S. A. Cook. Soundness and completeness of an axiomatic system for program verification. SIAM J. on Computing, 7:70--90, 1978.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....backwards axiom. For a sequence C of assignment statements it follows that is derivable from the basic axioms (in either the Reynolds or backwards forms) Sequencing, and Consequence exactly when it is true. Extending this result to loops would get us into the issue of expressiveness [10], which is outside the scope of our concerns here. The following notation will be convenient: if # then let h # denote the singleton heap in which # is mapped to h(#) also, let h # denote the heap like h except that it is undefined on #. It is evident that h = h #) h #) when ....

Cook, S. A. Soundness and completeness of an axiomatic system for program verification. SIAM J. on Computing 7 (1978), 70--90.

....C fQg The rst three rules are those for the three constructs for commands, and the fourth, the consequence rule, is needed to strengthen the precondition or weaken the postcondition of the triple. To extend consideration of completeness to loops would require consideration of expressiveness [5]; this, however, is outside the scope of our concerns here. 4. ASSIGNMENT The rst command we consider is assignment V : E: To de ne the relation ; we need to distinguish between variable assignment x : E and component assignment V:a : E. In the rst case we update the stack and in the ....

Cook, S. A. Soundness and completeness of an axiomatic system for program verication. SIAM J. on Computing 7 (1978), 70-90.

....statement can be expressed by the corresponding backwards axiom. For a sequence C of atomic satements it follows that fPgCfQg is derivable from the basic axioms, Sequencing, and Consequence exactly when it is true. Extending this result to loops would get us into the issue of expressiveness [7], which is outside the scope of our concerns here. Proof The soundness result above already shows that the pre conditions in the various axioms imply wp. We show the reverse implication, for each of the backwards axioms in turn. 17 Backwards Object component Assignment We use the instance of ....

....this result could be achieved for a language with an explicit type of sequences of values (as treated informally here and in [26] by encoding heaps as sequences of location value pairs. A side e ect of such a result would be a relative completenesss result for the program logic, including loops [7]. Acknowledgements. We are grateful to Richard Bornat, Cristiano Calcagno, David Pym, Uday Reddy and John Reynolds for helpful discussions. This research was supported by EPSRC Grant GR L54578. ....

Cook, S. A. Soundness and completeness of an axiomatic system for program verication. SIAM J. on Computing 7 (1978), 70-90.

....C fQg The rst three rules are those for the three constructs for commands, and the fourth, the consequence rule, is needed to strengthen the precondition or weaken the postcondition of the triple. To extend consideration of completeness to loops would require consideration of expressiveness [6]; this, however, is outside the scope of our concerns here. 4 Assignment The rst command we consider is assignment V : E: To de ne the relation ; we need to distinguish between variable assignment x : E and component assignment V:a : E. In the rst case we update the stack and in the ....

Cook, S. A. Soundness and completeness of an axiomatic system for program verication. SIAM J. on Computing 7 (1978), 70-90.

.... operator de nitions (which do have desirable properties) can be used and the proof system is sound, but incomplete [4] To solve this problem, Sanders [14] modi ed the Unity logic in such a way that the substitution axiom is no longer needed and the logic remains complete (in the sense of Cook [6]) Her de nition of the temporal operators is based on the concept of strongest invariant sst:F:INIT which exists for any program F and is unique. From a theoretical point of view this solution provides a convenient result of soundness and completeness for the resulting Unity logic. However, from ....

S.A. Cook. Soundness and completeness for an axiomatic system for program veriøcation. SIAM J. Comput., 7:7090, 1978.

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S. A. Cook. Soundness and completeness of an axiomatic system for program verification. SIAM J. on Computing, 7:70--90, 1978.

No context found.

Cook, S. A. Soundness and completeness of an axiomatic system for program veri cation. SIAM J. on Computing 7 (1978), 70-90.

No context found.

Cook, S. A. Soundness and completeness of an axiomatic system for program veri cation. SIAM J. on Computing 7 (1978), 70-90.

No context found.

S. A. Cook. Soundness and completeness of an axiomatic system for program verification. SIAM J. on Computing, 7:70--90, 1978.

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