Strong-separation Logic

Abstract

Most automated verifiers for separation logic are based on the symbolic-heap fragment, which disallows both the magic-wand operator and the application of classical Boolean operators to spatial formulas. This is not surprising, as support for the magic wand quickly leads to undecidability, especially when combined with inductive predicates for reasoning about data structures. To circumvent these undecidability results, we propose assigning a more restrictive semantics to the separating conjunction. We argue that the resulting logic, strong-separation logic, can be used for symbolic execution and abductive reasoning just like “standard” separation logic, while remaining decidable even in the presence of both the magic wand and inductive predicates (we consider a list-segment predicate and a tree predicate)—a combination of features that leads to undecidability for the standard semantics.

A separation logic for sequences in pointer programs and its decidability

“…We notice that in either separation logic or one of its fragments (symbolic heap [11] [26], strong-separation logic [17], etc. ), the singleton heap is defined with some fixed number n. It may not be suitable for describing properties on blocks, or graphs where each node is of unbounded outdegrees.…”

“…However, if list predicates are restricted to the list with length at most 2, one can get a decidable fragment SL( * , − * , reach 2 ) [10]. Besides, if we further restrict heap unions in separation model, one can get strong-separation logic [17]. It is proved that the strong-separation fragment SSL( * , − * ¬ , ls) with list predicates is decidable.…”