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We introduce a fragment of separation logic, called NOLL, for automated reasoning about programs manipulating overlaid and nested linked lists, where overlaid means that the lists share the same set of objects. The distinguishing features of NOLL are: (1) it is parametrized by a set of user-defined predicates specifying nested linked list segments, (2) a "per-field" version of the separating conjunction allowing to share object locations but not record field locations, and (3) it can express sharing constraints between list segments. We prove that checking the entailment between two NOLL formulas is co-NP complete using a small model property. We also provide an effective procedure for checking entailment in NOLL, which first constructs a Boolean abstraction of the two formulas in order to infer all the implicit constraints, and then, it checks the existence of a homomorphism between the two formulas, viewed as graphs. We have implemented this procedure and applied it on verification conditions generated from several interesting case studies that manipulate overlaid and nested data structures.

Compositional Invariant Checking for Overlaid and Nested Linked Lists