Abstract
In this paper we investigate the relationship between the algebraic definition of graph grammars and logic programming. In particular, we show that the operational semantics of any logic program can be faithfully simulated by a particular context-free hypergraph grammar. In the process of doing that, we consider the issue of representing terms, formulas, and clauses as particular graphs or graph productions, by first evaluating the approaches already proposed for Term Rewriting Systems (TRS), and then by giving an original extension of those approaches, to be able to deal with the unique features of logic programming. Actually, not only does our representation of definite clauses by graph productions allow us to deal correctly with logical unification, but also it overcomes some of the problems encountered by other approaches for representing TRS's as graph grammars. The main result of the paper states the soundness and completeness of the representation of clauses by productions, and this correspondence is extended to entire computations, showing how a context-free grammar (over a suitable category of graphs) can be associated with a logic program. The converse holds as well, i.e. given any context-free graph grammar (over that category), a logic program can be extracted from it.
Research supported by the GRAGRA Basic Research Esprit Working Group n. 3299.
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6. References
A. Asperti, S. Martini, Projections instead of variables, A category theoretic interpretation of logic programs, Proc. 6th Int. Conf. on Logic Programming, MIT Press, 1989, pp. 337–352.
M. Bauderon, B. Courcelle, Graph Expressions and Graph Rewritings, Mathematical System Theory 20, 1987, pp. 83–127.
H.P. Barendregt, M.C.J.D. van Eekelen, J.R.W. Glauert, J.R. Kennaway, M.J. Plasmeijer, M.R. Sleep, Term graph reduction, in Proc. PARLE, LNCS 259, 1987, pp. 141–158.
V. Claus, H. Ehrig, G. Rozenberg, (Eds.) Proceedings of the 1 st International Workshop on Graph-Grammars and Their Application to Computer Science and Biology, LNCS 73, 1979.
B. Courcelle, On using context-free graph grammars for analyzing recursive definitions, in Programming of Future Generation Computers II, K. Fuchi, L. Kott (Eds.), Elsevier-North-Holland, 1988, pp. 83–122.
H. Ehrig, Aspects of concurrency in graph grammars, in [ENR83], pp. 58–81.
H. Ehrig, Tutorial introduction to the algebraic approach of graph-grammars, in [ENRR87] pp. 3–14.
H. Ehrig, A. Habel, H.-J. Kreowski, F. Parisi-Presicce, High-Level Replacement Systems, in [EKR91].
H. Ehrig, H.-J. Kreowski, G. Rozenberg, (Eds.) Proceedings of the 4 th International Workshop on Graph-Grammars and Their Application to Computer Science, LNCS, 1991, this volume.
H. Ehrig, M. Nagl, G. Rozenberg, (Eds.) Proceedings of the 2 nd International Workshop on Graph-Grammars and Their Application to Computer Science, LNCS 153, 1983.
H. Ehrig, M. Nagl, G. Rozenberg, A. Rosenfeld, (Eds.) Proceedings of the 3 rd International Workshop on Graph-Grammars and Their Application to Computer Science, LNCS 291, 1987.
H. Ehrig, M. Pfender, H.J. Schneider, Graph-grammars: an algebraic approach, Proc, IEEE Conf. on Automata and Switching Theory, 1973, pp. 167–180.
M. Falaschi, G. Levi, M. Martelli, C. Palamidessi, Declarative Modeling of the Operational Behaviour of Logic Languages, Theoretical Computer Science, 69(3), 1989, pp. 289–318.
M. Falaschi, G. Levi, C. Palamidessi, A Synchronization Logic: Axiomatics and Formal Semantics of Generalized Horn Clauses, in Information and Control, 60(1–3), Academic Press, 1984.
J.A. Goguen, What is Unification? A Categorical View of Substitution, Equation and Solution, in M. Nivat and H. Aït-Kaci (Eds.), Resolution of Equations in Algebraic Structures, Academic Press, 1989.
A. Habel, Hyperedge Replacement: Grammars and Languages, Ph.D. Thesis, University of Bremen, 1989.
A. Habel, H-J. Kreowski, D. Plump, Jungle evaluation, in Proc. Fifth Workshop on Specification of Abstract Data Types, LNCS 332, 1988, pp. 92–112.
J.R. Kennaway, On ‘On Graph Rewritings', Theoretical Computer Science, 52, 1987, pp. 37–58.
J.R. Kennaway, Graph rewriting in some categories of partial morphisms, in [EKR91].
G. Levi, Models, Unfolding Rules and Fixpoint Semantics, in Proc. 5th Int. Conf. Symp. on Logic Programming, Seattle, MIT Press, pp. 1649–1665, 1988.
J.W. Lloyd, Foundations of Logic Programming, Springer Verlag, 1984, (Second Edition 1987).
S. Mac Lane, Categories for the Working Mathematician, Springer Verlag, New York, 1971.
F. Parisi-Presicce, H. Ehrig and U. Montanari, Graph Rewriting with Unification and Composition, in [ENRR87], pp. 496–514.
J.C. Raoult, On Graph Rewritings, Theoretical Computer Science, 32, 1984, pp. 1–24.
D.E. Rydeheard, R.M. Burstall, A Categorical Unification Algorithm, Proc. of the Workshop on Category Theory and Computer Programming, LNCS 240, 1985.
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Corradini, A., Montanari, U., Rossi, F., Ehrig, H., Löwe, M. (1991). Graph grammars and logic programming. In: Ehrig, H., Kreowski, HJ., Rozenberg, G. (eds) Graph Grammars and Their Application to Computer Science. Graph Grammars 1990. Lecture Notes in Computer Science, vol 532. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0017392
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