Completeness and expressiveness of pointer program verification by separation logic

Reynolds' separation logical system for pointer program verification is investigated. This paper proves its completeness theorem that states that every true asserted program is provable in the logical system. In order to prove the completeness, this paper shows the expressiveness theorem that states the weakest precondition of every program and every assertion can be expressed by some assertion. This paper also introduces an extension of the assertion language with inductive definitions and proves the soundness theorem, the expressiveness theorem, and the completeness theorem.