Completeness of Pointer Program Verification by Separation Logic

Abstract

Reynolds' separation logical system for pointer program verification is investigated. This paper proves its completeness theorem as well as the expressiveness theorem that states the weakest precondition of every program and every assertion can be expressed by some assertion. This paper also introduces the predicate that represents the next new cell, and proves the completeness and the soundness of the extended system under deterministic semantics.

Separation logics and modalities: a survey

“…Ob-viously, completeness depends on the programming language, on the assertion logic and on the set of inference rules. More details can be found in [Loz12], see also related results in [COY07,TCA09] or in [TC14].…”

Relatively complete verification of probabilistic programs: an expressive language for expectation-based reasoning

“…To deal with the first issue, there is a standard solution in proofs of expressiveness (cf. [Loeckx and Sieber 1987;Tatsuta et al 2009Tatsuta et al , 2019Winskel 1993]): We employ Gödelization to encode both program states and finite sequences of program states as natural numbers in syntactic expectations. The details are found in Section 7.…”

“…Winskel [1993] and Loeckx et al [1984] proved expressiveness of first-order arithmetic for Dijkstra's weakest precondition calculus. For separation logic [Reynolds 2002]Ða very successful logic for compositional reasoning about pointer programsÐexpressiveness was shown by Tatsuta et al [2009Tatsuta et al [ , 2019, almost a decade later than the logic was originally developed and started to be used.…”