à s’informer, à s’enflammer pour les causes qu’il 1. Institut de recherche en informatique fondamentale (IRIF, UMR 8243), CNRS et université Paris- Diderot. 1024 – Bulletin de la société informatique de France, numéro 12, juin 2018, pp. 87–107 88 PIERRE-LOUIS CURIEN ◦◦◦◦••◦◦ défendait. Je me souviendrai de la gourmandise qu’il avait encore dans les yeux et dans le verbe pour me parler, sur son lit d’hôpital, de sa fascination pour les iguanes, alors que je revenais d’une conférence aux îles Galápagos.
    [Show full text]
  • Around the Domino Problem - Combinatorial Structures and Algebraic Tools Etienne Moutot
    Around the Domino Problem - Combinatorial Structures and Algebraic Tools Etienne Moutot To cite this version: Etienne Moutot. Around the Domino Problem - Combinatorial Structures and Algebraic Tools. Dis- crete Mathematics [cs.DM]. Université de Lyon; Turun yliopisto, 2020. English. NNT : 2020LY- SEN027. tel-02967024 HAL Id: tel-02967024 https://tel.archives-ouvertes.fr/tel-02967024 Submitted on 14 Oct 2020 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. N◦ National de Thèse : 2020LYSEN027 Thèse de Doctorat de l’Université de Lyon opérée par l’École Normale Supérieure de Lyon en cotutelle avec Turun Yliopisto École doctorale n◦ 512 École doctorale en Informatique et Mathématiques de Lyon Spécialité : Informatique Soutenue publiquement le 15 juillet 2020 par Etienne Moutot Autour du problème du domino Structures combinatoires et outils algébriques Devant le jury composé de : Valérie Berthé Directrice de Recherche, Universite Paris Diderot Rapporteure Fabien Durand Professeur, Université de Picardie Jules Verne Rapporteur Bryna Kra Professeure, Northwestern University Rapporteure Andrei Romashchenko Chargé de Recherche, Université de Montpellier Examinateur Guillaume Theyssier Chargé de Recherche, Université Aix-Marseille Examinateur Stéphan Thomassé Professeur, ENS de Lyon Directeur Jarkko Kari Professeur, University of Turku Co-tuteur Nathalie Aubrun Chargée de Recherche, ENS de Lyon Co-encadrante Acknowledgements Finally.
    [Show full text]
  • Transductions Des Langages De Chomsky Annales De L’Institut Fourier, Tome 18, No 1 (1968), P
    ANNALES DE L’INSTITUT FOURIER MAURICE NIVAT Transductions des langages de Chomsky Annales de l’institut Fourier, tome 18, no 1 (1968), p. 339-455 <http://www.numdam.org/item?id=AIF_1968__18_1_339_0> © Annales de l’institut Fourier, 1968, tous droits réservés. L’accès aux archives de la revue « Annales de l’institut Fourier » (http://annalif.ujf-grenoble.fr/) implique l’accord avec les conditions gé- nérales d’utilisation (http://www.numdam.org/conditions). Toute utilisa- tion commerciale ou impression systématique est constitutive d’une in- fraction pénale. Toute copie ou impression de ce fichier doit conte- nir la présente mention de copyright. Article numérisé dans le cadre du programme Numérisation de documents anciens mathématiques http://www.numdam.org/ Ann. Inst Fourier, Grenoble 18, 1 (1968), 339^456 TRANSDUCTIONS DES LANGAGES DE CHOMSKY par Maurice NIVAT Introduction. I. L'origine de ce travail est pratique. Les langages de programmation sont définis par des règles précises qui en font pour l'essentiel des langages "context-free", (désignés plus loin sous le nom de C-langages). Ce fut le mérite de N. Chomsky d'introduire à des fins purement lin- guistiques cette structure [2], et celui des créateurs du langage Algol de voir tout le parti qu'en pouvait tirer les utilisateurs de machines à calculer [14] : restaient à résoudre deux problèmes d'ailleurs étroi- tement liés l'un à l'autre : — décrire des algorithmes de reconnaissance, c'est-à-dire des algorithmes permettant de décider connaissant les règles de formation des phrases d'un tel langage si une phrase donnée appartient ou non à ce langage et retrouver en cas de réponse favorable la suite des règles au moyen desquelles cette phrase peut être formée (comme phrase du langage).
    [Show full text]
  • THE TREE NEWSLETTER June 2007 Issue 23
    ACADEMIA The Academy of Europe EUROPAEA } THE TREE NEWSLETTER JUNE 2007 ISSUE 23 From the President issues of relevance to modern society given the pace of development in the from the perspectives of impartial European research landscape, we cannot This is the fifth year analysis. As individual members we claim yet to be fully representative of my presidency should be more active in support of our of the very best across all fields of and the penultimate journal. For any members who feel that scholarship. Nomination of candidates one for my period of we have no impact: it may be worth for membership is the responsibility of office. I will leave my browsing the pages of the European all members. To be credible, we need personal reflections Research Council website, where our to ensure that we reflect the best in on the past to next members serve both on the Council our community. So, I would ask all year, when we will itself and also in large numbers on the members to try this coming year to also celebrate our 20th anniversary as a many expert review panels. Similarly nominate at least one new member. fully functioning international academy our “HERCULES” group of members, are Please remember that you can nominate – a very fitting moment in time ‘to take active in organising annual conferences candidates outside of your own field stock’. on issues of research policy relevant to and section. institutions of higher education and As with all organisations, we have we are strong and active supporters of ANNUAL MEETING, our critics and our champions, who the work of the European Academies 2007 Science Advisory Council (EASAC) collectively reflect a wide range of Toledo “Dialogue of Three Cultures – a group of Academies that provide perspectives and views, both on our and Our European Heritage (Toledo, coordinated, expert scientific advice to role and also on the extent to which the cradle of the renaissance)” the institutions of the European Union.
    [Show full text]
  • A Step-Indexed Semantics of Imperative Objects∗ 1
    Logical Methods in Computer Science Vol. 5 (4:2) 2009, pp. 1–48 Submitted Mar. 3, 2009 www.lmcs-online.org Published Dec. 17, 2009 A STEP-INDEXED SEMANTICS OF IMPERATIVE OBJECTS ∗ CAT˘ ALIN˘ HRIT¸CU a AND JAN SCHWINGHAMMER b a Department of Computer Science, Saarland University, Saarbr¨ucken, Germany e-mail address: [email protected] b Programming Systems Lab, Saarland University, Saarbr¨ucken, Germany e-mail address: [email protected] Abstract. Step-indexed semantic interpretations of types were proposed as an alternative to purely syntactic proofs of type safety using subject reduction. The types are interpreted as sets of values indexed by the number of computation steps for which these values are guaranteed to behave like proper elements of the type. Building on work by Ahmed, Appel and others, we introduce a step-indexed semantics for the imperative object calculus of Abadi and Cardelli. Providing a semantic account of this calculus using more ‘traditional’, domain-theoretic approaches has proved challenging due to the combination of dynamically allocated objects, higher-order store, and an expressive type system. Here we show that, using step-indexing, one can interpret a rich type discipline with object types, subtyping, recursive and bounded quantified types in the presence of state. 1. Introduction The imperative object calculus of Abadi and Cardelli is a very small, yet very expressive object-oriented language [2]. Despite the extreme simplicity of its syntax, the calculus models many important concepts of object-oriented programming, as well as the often subtle interaction between them. In particular it raises interesting and non-trivial questions with respect to typing.
    [Show full text]