Satisfiability Modulo Abstraction for Separation Logic with Linked Lists
University of Wisconsin-Madison Department of Computer Sciences
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Separation logic is an expressive logic for reasoning about heap structures in programs. This paper presents a semi-decision procedure for checking unsatisfiability of formulas in a fragment of separation logic that includes points-to assertions (x |-> y), acyclic-list-segment assertions (ls(x,y)), logical-and, logical-or, separating conjunction, and septraction (the DeMorgan-dual of separating implication). The fragment that we consider allows negation at leaves, and includes formulas that lie outside other separation-logic fragments considered in the literature. The semi-decision procedure is designed using concepts from abstract interpretation. The procedure uses an abstract domain of shape graphs to represent a set of heap structures, and computes an abstraction that over-approximates the set of satisfying models of a given formula. If the over-approximation is empty, then the formula is unsatisfiable. We have implemented the method, and evaluated it on a set of formulas taken from the literature. The implementation is able to establish the unsatisfiability of formulas that cannot be handled by previous approaches.