Algebraic and Logic Programming: 6th International Joint Conference ALP '97 — HOA '97 Southampton, UK, September 3–5, 1997 Proceedings

294 Pages·1997·18.8 MB·English

by  M. Alpuente

Lecture Notes in Computer Science 1298
Edited by G. Goos, J. Hartmanis and J. van Leeuwen
Advisory Board: .W Brauer D. Gries J. Stoer
Michael Hanus naJ Heering
Karl Meinke (Eds.)
ciarbeglA dna Logic
gnimmargorP
6th International Joint Conference
ALP '97 HOA '97
Southampton, UK, September 3-5, 1997
Proceedings
r e g n~ i r p S
Series Editors
Gerhard Goos, Karlsruhe University, Germany
Juris Hartmanis, Cornell University, NY, USA
Jan van Leeuwen, Utrecht University, The Netherlands
Volume Editors
Michael Hanus
RWTH Aachen, Forschungsgebiet Informatik II
Ahornstr. 55, D-52074 Aachen, Germany
E-mail: hanus @informatik.rwth-aachen.de
Jan Heering
CWI
P.O. Box 94079, 1090 GB Amsterdam, The Netherlands
E-mail: [email protected]
Karl Meinke
Royal Institute of Technology/NADA
Osquars backe 2, S-100 44 Stockholm, Sweden
E-mail: [email protected]
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Die Deutsche Bibliothek - CIP-Einheitsaufnahme
Algebraic and logic programming : 6th international joint
conference ; proceedings / ALP '97 ; HOA '97, Southampton, UK,
September 3 - 5, 1997. Michael Hanus ... (ed.). - Berlin ; Heidelberg ;
New York ; Barcelona ; Budapest ; Hong Kong ; London ; Milan ;
Paris ; Santa Clara ; Singapore ; Tokyo : Springer, 1997
(Lecture notes in computer science ; Vol. 1298)
ISBN 3*540-63459-2
CR Subject Classification (1991): D.3,F.3-4, 1.2.3
ISSN 0302-9743
ISBN 3-540-63459-2 Springer-Verlag Berlin Heidelberg New York
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Preface
This volume contains the proceedings of the Sixth International Conference
on Algebraic and Logic Programming (ALP'97) and the Third International
Workshop on Higher-Order Algebra, Logic and Term Rewriting (HOA'97), held
in Southampton (Great Britain) during September 3-5, 1997. The conference
ALP'97 was preceded by meetings in Gaussig (1988), Nancy (1990), Volterra
(1992), Madrid (1994), and Aachen (1996). The proceedings of these conferences
have been published by Springer-Verlag, as Lecture Notes in Computer Science
volumes 343, 463, 632, 850, and 1139, respectively. The workshop HOA'97 was
preceded by meetings in Amsterdam (1993) and Paderborn (1995). The proceed-
ings of these workshops have also been published as Lecture Notes in Computer
Science volumes 816 and 1074 respectively.
The ALP conference aims at strengthening the connections between alge-
braic techniques and logic programming. On the one hand, logic programming
has been very successful during the last two decades, and many efforts have
been made to enhance its expressive power and efficiency, including in particu-
lar the emergence of constraint logic programming. On the other hand, concepts
such as functions, types, equational theories, and modularity are particularly
well handled in an algebraic framework. As during the previous conferences,
ALP promotes the cross-fertilizing exchange of ideas and experiences among
researchers from the algebraic and logic programming communities.
The HOA workshop aims to provide an overview of current research, and to
suggest new research directions, in the area of higher-order methods. These are
now widely applied in declarative programming languages, as well as in software
and hardware specification and verification. The scope of the workshop includes
higher-order aspects of: algebra, logic and model theory, term rewriting, spec-
ification and verification languages, computational logic and theorem proving,
and also system implementations and case studies.
On this occasion, ALP'97 and HOA'97 were held jointly, allowing contribu-
tors and participants to exploit the overlap in these subject areas. ALP'97 and
HOA'97 were also held concurrently with the Ninth International Symposium on
Programming Languages, Implementations, Logics, and Programs (PLILP'97).
The joint ALP'97/HOA'97 Program Committee met electronically during
the final week of May, 1997. There was an email discussion of those papers for
which there was a significant disagreement about the judgement. Finally, the
combined Program Committees selected 81 papers from 13 submissions.
We would like to thank all the members of the Program Committee and all
the referees for their careful work in the reviewing and selection process.
The ALP'97 and HOA'97 conferences were organised in cooperation with
the British Computer Society, the Association of Logic Programming, the Euro-
pean Association for Programming Languages and Systems, Compulog Net (the
ESPRIT Network of Excellence in Computational Logic), and the European
Association for Computer Science Logic (EACSL).
Iv
Finally, we express our gratitude to all members of the local Organizing Com-
mittee for their help in organizing a successful event.
Aachen Michael Hanus
Amsterdam Jan Heering
Stockholm Karl Meinke
June 1997 Proceedings Editors
iiv
ALP'97 Program Committee Co-Chairs
M. Hanus (Germany)
K. Meinke (Sweden)
Program Committee
F. Benhamou (France) D. De Schreye (Belgium)
F. Fages (France) I. Guessarian (France)
M. Haveraaen (Norway) .S HSlldobler (Germany)
J.W. Klop (Netherlands) A. Middeldorp (Japan)
G. Nadathur (USA) C. Palamidessi (Italy)
P. Stuckey (Australia) R. St~rk (Switzerland)
S. Thompson (Great Britain) J.V. Tucker (Great Britain)
J. Tiuryn (Poland) A. Voronkov (Sweden)
M. Wirsing (Germany)
HOA'97 Program Committee Co-Chairs
J. Heering (Netherlands)
K. Meinke (Sweden)
B. re115M (Germany)
T. Nipkow (Germany)
Program Committee
D. Dougherty (USA) G. Dowek (France)
A. Felty (USA) J. Field (USA)
M. Gordon (Great Britain)
Local Organization
H. Glaser and P. Hartel
List of Referees
C. Baral, K. Van Belleghem, M. Bialasik, M. Carlsson, P. Cenciarelli, A. Degt-
yarev, U. Furbach, B. Gramlich, K. Hanna, J. Harland, J. Hodas, S. Kahrs, A.
Knapp, P. Kosiuczenko, V. Kriau~iukas, A. Leitsch, M. Leuschel, M. Marchiori,
T. Melham, D. Miller, E. Moggi, M. Okada, V. van Oostrom, P.C. Olveczky,
D. Plump, C. Prehofer, F. van Raamsdonk, G. Richard, H. Scndergaard, G.
St£1marck, C. Urban, H. Vandecasteele, E. Visser, H. Zantema.
Table of Contents
Functional and Logic Programming
Safe Folding/Unfolding with Conditional Narrowing ......................... 1
M. Alpuente, M. Falaschi, .G Moreno and .G Vidal
Optimal Non-deterministic Functional Logic Computations ................ 61
S. Antoy
A Semantic Basis for Termination Analysis of Logic Programs and Its
Realization Using Symbolic Norm Constraints ............................. 13
M. Codish and .C Taboch
Parallelizing Functional Programs by Generalization ....................... 46
A. Geser and S. Gorlatch
Higher-Order Methods
Higher-Order Equational Unification via Explicit Substitutions ............. 16
C. Kirchner and .C Ringeissen
Parameterised Higher-Order Algebraic Specifications ....................... 67
L.J. Steggles
Higher-Order Lazy Narrowing Calculus: A Computation Model for a
Higher-Order Functional Logic Language ................................... 99
T. Suzuki, K. Nakagawa and T. Ida
Term Rewriting
On Composable Properties of Term Rewriting Systems ................... 411
T. Aoto and Y. Toyama
Needed Reductions with Context-Sensitive Rewriting ..................... 921
S. Lucas
Conditional Term Graph Rewriting ....................................... 441
E. Ohlebusch
Types
Lazy Narrowing with Parametric Order Sorted Types ..................... 159
J.M. Almendros-Jimgnez and A. Gil-Luezas
Termination of Algebraic Type Systems: The Syntactic Approach ......... 471
.G Barthe and F. van Raamsdonk
Proof Net Semantics of Proof Search Computation ........................ 491
L. Caires and L. Monteiro
Lambda-Calculus
Explicit Substitutions for the AA Calculus ................................ 209
G. Barthe, F. Kamareddine and A. Rios
A Left-Linear Variant of Aa .............................................. 224
A. Cdsar and H. Mu~oz
Perpetuality and Uniform Normalization .................................. 240
Z. Khasidashvili and M. Ogawa
Theorem Proving Methods
Model Generation with Existentially Quantified Variables and Constraints 256
S. Abdennadher and H. Schlitz
Optimal Left-to-Right Pattern-Matching Automata ....................... 273
N. Nedjah, C.D. Walter and S.E. Eldridge
Safe Folding/Unfolding with Conditional
Narrowing*
M. Alpuente 1 and M. Falaschi 2 and G. Moreno 3 and G. Vidal 1
1 DSIC, Universidad Polit6cnica de Valenda, Camino de Vera s/n, Apdo. 22012,
46020 Valencia, Spain. e.mail:{alpuente,gvidal}@dsic.upv.es.
Dipartimento di Matematica e Informatica, Universit~ di Udine, Via delle Scienze
206, 33100 Udine, Italy. e.mail:falaschi~dimi.uniud.it.
3 Departamento de Informgtica, Universidad de Castina-La Mancha, Campus
Universitario s/n, 02071 Albacete, Spain. e.mail:[email protected].
Abstract. Functional logic languages with a complete operational se-
mantics are based on narrowing, a generalization of term rewriting where
unification replaces matching. In this paper, ew study the semantic prop-
erties of a general transformation technique ca~ed gnidlofnu in the con-
text of functional logic languages. Unfolding a program is defined as
the application of narrowing steps to the calls in the program rules in
some appropriate form. We show that, unlike the case of pure logic or
pure functional programs, where unfolding is correct w.r.t, practically
all available semantics, unrestricted unfolding using narrowing does not
preserve program meaning, even when we consider the weakest notion of
semantics the program can be given. We single out the conditions which
guarantee that an equivalent program w.r.t, the semantics of computed
answers si produced. Then, we study the combination of this technique
with a folding transformation rule in the case of innermost conditional
narrowing, and prove that the resulting transformation still preserves the
computed answer semantics of the initial program, under the usual condi-
tions for the completeness of innermost conditional narrowing. We also
discuss a relationship between unfold/fold transformations and partial
evaluation of functional logic programs.
1 Introduction
The problem of integration of functional and logic programming is an important
challenge for research in declarative programming (see [15] for a recent survey).
A functional logic program can be seen as a Conditional Term t~ewriting System
(CTRS for short), i.e. a set of conditional equations where the equation in the
conclusion is implicitly oriented from left to right. Functional logic languages
obtain the power of logic variables, automatic search and constraint solving from
logic programming. From functional programming, they obtain the expressivity
of functions and types, and a more efficient evaluation mechanism thanks to
* This work has been partially supported by CICYT under grant TIC 95-0433-C03-03
and by HCM project CONSOLE.
the deterministic reduction of functional expressions [14, 15]. The operational
semantics is usually based on some variant of narrowing, an execution mechanism
which consists of the instantiation of goal variables followed by a reduction step
on the instantiated goal. The standard declarative semantics of a program g is
given by the least Herbrand g-model of the program, i.e. the set of all ground
equations which hold in the underlying theory [17].
The folding and unfolding transformations, which were first introduced by
Burstall and Darlington in ]7[ for functional programs, are the most basic and
powerful techniques for a framework to transform programs. Unfolding is es-
sentially the replacement of a call by its body, with appropriate substitutions.
Folding is the inverse transformation, the replacement of some piece of code by
an equivalent function call. For functional programs, folding and unfolding steps
involve only pattern matching. The fold/unfold transformation approach was
first adapted to logic programs by Tamaki and Sato [28] by replacing matching
with unification in the transformation rules. A lot of literature has been devoted
to proving the correctness of unfold/fold systems w.r.t, the various semantics
proposed for functional programs ,7[ 20], logic programs [18, 25, 27, 28], and
constraint logic programs [12]. However, to the best of our knowledge, these
techniques have not been studied for functional logic programs so far.
The purpose of this paper is to consider unfold/fold transformations which
preserve the semantics of computed answer substitutions of functional logic pro-
grams. This type of program behavior is naturally observed by the programmers.
However, for the sake of simplicity, most often logic program transformation tech-
niques are only proved correct w.r.t, the declarative semantics of ground logical
consequences. We first show what are the problems with ngive extensions of these
transformation rules to functional logic programs, considering unrestricted nar-
rowing as the language operational semantics.
Then we show a non standard and extremely useful relationship of partial
evaluation with unfolding. We show that a slightly modified transformation (gen-
eralized unfolding) can be formulated in terms of partial evaluation. As a conse-
quence, the conditions to ensure completeness of the partial evaluation process
(defined in [4]) can be used to formalize a sufficient condition for the complete-
ness of unfolding w.r.t, the computed answers for unrestricted narrowing. Note
that this is different from the case of pure logic programming, where no appli-
cability condition is required to produce an equivalent program.
The definitioh of a folding transformation for unrestricted narrowing requires
conditions which are too strong to preserve computed answers. For this reason
and in order to study the typical properties of a more efficient narrowing strat-
egy, we have defined a folding rule directly for innermost narrowing and have
instantiated the general unfolding definition to this case. We have then proved
that the unfolding/folding transformation preserve the computed answers under
the usual conditions for the completeness of innermost conditional narrowing.
In our formulation, unfolding allows the expansion of a single innermost call of
a program rule at each step, and hence can be 'selectively' applied. This allows
us to see the techniques of unfolding/folding as a base for the definition of a