Abstract
We present a definition of term graph rewriting as the taking of a pushout in a category of partial morphisms, adapting the rather ad hoc definitions we gave in [Ken87] so as to use a standard category-theoretic concept of partial morphism. This single-pushout construction is shown to coincide with the well-known double-pushout description of graph rewriting whenever the latter is defined. In general, the conditions for the single pushout to exist are weaker than those required for the double pushout. In some categories of graphs, no conditions at all are necessary.
This work was partially supported by ESPRIT basic research action no. 3074 (Semagraph), SERC grant no. GR/F 91582, and an SERC Advanced Fellowship.
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References
H. Ehrig, M. Pfender, and H.J. Schneider “Graph-grammars: an algebraic approach”, Proc. IEEE Conf. on Automata and Switching Theory, 167–180, 1973.
H. Ehrig and B.K. Rosen “Parallelism and concurrency of graph manipulations”, Theor. Comp. Sci., 11, 247–275, 1980.
W.M. Farmer, J.D. Ramsdell, and R.J. Watro, “A correctness proof for combinator reduction with cycles”, ACM TOPLAS, 12, n.1, 123–134, January 1990.
J.R.W. Glauert, J.R. Kennaway, and M.R. Sleep “Final specification of Dactl”, Report SYS-C88-11, University of East Anglia, Norwich, U.K., 1989
J.R.W.Glauert, J.R.Kennaway and M.R.Sleep “Dactl: An Experimental Graph Rewriting Language”, these proceedings, 1990.
J.R.W. Glauert, K. Hammond, J.R. Kennaway, G.A. Papadopoulos, and M.R. Sleep “Dactl: some introductory papers”, Report SYS-C88-08, University of East Anglia, Norwich, U.K., 1988
B. Hoffmann and D. Plump “Jungle evaluation for efficient term rewriting”, Report 4/88, Fachbereich Mathematik und Informatil, Universität Bremen, Postfach 330 440, D-2800 Bremen 33, Germany, 1988. An earlier version appeared in Proc. Int. Workshop on Algebraic and Logic Programming, 1988. Mathematical Research, 49. (Akademie-Verlag, Berlin, 1988).
J.R. Kennaway “On ‘On graph rewritings'", Th. Comp. Sci. 52, 37–58, 1987.
J.R. Kennaway, J.W. Klop, M.R. Sleep and F.-J. de Vries “Transfinite reductions in orthogonal term rewrite systems” (in preparation, 199-).
M. Löwe and H. Ehrig “Algebraic appraoch to graph transformation based on single pushout derivations” (unpublished, 1990).
F. Parisi-Presicce, H. Ehrig, and U. Montanari “Graph rewriting with unification and composition”, Proc. 3rd Int. Workshop on Graph Grammars, LNCS 291, 496–514, Springer-Verlag, 1986.
J.C. Raoult “On graph rewritings”, Th. Comp. Sci., 32, 1–24, 1984.
E. Robinson and G. Rosolini “Categories of partial maps”, Inf. & Comp., 79, 95–130, 1988.
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© 1991 Springer-Verlag Berlin Heidelberg
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Kennaway, R. (1991). Graph rewriting in some categories of partial morphisms. 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/BFb0017408
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DOI: https://doi.org/10.1007/BFb0017408
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