Internal Calculi for Separation Logics

Authors Stéphane Demri, Etienne Lozes, Alessio Mansutti

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Stéphane Demri
  • LSV, CNRS, ENS Paris-Saclay, Université Paris-Saclay, France
Etienne Lozes
  • Université Côte d’Azur, CNRS, I3S, France
Alessio Mansutti
  • LSV, CNRS, ENS Paris-Saclay, Université Paris-Saclay, France


We would like to thank the anonymous reviewers for their suggestions and remarks that help us to improve the quality of this paper.

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Stéphane Demri, Etienne Lozes, and Alessio Mansutti. Internal Calculi for Separation Logics. In 28th EACSL Annual Conference on Computer Science Logic (CSL 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 152, pp. 19:1-19:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


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.

Subject Classification

ACM Subject Classification
  • Theory of computation
  • Separation logic
  • internal calculus
  • adjunct/quantifier elimination


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