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Effective axiomatizations of Hoare logics. (English) Zbl 0627.68010
For a wide class of programming languages P and expressive interpretations I, it is shown that there exist sound and relatively complete Hoare logics for both partial-correctness and termination assertions. In fact, under mild assumptions on P and I it is shown that the assertions true in I are uniformly decidable in the theory of I (Th(I)) iff the halting problem for P is decidable for finite interpretations. Moreover the set of true termination assertions is uniformly recursively enumerable in Th(I) even if the halting problem for P is not decidable for finite interpretations. Since total-correctness assertions coincide with termination assertions for deterministic programming languages, this last result unexpectedly suggests that good axiom systems for total correctness may exist for a wider spectrum of languages than is the case for partial correctness.
MSC:
68Q60Specification and verification of programs