Abstract
We introduce a calculus for reasoning about programs in total correctness which blends UTP designs with von Wright’s notion of a demonic refinement algebra. We demonstrate its utility in verifying the familiar loop-invariant rule for refining a total-correctness specification by a while loop. Total correctness equates non-termination with completely chaotic behaviour, with the consequence that any situation which admits non-termination must also admit arbitrary terminating behaviour. General correctness is more discriminating in allowing non-termination to be specified together with more particular terminating behaviour. We therefore introduce an analogous calculus for reasoning about programs in general correctness which blends UTP prescriptions with a demonic refinement algebra. We formulate a loop-invariant rule for refining a general-correctness specification by a while loop, and we use our general-correctness calculus to verify the new rule.
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Dunne, S.E., Hayes, I.J., Galloway, A.J. (2010). Reasoning about Loops in Total and General Correctness. In: Butterfield, A. (eds) Unifying Theories of Programming. UTP 2008. Lecture Notes in Computer Science, vol 5713. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14521-6_5
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