A Complete Axiomatisation for Quantifier-Free Separation Logic

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

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

We present the first complete axiomatisation for quantifier-free separation logic. The logic is equipped with the standard concrete heaplet semantics and the proof system has no external feature such as nominals/labels. It is not possible to rely completely on proof systems for Boolean BI as the concrete semantics needs to be taken into account. Therefore, we present the first internal Hilbert-style axiomatisation for quantifier-free separation logic. The calculus is divided in three parts: the axiomatisation of core formulae where Boolean combinations of core formulae capture the expressivity of the whole logic, axioms and inference rules to simulate a bottom-up elimination of separating connectives, and finally structural axioms and inference rules from propositional calculus and Boolean BI with the magic wand.

Mots clés: separation logic; axiomatisation; Hilbert-style system; core formula; reduction axiom; quantifier elimination; separating conjunction; magic wand; bunched implications logic BI

Domaines: Informatique [cs]; Logique en informatique [cs.LO]

Stéphane Demri, Etienne Lozes, Alessio Mansutti. A Complete Axiomatisation for Quantifier-Free Separation Logic. Logical Methods in Computer Science, 2021, 17 (3), pp.17:1--17:64. ⟨10.46298/lmcs-17(3:17)2021⟩. ⟨hal-03005864⟩