On effective axiomatizations of Hoare logics

Authors:
Edmund M. Clarke, Jr.;Steven M. German;Joseph Y. Halpern
Affiliations:
Aiken Computation Laboratory, Harvard University, Cambridge;M.I.T., Cambridge, and Stanford University, Stanford;Harvard University, Cambridge, and Stanford University, Stanford,
Venue:
POPL '82 Proceedings of the 9th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Year:
1982

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Abstract

For a wide class of programming languages P and expressive interpretations I, we show that there exist sound and relatively complete Hoare-like logics for both partial correctness and termination assertions. In fact, under mild assumptions on P and I, we show that the assertions true for P in I are uniformly decidable in the theory of I (Th(I)) iff the halting problem for P is decidable for finite interpretations. Moreover termination assertions are uniformly r.e. 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 the class of languages with good axiom systems for total correctness may be wider than for partial correctness.