Extended Transitive Separation Logic

Separation logic (SL) is an extension of Hoare logic by operations and formulas to reason more flexibly about heap portions or, more concretely, about linked object/record structures. In the present paper we give an algebraic extension of SL at the data structure level. We define operations that, additionally to guaranteeing heap separation, make assumptions about the linking structure. Phenomena to be treated comprise reachability analysis, (absence of) sharing, cycle detection and preservation of substructures under destructive assignments. We demonstrate the practicality of this approach with examples of in-place list-reversal, tree rotation and threaded trees