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Proving total correctness of nondeterministic programs in infinitary logic

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It is shown how the weakest precondition approach to proving total correctness of nondeterministic programs can be formalized in infinitary logic. The weakest precondition technique is extended to hierarchically structured programs by adding a new primitive statement for operational abstraction, the nondeterministic assignment statement, to the guarded commands of Dijkstra. The infinitary logic L ω1ω is shown to be strong enough to express the weakest preconditions for Dijkstra's guarded commands, but too weak for the extended guarded commands. Two possible solutions are considered: going to the essentially stronger infinitary logic L ω1ω1 and restricting the power of the nondeterministic assignment statement in a way which allows the weakest preconditions to be expressed in L ω1ω.

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  1. R. J. R. Back

    Present address: Computing Centre, University of Helsinki, Tukholmankatu 2, 00250, Helsinki 25, Finland

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  1. Mathematisch Centrum, Kruislaan 413, 1098, SJ Amsterdam, The Netherlands

    R. J. R. Back

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Back, R.J.R. Proving total correctness of nondeterministic programs in infinitary logic. Acta Informatica 15, 233–249 (1981). https://doi.org/10.1007/BF00289263

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