A Semantic Foundation for TCOZ in Unifying Theories of Programming

  • Shengchao Qin
  • Jin Song Dong
  • Wei-Ngan Chin
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2805)


Unifying Theories of Programming (UTP) can provide a formal semantic foundation not only for programming languages but also for more expressive specification languages. We believe UTP is particularly well suited for presenting the formal semantics for integrated specification languages which often have rich language constructs for state encapsulation, event communication and real-time modeling. This paper uses UTP to formalise the semantics of Timed Communicating Object Z (TCOZ) and captures some TCOZ new features for the first time. In particular, a novel unified semantic model of the channel based synchronisation and sensor/actuator based asynchronisation in TCOZ is presented. This semantic model will be used as a reference document for developing tools support for TCOZ and as a semantic foundation for proving soundness of those tools.


UTP semantics integrated formal specifications 


  1. 1.
    Bengtsson, J., Larsen, K., Larsson, F., Pettersson, P., Wang, Y.: UPPAAL - a Tool Suite forAutomatic Verification of Real-Time Systems. In: Alur, R., Sontag, E.D., Henzinger, T.A. (eds.) HS 1995. LNCS, vol. 1066, pp. 232–243. Springer, Heidelberg (1996)CrossRefGoogle Scholar
  2. 2.
    Davies, J., Schneider, S.: A brief history of Timed CSP. Theoret. Comput. Sci. 138, 243–271 (1995)MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    Duke, D., Duke, R.: Towards a semantics for Object-Z. In: Langmaack, H., Hoare, C.A.R., Bjorner, D. (eds.) VDM 1990. LNCS, vol. 428, pp. 242–262. Springer, Heidelberg (1990)Google Scholar
  4. 4.
    Duke, R., Rose, G.: Formal Object Oriented Specification Using Object-Z, March 2000. Cornerstones of Computing Series. Macmillan, Basingstoke (2000)Google Scholar
  5. 5.
    He, J., Liu, Z., Li, X.: A relational model for specification of object-oriented systems. Technical Report 262, UNU/IIST (October 2002)Google Scholar
  6. 6.
    Hoare, C.A.R., He, J.: Unifying Theories of Programming. Prentice-Hall, Englewood Cliffs (1998)Google Scholar
  7. 7.
    Mahony, B., Dong, J.S.: Sensors and Actuators in TCOZ. In: Woodcock, J.C.P., Davies, J., Wing, J.M. (eds.) FM 1999. LNCS, vol. 1709, pp. 1166–1185. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  8. 8.
    Mahony, B., Dong, J.S.: Timed Communicating Object Z. IEEE Transactions on Software Engineering 26(2), 150–177 (2000)CrossRefGoogle Scholar
  9. 9.
    Mahony, B., Dong, J.S.: Overview of the semantics of TCOZ. In: Araki, K., Galloway, A., Taguchi, K. (eds.) IFM 1999: Integrated Formal Methods, pp. 66–85. Springer, Heidelberg (1999)Google Scholar
  10. 10.
    Mislove, M., Roscoe, A., Schneider, S.: Fixed Points Without Completeness. Theoret. Comput. Sci. 138, 273–314 (1995)MathSciNetzbMATHCrossRefGoogle Scholar
  11. 11.
    Reed, G., Roscoe, A.: A timed model for communicating sequential processes. Theoret. Comput. Sci. 58, 249–261 (1988)MathSciNetzbMATHCrossRefGoogle Scholar
  12. 12.
    Roscoe, A.W.: The Theory and Practice of Concurrency. Prentice-Hall, Englewood Cliffs (1998)Google Scholar
  13. 13.
    Schneider, S., Davies, J., Jackson, D., Reed, G., Reed, J., Roscoe, A.: Timed CSP: Theory and practice. In: Huizing, C., de Bakker, J.W., Rozenberg, G., de Roever, W.-P. (eds.) REX 1991. LNCS, vol. 600, pp. 640–675. Springer, Heidelberg (1992)CrossRefGoogle Scholar
  14. 14.
    Sherif, A., He, J.: Towards a timed model for circus. In: George, C.W., Miao, H. (eds.) ICFEM 2002. LNCS, vol. 2495, pp. 613–624. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  15. 15.
    Smith, G.: A fully abstract semantics of classes for Object-Z. Formal Aspects of Computing 7(3), 289–313 (1995)CrossRefGoogle Scholar
  16. 16.
    Smith, G.: The Object-Z Specification Language. Kluwer Academic Publishers, Dordrecht (2000)zbMATHCrossRefGoogle Scholar
  17. 17.
    Woodcock, J., Cavalcanti, A.: Circus: a concurrent refinement language. Technical report, Oxford University Computing Laboratory, Oxford OX1 3QD, UK (July 2001)Google Scholar
  18. 18.
    Woodcock, J., Cavalcanti, A.: The Semantics of Circus. In: Bert, D., Bowen, J.P., Henson, M.C., Robinson, K. (eds.) B 2002 and ZB 2002. LNCS, vol. 2272, pp. 184–203. Springer, Heidelberg (2002)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Shengchao Qin
    • 1
  • Jin Song Dong
    • 2
  • Wei-Ngan Chin
    • 1
    • 2
  1. 1.Singapore-MIT AllianceNational University of SingaporeSingapore
  2. 2.School of ComputingNational University o SingaporeSingapore

Personalised recommendations