Boolean Heaps

We show that the idea of predicates on heap objects can be cast in the framework of predicate abstraction. This leads to an alternative view on the underlying concepts of three-valued shape analysis by Sagiv, Reps and Wilhelm. Our construction of the abstract post operator is analogous to the corresponding construction for classical predicate abstraction, except that predicates over objects on the heap take the place of state predicates, and boolean heaps (sets of bitvectors) take the place of boolean states (bitvectors). A program is abstracted to a program over boolean heaps. For each command of the program, the corresponding abstract command is effectively constructed by deductive reasoning, namely by the application of the weakest precondition operator and an entailment test. We thus obtain a symbolic framework for shape analysis.