The Functional Treatment of Parsing

165 Pages·1993·5.235 MB·English

by  René Leermakers (auth.)

THE FUNCTIONAL TREATMENT OF PARSING
THE KLUWER INTERNATIONAL SERIES
IN ENGINEERING AND COMPUTER SCIENCE
NATURAL LANGUAGE PROCESSING
AND MACHINE TRANSLATION
Consulting Editor
Ja ime Carbonell
Other books in the series:
NATURAL LANGUAGE PROCESSING: TUE PLNLP APPROACH, Karen Jensen, George E.
Heidom, Stephen D. Richardson
ISBN: 0-7923-9279-5
ADAPTIVE PARSING: Selr-Extending Natural Language Interfaces, J. F. Lehman
ISBN: 0-7923-9183-7
GENERALIZED L. R. PARSING, M. Tomita
ISBN: 0-7923-9201-9
CONCEPTUAL INFORMATION RETRIEVAL: A Case Study in Adaptive Partial Parsing,
M. L. Mauldin
ISBN: 0-7923-9214-0
CURRENT ISSUES IN PARSING TECI-INOLOGY. M. Tomita
ISBN: 0-7923-9131-4
NATURAL LANGUAGE GENERATION IN ARTIF1CIAL INTELLIGENCE AND
COMPUTATIONAL LINGUISTICS, C. L. Paris, W. R. Swartout, W. C. Mann
ISBN: 0-7923-9098-9
UNDERSTANDING EDITORIAL TEXT: A Computer Model or Argument Comprebension,
S. J. Alvarado
ISBN: 0-7923-9123-3
NAIVE SEMANTICS FOR NATURAL LANGUAGE UNDERSTANDING, K. Dahlgren
ISBN: 0-89838-287-4
INTEGRATED NATURAL LANGUAGE DIALOGUE: A Computatiooal Model, R. E.
Frederking
ISBN: 0-89838-255-6
A NATURAL LANGUAGE INTERFACE FOR COMPUTER AIDED DESIGN, T. Samad
ISBN: 0-89838-222-X
EFF1CIENT PARSING FOR NATURAL LANGUAGE: A Fast AIgorithm ror Practical
Systems, M. Tomita
ISBN: 0-89838-202-5
THE FUNCTIONAL TREATMENT
OFPARSING
by
Rene Leermakers
Institute for Perception Research,
Eindhoven, The Netherlands
SPRINGER SCIENCE+BUSINESS MEDIA, B.V.
Library of Congress Cataloging-in-Publication Data
Leermakers. Rena
The functional treatment of parsing / by Rena Leermakers.
p. cm. -- (Kluwer international series in engineering and
computer science ; v. 242)
Includes bibliographical references and index.
1. Natural language processing (Computer science) 2. Parsing
(Computer grammar) 3. Functional programming (Computer science)
I. Title. II. Series: Kluwer international series in engineering
and computer science SECS 242.
QA76.9.N38L42 1993
005.13' 1--dc20 93-22799
ISBN 978-1-4613-6397-2 ISBN 978-1-4615-3186-9 (eBook)
DOI 10.1007/978-1-4615-3186-9
Printed on acid-free paper
All Rights Reserved
© 1993 Springer Science+Business Media Dordrecht
Originally published by Kluwer Academic Publishers in 1993
Softcover reprint of the hardcover 1s t edition 1993
No part of the material protected by this copyright notice may be reproduced or
utilized in any form or by any means, electronic or mechanical,
inc1uding photocopying, recording Of by any information stofage and
retrieval system, without written permission from the copyright owner.
To my family
but in particular
to my son Arjeh
who made bis first steps
as this book went to press
and to my daughter Mirjam
FOREWORD
Formal-Ianguage thoory, thooreticallinguistics and computationallinguistics
have shared roots in the 1950s, with the seminal work of Kleene, Chomsky,
Miller and Bar-Hille1 on regular languages and phrase-structure grammars.
However, various social, cultural and technological factors have since then
conspired to split those disciplines and weaken their understanding and ap
preciation of each other. Efficiency considerations and the fact that program
ming languages are human artifacts may partly justify the focus on determin
istic languages and parsers in the theory of context-free parsing. However,
naturallanguages are highly ambiguous and thus non-deterministic, making
much of that theory seem irrelevant 10 natural-Ianguage parsing. It has thus
been difficult to convince the computational linguist of the importance of
context-free-parsing thoory, if not for specific algorithms, then for concepts
and techniques essential to the rigorous analysis of natural-Ianguage parsers.
Looking in the other direction, the formal-Ianguage theorist is mostly un
aware of the special problems of natural-Ianguage parsing, and thus not only
misses a potentially rich area for new research but also falls to appreciate
the efforts of computational linguists. For these reasons, the publication of
The Functional Treatment 0/ Parsing is doubly welcome.
For the computationallinguist, Rene Leermakers's book brings out the rele
vance of the thoory of context-free parsing to natural-Ianguage parsing. His
innovative use of functional notation makes algorithrns and their derivation
less mysterious, and eliminates much of the need for the laborious inductive
proofs of correctness found in other parsing thoory texts. In addition, the
functional approach ties well with the widespread acquaintance of current
and recent students with the functional programming paradigm through lan
guages such as Scheme and ML. Delicate data structure issues in parsing
are c1early located in elegant abstractions representing nondeterminism and"
result reuse.
For the computer scientist, The Functional Treatment 0/ Parsing offers a
fresh and unified perspective on a variety of parsing algorithms, some well
known and some less so. This new perspective offers much simpler proofs
vii
viii THE FUNCTIONAL TREATMENT OF PARSING
of correctness and computational complexity, and eliminates the artificial
distinction between stack-based and tabular parsers. The use of equational
reasoning rather than special-purpose inductive proofs to relate algorithms
to their specifications is an excellent application of an approach to program
derivation and verification that has received strong support in the wodes
of Boyer, Moore, Dijkstra and Gries. From a more practical angle, Leer
makers' s approach provides a theoretical basis for the parsing component
of interactive language-development environments, for which the standard
detenninistic parsing methods have been proven unwieldy.
Parsing theory has many subtleties, requiring attentive and thoughtful study.
While the present book does not excuse the student from those obligations,
it will provide ample rewards to readers at all levels. In addition to a self
contained and elegant treatment of all the main ideas of context-free parsing,
it brings out the underlying unity of the subject as no other book I know of,
and ofIers a wealth of conceptual and technical riches, of which I particularly
enjoyed the application of Lambek types to the analysis of grammatical
covers and attribute grammars.
There have been increasing signs in the research literature of a long-overdue
convergence between fonnal-Ianguage theory and computationallinguistics,
in particular in the area of context-free parsing. The Functional Treatment
0/ Parsing not only demonstrates that convergence for the first time in book
fonn, but also revives context-free parsing theory as an interesting and rele
vant topic for computationallinguists and computer scientists alike.
Femando C.N. Pereira.
CONTENTS
FOREWORD by Fernando Pereira vii
PREFACE xiii
1 CONTEXT-FREE GRAMMARS 1
2 BUNCH NOTATION 7
2.1 Bunches 8
2.2 Algorithmic interpretation 12
3 GRAMMAR INTERPRETATIONS IS
3.1 The natural interpretation 15
3.2 Derivation 20
3.3 The Lambek types 23
3.4 Recognition functions 26
3.5 Generation 28
3.6 Summary of interpretations 29
4 RECURSIVE DESCENT 33
4.1 The functional interpretation 33
4.2 Termination 35
4.3 Complexity and memoization 35
4.4 Look ahead 38
4.5 Error recovery 42
S GRAMMAR TRANSFORMATIONS 4S
5.1 Making grammars bilinear 45
ix
x THE FUNCTIONAL TREATMENT OF PARSING
5.2 Recursive descent for EG 48
5.3 Partial elimination of left recursion 49
5.4 Recursive descent for F G 57
6 RECURSIVE ASCENT 61
6.1 The algorithm 62
6.2 Tennination 65
6.3 A variant that works with strings 66
6.4 Complexity 68
6.5 EBNF grammars 69
7 PARSE FOREST 75
7.1 Infonnal introduction 75
7.2 The gramm ar E~ 77
7.3 Forest for bilinear grammars 78
7.4 The set Q 82
7.5 Standard Earley parser 85
7.6 Earley versos Earley 87
8 ATTRIBUTE GRAMMARS 91
8.1 Notational conventions 92
8.2 Attribute functions 94
8.3 Example 96
8.4 Function graphs 100
8.5 Attribute grammar parser 103
8.6 Direct attribute evaluation 104
9 LR PARSERS 115
9.1 LR(O) recognizer 115
9.2 The detenninistic case 120
9.3 Implementation with stacks 123
9.4 Some variants 126
9.5 Look ahead 128
9.6 Attributes 130
9.7 Continuations 131
9.8 Error recovery 134
Contents xi
9.9 The methods by Lang and Tomita 137
9.10 Evaluation w.r.t. standard approaches 138
9.11 Earley versos LR 140
10 SOMENOTES 143
10.1 Context-free grammars 143
10.2 Names 144
10.3 Bunches 145
10.4 Functional programming 145
10.5 Grammar transfonnations 146
10.6 Memo-functions 146
10.7 Parse forests 147
10.8 Earley 147
10.9 Attribute grammars 147
10.10 Naturallanguage 148
10.11 Other applications 148
10.12 LR parsing 149
10.13 EBNF 149
10.14 Conclusion 150
REFERENCES ISI
INDEX 157