A theory of nondeterminism

  • J. R. Kennaway
  • C. A. R. Hoare
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 85)


A construction is described which takes an arbitrary set of machines, an arbitray set of tests, and an arbitrary relation on machines and tests defining which machines pass which tests. It produces a domain of specifications, which is a retract of the lattice of sets of tests (with the subset ordering), and a domain of nondeterministic machines (ndms), which is a retract of the lattice of sets of machines (with the superset ordering). These two domains are isomorphic. Simple conditions ensure that they are ω-algebraic.

Functions on such domains may be defined equivalently either as transformations of ndms (an operational definition) or as transformations of specifications (an axiomatic definition). Conditions for the "realism" of such functions are formulated.


axiomatic sematnics operational semantics complementary definitions nondeterminism powerdomains 


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  1. 1.
    Bell, J.L. and Slomson, A.B., "Models and ultraproducts" (North-Holland, 1969).Google Scholar
  2. 2.
    Milne, R.E. and Strachey, C., "A theory of programming language semantics", (Chapman & Hall, 1976).Google Scholar
  3. 3.
    Scott, D., "Data types as lattices", SIAM J. Computing 5, 522–587 (1976).Google Scholar
  4. 4.
    Smyth, M.J., "Powerdomains", J. Computer System Science 16, 23–36 (1978).Google Scholar
  5. 5.
    Stoy, J.E., "Denotational Semantics", (M.I.T., 1977).Google Scholar
  6. 6.
    Tarski, A., "A lattice-theoretical fixpoint theorem and its applications", Pacific J. Math. 5, 285–309, (1955).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1980

Authors and Affiliations

  • J. R. Kennaway
    • 1
  • C. A. R. Hoare
    • 2
  1. 1.Department of Computer ScienceEdinburgh UniversityUK
  2. 2.Programming Research GroupOxford UniversityUK

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