Table Of ContentLecture Notes ni
Computer Science
Edited by G. Goos and .J Hartmanis
355
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3rd Conference, International RTA-89
Chapel Hill, North Carolina, USA
April 3-5, 1989
Proceedings
galreV-regnirpS
nilreB Heidelberg NewYork London Paris oykoT
Editorial Board
D. Barstow W. Brauer .P Brinch Hansen D. Gries D. Luckham
C. Moler A. Pnueli G. Seegm~ller J. Stoer N. Wirth
Editor
Nachum Dershowitz
Department of Computer Science, University of Illinois
1304 W. Springfield Ave., Urbana, IL 61801-2987, USA
CR Subject Classification (1987): D.3, F.3.2, F.4, 1.1, 1.2.2-3
ISBN 3-540-51081-8 Springer-Verlag Berlin Heidelberg New York
tSBN 0-387-51081-8 Springer-Verlag New York Berlin Heidelberg
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PREFACE
This volume contains the proceedings of the Third International Conference on
Rewriting Techniques and Applications (RTA-89). The conference was held April
3-5, 1989, in Chapel Hill, North Carolina, U.S.A. Professor Garrett Birkhoff of Harvard
University delivered an invited lecture.
The two previous conferences were held in France:
• Dijon, May 1985 (Lecture Notes in Computer Science 202, Springer-Verlag);
• Bordeaux, May 1987 (Lecture Notes in Computer Science 256, Springer-Verlag).
For the third conference, papers were solicited in the following (or related) areas:
Term rewriting systems Symbolic and algebraic computation
Conditional rewriting Equational programming languages
Graph rewriting and grammars Completion procedures
Algebraic semantics Rewrite-based theorem proving
Equational reasoning Unification and matching algorithms
Lambda and combinatory calculi Term-based architectures
The 34 regular papers in this volume were selected from 84 submissions by a ten-
member committee, consisting of the following individuals:
Bruno Courcelle (Bordeaux) Deepak Kaput (Albany)
Nachum Dershowitz (Urbana) Claude Kirchner (Nancy)
Jean Gallier (Philadelphia) Jan Willem Klop (Amsterdam)
Jieh Hsiang (Stony Brook) Dallas Lankford (Ruston)
Jean-Pierre Jouannaud (Orsay) Mark Stickel (Menlo Park)
Each paper was graded by two to six people (committee members and outside referees).
Also included in this volume are short descriptions of a dozen of the implemented
equational reasoning systems demonstrated at the meeting.
Local arrangements were organized by:
David A. Plaisted
Department of Computer Science
Universitoyf North Carolina at Chapel Hill
Chapel-Hill, NC 27599
U.S.A.
The meeting was in cooperation with the Association for Computing Machinery and
received support from the University of Illinois at Urbana-Champaign and the University
of North Carolina at Chapel Hill.
Nachum Dershowitz
Program Chairperson
the committee acknowledges the help of the following referees:
Leo Bachmair A. Megrelis
J. C. M. Baeten Yves Metivier
M. Bezem Aart Middeldorp
Maria Paola Bonacina David Musser
Alexandre Boudet Paliath Narendran
Hans-Jfirgen Burckert Tobias Nipkow
Robert Cori Friedrich Otto
Herv$ Devie Uday Reddy
Francois Fages Jean-Luc R~my
Isabelle Gnaedig Michael Rusinowitch
Miki Hermann Manfred Schmidt-Schau$
Bharat Jayaraman Sabine Stiffer
Simon Kaplan Jonathan Stillman
StSphane Kaplan F.-J. de Vries
H61~ne Kirchner R. C. de Vrijer
Pierre Lescanne Hantao Zhang
D. Luggiez
CONTENTS
Invited Lecture
Rewriting Ideas from Universal Algebra (Abstract)
Garrett Birkhoff .................................................................... 1
Regular Papers
Characterizations of Unification Type Zero
Franz Baader ...................................................................... 2
Proof Normalization for Resolution and Paramodulation
Leo Bachmair ..................................................................... 51
Complete Sets of Reductions Modulo Associativlty, Commutativity and Identity
Timothy B. Baird, Gerald E Peterson, Ralph W. ~Vilkerson ........................ 29
Completion-Time Optimization of Rewrite-Time Goal Solving
Hubert Bertling, Harald Ganzinger ................................................ 45
Computing Ground Reducibility and Inductively Complete Positions
Reinhard Biindgen, Wolfgang Kiichlin ............................................. 59
Inductive Proofs by Specification Transformations
Hubert Comon .................................................................... 67
Narrowing and Unification in Functional Programming--An Evaluation
Mechanism for Absolute Set Abstraction
John Darlington, Yi-ke Guo ....................................................... 92
Simulation of Turing Machines by a Left-Linear Rewrite Rule
Max Dauchet .................................................................... 901
Higher-order Unification with Dependent Function Types
ConaI M. Elliott ................................................................. 121
An Overview of LP, The Larch Prover
Stephen J. Garland, John V. Guttag .............................................. 731
Graph Grammars, A New Paradigm for Implementing Visual Languages
Herbert GSttler .................................................................. 251
Termination Proofs and the Length of Derivations (Preliminary Version)
Dieter Hofbauer, Clemens Lautemann ............................................ 167
Abstract Rewriting with Concrete Operators
Stephane Kaplan, Christine Choppy .............................................. 871
On How to Move Mountains ~Assoclatively and Commutatively'
Mike Lai ......................................................................... 187
Generalized GrSbner Bases: Theory and Applications. A Condensation
Dallas Lankford .................................................................. 203
IV
A Local Termination Property for Term Rewriting Systems
Dana May Latch, Ron Sigal ...................................................... 222
An Equational Logic Sampler
George F. MeNulty .............................................................. 234
Modular Aspects of Properties of Term Rewriting Systems Related to Normal Forms
Aart Middetdorp ................................................................. 263
Priority Rewriting: Semantics, Confluence, and Conditionals
Chilukuri K. Mohan ............................................................. 278
Negation with Logical Variables in ConditionM Rewriting
Chilukuri K. Mohan, Mandayam K. Srivas ....................................... 292
Algebraic Semantics and Complexity ofT erm Rewriting Systems
Tohru Naoi, Yasuyoshi Inagaki ................................................... 113
Optimization by Non-deterministic, Lazy Rewriting
Sanjai Narain ................................................................... 623
Combining Matching Algorithms: The Regular Case
Tobias Nipkow ................................................................... 343
Restrictions of Congruences Generated by Finite Canonical Strlng-Rewriting Systems
])biedrich Otto ................................................................... 953
Embedding with Patterns and Associated Recursive Path Ordering
Laurence Puel ................................................................... 173
Rewriting Techniques for Program Synthesis
Uday S. Reddy ................................................................... 388
Transforming Strongly Sequential Rewrite Systems with Constructors for Efficient
Parallel Execution
R. C. Sekar~ Shaunak Pawagi, I. V. Ramakrishnan ............................... 404
Efficient Ground Completion: An O(n log n) Algorithm for Generating Reduced Sets
of Ground Rewrite Rules Equivalent to a Set of Ground Equations E
Wayne Snyder ................................................................... 419
Extensions and Comparison of Simplification Orderings
Joachim Steinbach ............................................................... 434
Classes of Equational Programs that Compile into Efficient Machine Code
Robert L Strandh ................................................................ 449
Fair Termination is Decidable for Ground Systems
Sophie Tison .................................................................... 462
Termination for the Direct Sum of Left-Linear Term Rewriting Systems
(Preliminary Draft)
Yoshihito Toyama, Jan Willem Klop, Hendrik Pieter Barendregt .................. 477
Conditional Rewrite Rule Systems with Built-In Arithmetic and Induction
Sergey G. Vorobyov .............................................................. 492
VII
Consider Only General Superpositions in Completion Procedures
Hantao Zhang, Deepak Kaput .................................................... 513
System Descriptions
Solving Systems of Linear Diophantine Equations and Word Equations
Habib Abdulrab, Jean-Pierre Pdcuchet ............................................ 530
SbReve2: A Term Rewriting Laboratory with (AC-)Unfailing Completion
Siva Anantharaman, Jieh Hsiang, Jalel Mzali ..................................... 533
THEOPOGLES -- An Efficient Theorem Prover Based on Rewrite-Techniques
J. Avenhaus, J. Denzinger, J. 315ller ............................................. 538
COMTES -- An Experimental Environment for the Completion of Term Rewriting
Systems
Jiirgen Avenhaus, Klaus Madlener, Joachim Steinbach ............................ 542
ASSPEGIQUE: An Integrated Specification Environment
Michel Bidoit, Francis Capy, Christine Choppy, Stephane Kaplan,
Francoise Schlienger, Frederic Voisin ............................................. 547
KBlab: An Equational Theorem Prover for the Macintosh
Maria Paola Bonacina, Giancarlo Sanna ......................................... 548
Fast Knuth-Bendix Completion: Summary
Jim Christian .................................................................... 551
Compilation of Ground Term Rewriting Systems and Applications
M. Dauchet, A. Deruyver ........................................................ 556
An Overview of Rewrite Rule Laboratory (RRL)
Deepak Kaput, Hantao Zhang .................................................... 559
InvX: An Automatic Function Inverter
H. Khoshnevisan, K. M. Sephton ................................................. 564
A Parallel Implementation o{ Rewriting and Narrowing
Naomi Lindenstrauss ............................................................. 569
Morphocompletion for One-Relation Monoids
John Pedersen ................................................................... 574
Author Index .................................................................. 579
Term Rewriting and Universal Algebra in Historical Perspective
Invited Lecture m
Garrett Birkhoff
Harvard University
Department of Mathematics
Science Center 325
One Oxford Street
Cambridge, MA 02138
USA
Abstract
"Term rewriting" is obviously concerned with the logic of algebra. Closely related to
symbolic logic and mathematical linguistics, it derives much of its stimulus from the idea of
exploiting the enormous power of modern computers.
My talk will fall into two parts. The first part will review term rewriting from the
general standpoint of "universal algebra" in historical perspective. The perspective suggests
as especially interesting and/or challenging.
Characterizations of Unification Type Zero
Franz Baader
IMMD 1, Universitiit Erlangen-Niimberg
MartensstraBe 3, D-8520 Erlangen (West Germany)
Abstract
In the literature several methods have hitherto been used to show that an equational theo-
ry has unification type zero. These methods depend on conditions which are candidates for
alternative characterizations of unification type zero. In this paper we consider the logical
connection between these conditions on the abstract level of partially ordered sets. Not all
of them are really equivalent to type zero.
The conditions may be regarded as tools which can be used to determine the unification
type of given theories. They are also helpful in understanding what makes a theory to be
of type zero.
1. Introduction.
Let E be an equational theory and =E be the equality of terms, induced by E. A substitu-
tion 0 is called an E-unifier of the terms s, tiff Os =E .Ot The set of all E-unifiers of s, t is
denoted by UE(S,t). We are mostly interested in complete sets of E-unifiers, i.e. sets of
E-unifiers from which UE(S,t ) may be generated by instantiation. More formally, we
extend =E to UE(S,t) and define a quasi-ordering <E on UE(s,t) by
YC =E 0 iff xO =E x0 for all variables x occurring in s or t.
E<- 0 iff there exists a substitution ~ such that c 0 =E o ~.
In this case ~ is called an E-instance of 0. As usual the quasi-ordering E<- induces an
equivalence relation -E on UE(S,t), namely o --E 0 iff ~ E<- 0 and 0 <E ~. The ssalC-E=- of
an E-unifier c of s, t shall be denoted by [~].
A complete set CUE(S,t) of E-unifiers of s, t is defined as
(1) ~ CUE(S,t) UE(S,t ),
(2) For all 0 ~ UE(S,t) there exists c ~ CUE(S,t) such that 0 E<- ~"
A minimal complete set ~tUE(S,t) is a complete set of E-unifiers of s, t satisfying the mini-
mality condition
(3) For all c, 0 ~ ~tUE(S,t) c <E 0 implies c = 0.
This notion was introduced by Plotkin (1972). In the same paper he conjectured that there
exist an equational theory E and terms s, t such that ~tUE(S,t) does not exist. We say
that such a theory has unification type zero. The first example of a type zero theory is due
to Fages and Huet (1983). They constructed a theory E and terms s, t such that UE(S,t)
contains a strictly increasing chain with respect to <E which is a complete set of E-uni-
fiers of s, t. Under these circumstances, a complete set of E-unifiers can not satisfy the
minimality condition. Schmidt-SchauB (1986) and the present author (1986) showed that
the theory of idempotent semigroups is of unification type zero and in Baader (1987) I
have proved that almost all varieties of idempotent semigroups are defined by type zero
theories. In these cases, complete sets of unifiers are not simply chains. Thus other meth-
ods had to be developed to obtain the results. In this paper we consider some of these
methods and their logical connection. We shall thus obtain alternative characterizations of
unification type zero and sufficient conditions ( resp. necessary conditions ) for a theory to
be type zero. This provides tools which may be used to determine the unification types of
given theories. It also helps to understand what it means that a theory is of type zero.
2. Minimal complete sets and maximal elements.
For terms s, t the quasi-ordering E<- on UE(S,t) induces a partial ordering ( po ) < on U :=
{ [~]; ~ ~ UE(S,t) ,} namely [c] <_ [x] iff ~ E<- .c" The existence of a set gUE(S,t) can be
described with the help of the set of all <-maximal elements in U. But ftrst we extent the
notion of complete and minimal complete sets to subsets of partially ordered sets ( see
also Btittner (1986), Schmidt-Schaul3 (1986a) and Btirckert (1987)). Parts of our proofs
can be done on this abstract level.
