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J S. Moore, “
Inductive Assertions and Operational Semantics”, in D. Geist,
editor, CHARME 2003,, Springer Verlag, LNCS 2860, pp. 289-303, 2003.
Relevance:The URL above points to a longer version
of the paper presented at CHARME. Using a subset of M5 the paper shows how
partial symbolic evaluation of a program can be used to generate and prove
verification conditions produced from inductive assertions
Abstract
This paper shows how classic inductive assertions can be used in conjunction with an operational semantics to prove partial correctness properties of programs. The method imposes only the proof obligations that would be produced by a verification condition generator but does not require the definition of a verification condition generator. The paper focuses on iterative programs but recursive programs are briefly discussed. Assertions are attached to the program by defining a predicate on states. This predicate is then “completed” to an alleged invariant by the definition of a partial function defined in terms of the state transition function of the operational semantics. If this alleged invariant can be proved to be an invariant under the state transition function, it follows that the assertions are true every time they are encountered in execution and thus that the post-condition is true if reached from a state satisfying the pre-condition. But because of the manner in which the alleged invariant is defined, the verification conditions are sufficient to prove invariance. Indeed, the “natural” proof generates the classical verification conditions as subgoals. The invariant function may be thought of as a state-based verification condition generator for the annotated program. The method allows standard inductive assertion style proofs to be constructed directly in an operational semantics setting. The technique is demonstrated by proving the partial correctness of simple bytecode programs with respect to a pre-existing operational model of the Java Virtual Machine.
See also the paper bib::rm04.