A Tutorial Introduction to Designs in Unifying Theories of Programming

  • Jim Woodcock
  • Ana Cavalcanti
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2999)


In their Unifying Theories of Programming (UTP), Hoare & He use the alphabetised relational calculus to give denotational semantics to a wide variety of constructs taken from different programming paradigms. A key concept in their programme is the design: the familiar precondition-postcondition pair that describes the contract between a programmer and a client. We give a tutorial introduction to the theory of alphabetised relations, and its sub-theory of designs. We illustrate the ideas by applying them to theories of imperative programming, including Hoare logic, weakest preconditions, and the refinement calculus.


Unify Theory Propositional Calculus Healthiness Condition Program Correctness Programming Paradigm 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    Abrial, J.-R.: The B-Book: Assigning Progams to Meanings. Cambridge University Press, Cambridge (1996)CrossRefGoogle Scholar
  2. 2.
    Back, R.J.R., Wright, J.: Refinement Calculus: A Systematic Introduction. Graduate Texts in Computer Science. Springer, Heidelberg (1998)zbMATHGoogle Scholar
  3. 3.
    Cavalcanti, L.C., Sampaio, A.C.A., Woodcock, J.C.P.: A Refinement Strategy for Circus. Formal Aspects of Computing 15(2-3), 146–181 (2003)zbMATHCrossRefGoogle Scholar
  4. 4.
    Dijkstra, E.W.: A Discipline of Programming. Prentice-Hall, Englewood Cliffs (1976)zbMATHGoogle Scholar
  5. 5.
    Dunne, S.: Recasting Hoare and He’s Unifying Theories of Programs in the Context of General Correctness. In: Butterfield, A., Pahl, C. (eds.) IWFM 2001: 5th Irish Workshop in Formal Methods, BCS Electronic Workshops in Computing, Dublin, Ireland (July 2001)Google Scholar
  6. 6.
    Hoare, C.A.R., Jifeng, H.: Unifying Theories of Programming. Prentice-Hall, Englewood Cliffs (1998)Google Scholar
  7. 7.
    Jones, C.B.: Systematic Software Development Using VDM. Prentice-Hall International, Englewood Cliffs (1986)zbMATHGoogle Scholar
  8. 8.
    Morgan, C.C.: Programming from Specifications, 2nd edn. Prentice-Hall, Englewood Cliffs (1994)zbMATHGoogle Scholar
  9. 9.
    Morris, J.M.: A Theoretical Basis for Stepwise Refinement and the Programming Calculus. Science of Computer Programming 9(3), 287–306 (1987)zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Qin, S., Dong, J.S., Chin, W.N.: A Semantic Foundation for TCOZ in Unifying Theories of Programming. In: Araki, K., Gnesi, S., Mandrioli, D. (eds.) FME 2003. LNCS, vol. 2805, pp. 321–340. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  11. 11.
    Roscoe, W.: The Theory and Practice of Concurrency. Prentice-Hall Series in Computer Science. Prentice-Hall, Englewood Cliffs (1998)Google Scholar
  12. 12.
    Sherif, A., Jifeng, H.: Towards a Time Model for Circus. In: International Conference in Formal Engineering Methods, pp. 613–624 (2002)Google Scholar
  13. 13.
    Woodcock, J.C.P., Cavalcanti, A.L.C.: The Semantics of Circus. In: Bert, D., P. Bowen, J., C. Henson, M., Robinson, K. (eds.) B 2002 and ZB 2002. LNCS, vol. 2272, pp. 184–203. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  14. 14.
    Woodcock, J.C.P., Davies, J.: Using Z—Specification, Refinement, and Proof. Prentice-Hall, Englewood Cliffs (1996)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Jim Woodcock
    • 1
  • Ana Cavalcanti
    • 1
  1. 1.Computing LaboratoryUniversity of KentCanterburyUK

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