Non-termination in Unifying Theories of Programming

  • Walter Guttmann
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3929)


Within the shape Unifying Theories of Programming framework, program initiation and termination has been modelled by introducing a pair of variables in order to satisfy the required algebraic properties. We replace these variables with the improper value ⊥ that is frequently used to denote undefinedness. Both approaches are proved isomorphic using the relation calculus, and the existing operations and laws are carried over. We split the isomorphism by interposing “intuitive” relations.


Unify Theory Auxiliary Variable Complete Lattice Healthiness Condition Sequential Composition 
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  1. 1.
    Hoare, C.A.R., He, J.: Unifying theories of programming. Prentice Hall Europe, Englewood Cliffs (1998)MATHGoogle Scholar
  2. 2.
    Dunne, S.: Recasting Hoare and He’s unifying theory of programs in the context of general correctness. In: Butterfield, A., Strong, G., Pahl, C. (eds.) 5th Irish Workshop on Formal Methods. EWiC, The British Computer Society (2001)Google Scholar
  3. 3.
    Schmidt, G., Ströhlein, T.: Relationen und Graphen. Springer, Heidelberg (1989)CrossRefMATHGoogle Scholar
  4. 4.
    Szász, G.: Introduction to Lattice Theory, 3rd edn. Academic Press, London (1963)MATHGoogle Scholar
  5. 5.
    Hehner, E.C.R., Malton, A.J.: Termination conventions and comparative semantics. Acta Informatica 25(1), 1–14 (1988)MathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    Nelson, G.: A generalization of Dijkstra’s calculus. ACM Transactions on Programming Languages and Systems 11(4), 517–561 (1989)CrossRefGoogle Scholar
  7. 7.
    de Bakker, J.W.: Semantics and termination of nondeterministic recursive programs. In: Michaelson, S., Milner, R. (eds.) Third International Colloquium on Automata, Languages and Programming. Edinburgh University Press, pp. 435–477 (1976)Google Scholar
  8. 8.
    Broy, M., Gnatz, R., Wirsing, M.: Semantics of nondeterministic and noncontinuous constructs. In: Gerhart, S.L., Pair, C., Pepper, P.A., Wössner, H., Dijkstra, E.W., Guttag, J.V., Owicki, S.S., Partsch, H., Bauer, F.L., Gries, D., Griffiths, M., Horning, J.J., Wirsing, M. (eds.) Program Construction. LNCS, vol. 69, pp. 553–592. Springer, Heidelberg (1979)CrossRefGoogle Scholar
  9. 9.
    Berghammer, R., Zierer, H.: Relational algebraic semantics of deterministic and nondeterministic programs. Theoretical Computer Science 43(2-3), 123–147 (1986)MathSciNetCrossRefMATHGoogle Scholar
  10. 10.
    Apt, K.R., Plotkin, G.D.: Countable nondeterminism and random assignment. Journal of the ACM 33(4), 724–767 (1986)MathSciNetCrossRefMATHGoogle Scholar
  11. 11.
    Desharnais, J., Möller, B., Tchier, F.: Kleene under a modal demonic star. Journal of Logic and Algebraic Programming, special issue on Relation Algebra and Kleene Algebra (in press, 2005)Google Scholar
  12. 12.
    Guttmann, W., Möller, B.: Modal design algebra. In: First International Symposium on Unifying Theories of Programming (to appear, 2006)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Walter Guttmann
    • 1
  1. 1.Abteilung Programmiermethodik und CompilerbauUniversität UlmUlmGermany

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