Shape and Content: Incorporating Domain Knowledge into Shape Analysis

The verification community has studied dynamic data structures primarily in a bottom-up way by analyzing pointers and the shapes induced by them. Recent work in fields such as separation logic has made significant progress in extracting shapes from program source code. Many real world programs however manipulate complex data whose structure and content is most naturally described by formalisms from object oriented programming and databases. In this paper, we attempt to bridge the conceptual gap between these two communities. Our approach is based on Description Logics (DLs), a widely used knowledge representation paradigm which gives a logical underpinning for diverse modeling frameworks such as UML and ER. We show how DLs can be used on top of an existing shape analysis to add content descriptions to the shapes. Technically, we assume that we have separation logic shape invariants obtained from a shape analysis tool, and requirements on the program data in terms of description logic. We show that the two-variable fragment of first order logic with counting and trees (whose decidability was presented at LICS 2013) can be used as a joint framework to embed suitable DLs and separation logic.