Two for the Price of One: Lifting Separation Logic Assertions

Recently, data abstraction has been studied in thecontext of separation logic, with noticeable practicalsuccesses: the developed logics have enabled cleanproofs of tricky challenging programs, such as subject-observer patterns, and they have become the basis of ef-ficient verification tools for Java (jStar), C (VeriFast)and Hoare Type Theory (Ynot). In this paper, we givea new semantic analysis of such logic-based approachesusing Reynolds’s relational parametricity. The core ofthe analysis is our lifting theorems, which give a soundand complete condition for when a true implication be-tween assertions in the standard interpretation entailsthat the same implication holds in a relational inter-pretation. Using these theorems, we provide an algo-rithm for identifying abstraction-respecting client-sideproofs; the proofs ensure that clients cannot distinguishtwo appropriately-related module implementations.