Abstract
In the field of program refinement a specification construct has been proposed that does not have a standard operational interpretation. Its weakest preconditions are monotone but not necessarily conjunctive. In order to develop a corresponding calculus we introduce specification algebras. These algebras may have two choice operators: demonic choice and angelic choice. The wish to allow unbounded choice, of both modalities, leads to the question of defining and constructing completions of specification algebras. It is shown that, in general, a specification algebra need not have a completion. On the other hand, a formalism is developed that allows for any specific combination of unbounded demonic choice, unbounded angelic choice and sequential composition. The formalism is based on transition systems. It is related to the processes of De Bakker and Zucker.
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