Hoare Logics for Time Bounds
Which of the following Hoare triples are valid i. For all states st , " P where a is substituted for X " holds in the state st if and only if P holds in the state override st V aeval st a. A Hoare triple is of the form. Add new rules for repeat to ceval below. Next, the key definition. If all necessary variables are in the domain of the partial state ps , these new constructs coincide with their counterparts on full states.
Case "b is false". Similar ideas were used by Hoffmann et al.
If the command doesn't terminate, we can prove anything we like about the postcondition.
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Kluwer CrossRef Google Scholar. From Coq Require Import Arith. In our setting wp is defined like this Open image in new window. You will write the evaluation rule for repeat and add a new hoare logic theorem to the language for programs involving it. Case "Loop body preserves invariant". FM We design a VCG that collects the side conditions for an annotated program.
Often these variables are not modified by a command. Lemma silly2: Nipkow, T.: Submitted on 9 Feb v1 , last revised 14 Jan this version, v2.
Our main contributions are: Hoare triple with unknown variable in postcondition I am reasoning about an Hoare Logic's exercise. We'll return to this theme later in the course when we discuss types and type soundness. We'll write bassn b for the assertion " b evaluates to true in a given state. Case "Then". Hoffmann, J. Tremmer Scott Tremmer Scott 13 3. They also formally show soundness of their logic in Coq.
Now an automatic tool for program verification is one that checks the consistency of the theory with the actual text of the program, just like the analysis tools of other branches of science and engineering. Paraphrase the following Hoare triples in English. That is the dream that has for over thirty years driven research in basic Computing Science. By default c is a command and s a state. Lemma 4 Completeness of vc.
You should now get the idea, at least for chains of assignments. Whenever 'P' holds for a state before the execution of the command, C, then a Q will hold afterwards, or, b C does not terminate in this case, there would be no postcondition at all, so to make the expression true, Q could be anything.