Programming Language Constructs for Which It Is Impossible To Obtain Good Hoare Axiom Systems
Journal of the ACM (JACM)
On effective axiomatizations of Hoare logics
POPL '82 Proceedings of the 9th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
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In this paper a generalization of a certain Lipton's theorem (see Lipton [5]) is presented. Namely, we show that for a wide class of programming languages the following holds: the set of all partial correctness assertions true in an expressive interpretation I is uniformly decidable (in I) in the theory of I iff the halting problem is decidable for finite interpretations. In the effect we show that such limitations as effectiveness or Herbrand definability of interpretation (they are relevant in the previous proofs) can be removed in the case of partial correctness.