Abstract
Jungle evaluation is proposed as a new graph rewriting approach to the evaluation of functional expressions and, in particular, of algebraically specified operations. Jungles — being intuitively forests of coalesced trees with shared substructures — are certain acyclic hypergraphs (or equivalently, bipartite graphs) the nodes and edges of which are labeled with the sorts and operation symbols of a signature. Jungles are manipulated and evaluated by the application of jungle rewrite rules, which generalize equations or, more exactly, term rewrite rules. Indeed, jungle evaluation turns out to be a compromise between term rewriting and graph rewriting displaying some favorable properties: the inefficiency of term rewriting is partly avoided while the possibility of structural induction is maintained, and a good part of the existing graph grammar theory is applicable so that there is some hope that the rich theory of term rewriting is not lost forever without a substitute.
Work of this author is partially supported by the ESPRIT-project PROSPECTRA, ref. # 390.
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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 Reduction. University of East-Anglia and University of Nijmegen, Proc. PARLE Conference on Parallel Architectures and Languages, Eindhoven (1987).
H. Ehrig: Introduction to the Algebraic Theory of Graph Grammars. Proc. 1st Graph Grammar Workshop, Lect. Not. Comp. Sci. 73, 1–69 (1979).
H. Ehrig, H.-J. Kreowski: Parallelism of Manipulations in Multidimensional Information Structures. Proc. MFCS'76, Lect. Not. Comp. Sci. 45, 284–293 (1976).
H. Ehrig, B. Mahr: Fundamentals of Algebraic Specifications. Part I: Initial Semantics. Springer, Monographs in Computer Science, New York-Berlin-Heidelberg (1986).
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).
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).
J.W. Klop: Term Rewriting Systems. A Tutorial. EATCS Bulletin 32, 142–182 (1987).
H.-J. Kreowski: Is Parallelism Already Concurrency? — Part 1: Derivations in Graph Grammars. Proc. 3rd Graph Grammar Workshop, Lect. Not. Comp. Sci. 291, 343–360 (1987).
P. Padawitz: Graph Grammars and Operational Semantics. Theor. Comp. Sci. 19, 117–141 (1982).
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. Theor. Comp. Sci. 10, 171–185 (1980).
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© 1988 Springer-Verlag Berlin Heidelberg
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Habel, A., Kreowski, HJ., Plump, D. (1988). Jungle evaluation. In: Sannella, D., Tarlecki, A. (eds) Recent Trends in Data Type Specification. ADT 1987. Lecture Notes in Computer Science, vol 332. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-50325-0_5
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DOI: https://doi.org/10.1007/3-540-50325-0_5
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