Graph rewriting in some categories of partial morphisms

  • Richard Kennaway
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 532)


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.


graph rewriting partial morphism hypergraph term graph jungle category double pushout single pushout 


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  1. [EPS73]
    H. Ehrig, M. Pfender, and H.J. Schneider “Graph-grammars: an algebraic approach”, Proc. IEEE Conf. on Automata and Switching Theory, 167–180, 1973.Google Scholar
  2. [ER80]
    H. Ehrig and B.K. Rosen “Parallelism and concurrency of graph manipulations”, Theor. Comp. Sci., 11, 247–275, 1980.CrossRefGoogle Scholar
  3. [FRW90]
    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.CrossRefGoogle Scholar
  4. [GKS89]
    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., 1989Google Scholar
  5. [GKS90]
    J.R.W.Glauert, J.R.Kennaway and M.R.Sleep “Dactl: An Experimental Graph Rewriting Language”, these proceedings, 1990.Google Scholar
  6. [GHKPS88]
    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., 1988Google Scholar
  7. [HP88]
    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).Google Scholar
  8. [Ken87]
    J.R. Kennaway “On ‘On graph rewritings'", Th. Comp. Sci. 52, 37–58, 1987.CrossRefGoogle Scholar
  9. [KKSV9-]
    J.R. Kennaway, J.W. Klop, M.R. Sleep and F.-J. de Vries “Transfinite reductions in orthogonal term rewrite systems” (in preparation, 199-).Google Scholar
  10. [LE90]
    M. Löwe and H. Ehrig “Algebraic appraoch to graph transformation based on single pushout derivations” (unpublished, 1990).Google Scholar
  11. [PEM86]
    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.Google Scholar
  12. [Rao84]
    J.C. Raoult “On graph rewritings”, Th. Comp. Sci., 32, 1–24, 1984.CrossRefGoogle Scholar
  13. [Rob88]
    E. Robinson and G. Rosolini “Categories of partial maps”, Inf. & Comp., 79, 95–130, 1988.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Richard Kennaway
    • 1
  1. 1.School of Information SystemsUniversity of East AngliaNorwichU.K.

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