Term Graph Rewriting for the π-Calculus

  • Fabio Gadducci
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2895)


We propose a graphical implementation for (possibly) recursive processes of the π-calculus, encoding each process into a term graph. Our implementation is sound and complete with respect to the standard structural congruence for the calculus: Two processes are equivalent if and only if they are mapped into isomorphic term graphs. Most importantly, the encoding allows for using standard graph rewriting mechanisms in modelling the reduction semantics of the calculus.


Term graph rewriting process calculi reduction semantics 


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  1. 1.
    Baldan, A., Corradini, P., Montanari, U.: Bisimulation equivalences for graph grammars. In: Brauer, W., Ehrig, H., Karhumäki, J., Salomaa, A. (eds.) Formal and Natural Computing. LNCS, vol. 2300, pp. 158–190. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  2. 2.
    Baldan, P., Corradini, A., Ehrig, H., Löwe, M., Montanari, U., Rossi, F.: Concurrent semantics of algebraic graph transformation. In: Ehrig, H., Kreowski, H.-J., Montanari, U., Rozenberg, G. (eds.) Handbook of Graph Grammars and Computing by Graph Transformation, vol. 3, pp. 107–187. World Scientific, Singapore (1999)Google Scholar
  3. 3.
    Barendregt, H.P., van Eekelen, M.C.J.D., Glauert, J.R.W., Kennaway, J.R., Plasmeijer, M.J., Sleep, M.R.: Term graph reduction. In: de Bakker, J.W., Nijman, A.J., Treleaven, P.C. (eds.) PARLE 1987. LNCS, vol. 259, pp. 141–158. Springer, Heidelberg (1987)Google Scholar
  4. 4.
    Berry, G., Boudol, G.: The chemical abstract machine. Theor. Comp. Sci. 96, 217–248 (1992)zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Bruni, R., Gadducci, F., Montanari, U.: Normal forms for algebras of connections. Theor. Comp. Sci. 286, 247–292 (2002)zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Corradini, A., Gadducci, F.: An algebraic presentation of term graphs, via gs-monoidal categories. Applied Categorical Structures 7, 299–331 (1999)zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Corradini, A., Gadducci, F.: Rewriting on cyclic structures: Equivalence between the operational and the categorical description. Informatique Théorique et Applications/Theoretical Informatics and Applications 33, 467–493 (1999)zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Corradini, A., Montanari, U., Rossi, F.: An abstract machine for concurrent modular systems: CHARM. Theor. Comp. Sci. 122, 165–200 (1994)zbMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Corradini, A., Montanari, U., Rossi, F., Ehrig, H., Heckel, R., Löwe, M.: Algebraic approaches to graph transformation I: Basic concepts and double pushout approach. In: Rozenberg, G. (ed.) Handbook of Graph Grammars and Computing by Graph Transformation, vol. 1, World Scientific, Singapore (1997)Google Scholar
  10. 10.
    Căzănescu, V.-E., Ştefănescu, G.: A general result on abstract flowchart schemes with applications to the study of accessibility, reduction and minimization. Theor. Comp. Sci. 99, 1–63 (1992)zbMATHCrossRefGoogle Scholar
  11. 11.
    Drewes, F., Habel, A., Kreowski, H.-J.: Hyperedge replacement graph grammars. In: Rozenberg, G. (ed.) Handbook of Graph Grammars and Computing by Graph Transformation, vol. 1, World Scientific, Singapore (1997)Google Scholar
  12. 12.
    Fu, Y.: Variations on mobile processes. Theor. Comp. Sci. 221, 327–368 (1999)zbMATHCrossRefGoogle Scholar
  13. 13.
    Gadducci, F., Heckel, R., Llabrés, M.: A bi-categorical axiomatisation of concurrent graph rewriting. In: Hofmann, M., Pavlovic̀, D., Rosolini, G. (eds.) Category Theory and Computer Science. Electr. Notes in Theor. Comp. Sci., vol. 29, Elsevier Science, Amsterdam (1999)Google Scholar
  14. 14.
    Gadducci, F., Montanari, U.: A concurrent graph semantics for mobile ambients. In: Brookes, S., Mislove, M. (eds.) Mathematical Foundations of Programming Semantics. Electr. Notes in Theor. Comp. Sci., vol. 45, Elsevier Science, Amsterdam (2001)Google Scholar
  15. 15.
    Gadducci, F., Montanari, U.: Comparing logics for rewriting: Rewriting logic, action calculi and tile logic. Theor. Comp. Sci. 285, 319–358 (2002)zbMATHCrossRefMathSciNetGoogle Scholar
  16. 16.
    Gardner, P.: From process calculi to process frameworks. In: Palamidessi, C. (ed.) CONCUR 2000. LNCS, vol. 1877, pp. 69–88. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  17. 17.
    Goguen, J., Meseguer, J.: Order sorted algebra I: Equational deduction for multiple inheritance, overloading, exceptions and partial operations. Theor. Comp. Sci. 105, 217–273 (1992)zbMATHCrossRefMathSciNetGoogle Scholar
  18. 18.
    Hasegawa, M.: Models of Sharing Graphs. PhD thesis, Department of Computer Science, University of Edinburgh (1997)Google Scholar
  19. 19.
    Jeffrey, A.: Premonoidal categories and a graphical view of programs. Technical report, School of Cognitive and Computing Sciences, University of Sussex (1997), Available at
  20. 20.
    König, B.: Generating type systems for process graphs. In: Baeten, J.C.M., Mauw, S. (eds.) CONCUR 1999. LNCS, vol. 1664, pp. 352–367. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  21. 21.
    Laneve, C., Parrow, J., Victor, B.: Solo diagrams. In: Kobayashi, N., Pierce, B.C. (eds.) TACS 2001. LNCS, vol. 2215, pp. 127–144. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  22. 22.
    Meseguer, J.: Conditional rewriting logic as a unified model of concurrency. Theor. Comp. Sci. 96, 73–155 (1992)zbMATHCrossRefMathSciNetGoogle Scholar
  23. 23.
    Milner, R.: Communication and Concurrency. Prentice Hall, Englewood Cliffs (1989)zbMATHGoogle Scholar
  24. 24.
    Milner, R.: The polyadic π-calculus: A tutorial. In: Bauer, F.L., Brauer, W., Schwichtenberg, H. (eds.) Logic and Algebra of Specification. Nato ASI Series F, vol. 94, pp. 203–246. Springer, Heidelberg (1993)Google Scholar
  25. 25.
    Milner, R.: Pi-nets: A graphical formalism. In: Sannella, D. (ed.) ESOP 1994. LNCS, vol. 788, pp. 26–42. Springer, Heidelberg (1994)Google Scholar
  26. 26.
    Milner, R.: Calculi for interaction. Acta Informatica 33, 707–737 (1996)MathSciNetGoogle Scholar
  27. 27.
    Milner, R.: Bigraphical reactive systems. In: Larsen, K.G., Nielsen, M. (eds.) CONCUR 2001. LNCS, vol. 2154, pp. 16–35. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  28. 28.
    Montanari, U., Pistore, M., Rossi, F.: Modeling concurrent, mobile and coordinated systems via graph transformations: Concurrency, parallellism, and distribution. In: Ehrig, H., Kreowski, H.-J., Montanari, U., Rozenberg, G. (eds.) Handbook of Graph Grammars and Computing by Graph Transformation, vol. 3, pp. 189–268. World Scientific, Singapore (1999)Google Scholar
  29. 29.
    Parrow, J.: Interaction diagrams. Nordic Journal of Computing 2, 407–443 (1995)MathSciNetGoogle Scholar
  30. 30.
    Plotkin, G.: A structural approach to operational semantics. Technical Report DAIMI FN-19, Computer Science Department, Aarhus University (1981)Google Scholar
  31. 31.
    Plump, D.: Term graph rewriting. In: Ehrig, H., Engels, G., Kreowski, H.-J., Rozenberg, G. (eds.) Handbook of Graph Grammars and Computing by Graph Transformation, vol. 2, pp. 3–61. World Scientific, Singapore (1999)Google Scholar
  32. 32.
    Sangiorgi, S., Walker, D.: The π-calculus: A Theory of Mobile Processes. Cambridge University Press, Cambridge (2001)Google Scholar
  33. 33.
    Yoshida, N.: Graph notation for concurrent combinators. In: Ito, T., Yonezawa, A. (eds.) TPPP 1994. LNCS, vol. 907, pp. 393–412. Springer, Heidelberg (1995)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Fabio Gadducci
    • 1
  1. 1.Dipartimento di InformaticaUniversità di PisaPisa

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