Checking Entailment Between Separation Logic Symbolic Heaps: Beyond Connected and Established Systems

We show that the entailment problem φ |= ψ in Separation Logic is decidable for separated conjunctions of atoms φ and ψ, that contain predicate symbols whose interpretation is given inductively by a set of recursive rules. The proof is based on a reduction to a class of entailment problems shown to be decidable in [9]. In contrast with the works of [9, 12, 13], the considered inductive rules may introduce memory locations without allocating them, which strongly extends the class of structures that can be constructed. Moreover, the result is more general than the one given in [8], because the conditions on the inductive rules corresponding to the left-hand side of the considered entailment are strongly relaxed: it is only assumed that the rules are progressing, i.e. that they allocate exactly one memory location.