Abstract
Jungles are acyclic hypergraphs that represent sets of terms over a signature so that equal subterms can be shared.
Term rewrite rules can be translated into jungle evaluation rules having the property that each evaluation step performs several term rewrite steps simultaneously.
It is shown that the translation preserves termination. Confluent and terminating term rewriting systems are translated into confluent and terminating jungle evaluation systems which are complete in the sense that each term normal form is represented by some jungle normal form.
Moreover, jungle evaluation can be speeded up by additional hypergraph rules that fold equal terms without loosing termination and confluence. Using these folding rules, even non-linear term rewriting systems can be modelled.
This work is supported by the Commission of the European Communities under Contract 390 (PROSPECTRA Project) in the ESPRIT Programme.
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References
H.P. Barendregt, M.C.J.D. van Eekelen, J.R.W Glauert, J.R. Kennaway, M.J. Plasmeijer, M.R. Sleep: Term Graph Rewriting. Proc. PARLE, Lecture Notes in Comp. Sci. 259, 141–158 (1987)
N. Dershowitz: Computing with Rewrite Systems. Information and Control 64, 122–157 (1985)
H. Ehrig: Introduction to the Algebraic Theory of Graph Grammars. Proc. 1st Graph Grammar Workshop, Lecture Notes in Comp. Sci. 73, 1–69 (1979)
H. Ehrig, B. Mahr: Fundamentals of Algebraic Specification 1 — Equations and Initial Semantics. Springer, Monographs in Computer Science, New York-Berlin-Heidelberg (1985)
H. Ehrig, B.K. Rosen: Commutativity of Independent Transformations on Complex Objects. Research Report RC 6251, IBM T.J. Watson Research Center, Yorktown Heights (1976)
K. Futatsugi, J. Goguen, J.P. Jouannoud, J. Meseguer: Principles of OBJ2. Proc. 1985 Symposium on Principles of Programming Languages, 52–66 (1985)
A. Habel, H.-J. Kreowski, D. Plump: Jungle Evaluation. To appear in Proc. Fifth Workshop on Specification of Abstract Data Types (1988)
B. Hoffmann: Compiler Generation: From Language Descriptions to Abstract Compilers. Dissertation, TU Berlin (1983)
G. Huet, D.C. Oppen: Equations and Rewrite Rules, A Survey. In R.V. Book (ed.): Formal Language Theory: Perspectives and Open Problems. Academic Press, 349–405 (1980)
B. Hoffmann, D. Plump: Jungle Evaluation for Efficient Term Rewriting. Technical Report, Universität Bremen, (1988)
J. Hsiang: Refutational Theorem Proving using Term Rewriting Systems. Artificial Intelligence 25, 255–300 (1985)
J.W. Klop: Term Rewriting Systems: A Tutorial. EATCS Bulletin 32, 143–182, (1987)
H.-J. Kreowski: Is Parallelism Already Concurrency? — Part 1: Derivations in Graph Grammars. Proc. 3rd Graph Grammar Workshop, Lecture Notes in Comp. Sci. 291, 343–360 (1987)
M.J. O'Donnell: Term Rewriting Implementation of Equational Logic Programming. Proc. 2nd Conference on Rewriting Techniques and Applications, Lecture Notes in Comp. Sci. 256, 1–12 (1987)
P. Padawitz: Graph Grammars and Operational Semantics. Theoretical Comp. Sci. 19, 117–141 (1982)
P. Padawitz: Correctness, Completeness, and Consistency of Equational Data Type Specifications. Bericht Nr. 83-15, Technische Universität Berlin (1983)
S.L. Peyton Jones: The Implementation of Function Programming Languages. Prentice-Hall, Englewood Cliffs (1987)
D. Plump: Im Dschungel: Ein neuer Graph-Grammatik-Ansatz zur effizienten Auswertung rekursiv definierter Funktionen. Diplomarbeit, Studiengang Informatik, Universität Bremen (1986)
J. Staples: Computation on Graph-like Expressions. Theoretical Comp. Sci. 10, 171–185 (1980)
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© 1988 Akademie-Verlag Berlin
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Hoffmann, B., Plump, D. (1988). Jungle evaluation for efficient term rewriting. In: Grabowski, J., Lescanne, P., Wechler, W. (eds) Algebraic and Logic Programming. ALP 1988. Lecture Notes in Computer Science, vol 343. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-50667-5_71
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DOI: https://doi.org/10.1007/3-540-50667-5_71
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