Internal Calculi for Separation Logic

Stéphane Demri (1, 2) , Etienne Lozes (3) , Alessio Mansutti (1, 2)

1 CNRS - Centre National de la Recherche Scientifique
2 LSV - Laboratoire Spécification et Vérification [Cachan]
3 I3S - Laboratoire d'Informatique, Signaux, et Systèmes de Sophia Antipolis

We present a general approach to axiomatise separation logics with heaplet semantics with no external features such as nominals/labels. To start with, we design the first (internal) Hilbert-style axiomatisation for the quantifier-free separation logic SL(*, −*). We instantiate the method by introducing a new separation logic with essential features: it is equipped with the separating conjunction, the predicate ls, and a natural guarded form of first-order quantification. We apply our approach for its axiomatisation. As a by-product of our method, we also establish the exact expressive power of this new logic and we show PSpace-completeness of its satisfiability problem.

Mots clés: separation logic; internal calculus; adjunct elimination; quantifier elimination; Hilbert-style proof system; guarded quantification; list segment predicate; complexity; core formula

Domaines: Logique en informatique [cs.LO]

Stéphane Demri, Etienne Lozes, Alessio Mansutti. Internal Calculi for Separation Logic. Computer Science Logic, Jan 2020, Barcelona, Spain. ⟨10.4230/LIPIcs.CSL.2020.19⟩. ⟨hal-02883558⟩