General correctness: a unification of partial and total correctness
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We give an algebraic semantics of non-deterministic, sequential programs which is valid for partial, total and general correctness. It covers full recursion based on a unified approximation order. We provide explicit solutions in terms of the refinement order. As an application, we systematically derive a semantics of while-programs common to the three correctness approaches. UTP's designs and prescriptions represent programs as pairs of termination and state transition information in total and general correctness, respectively. We show that our unified semantics induces a pair-based representation which is common to the correctness approaches. Operations on the pairs, including finite and infinite iteration, can be derived systematically. We also provide the effect of full recursion on the unified, pair-based representation.