Quantitative Separation Logic and Programs with Lists

Marius Bozga (1) , Radu Iosif (1) , Swann Perarnau (1)

1 VERIMAG - IMAG - VERIMAG

This paper presents an extension of a decidable fragment of Separation Logic for singly-linked lists, defined by Berdine, Calcagno and O'Hearn [8]. Our main extension consists in introducing atomic formulae of the form ls k (x, y) describing a list segment of length k, stretching from x to y, where k is a logical variable interpreted over positive natural numbers, that may occur further inside Presburger constraints. We study the decidability of the full first-order logic combining unrestricted quan-tification of arithmetic and location variables. Although the full logic is found to be undecidable, validity of entailments between formulae with the quantifier prefix in the language ∃ * {∃ N , ∀ N } * is decidable. We provide here a model theoretic method, based on a parametric notion of shape graphs. We have implemented our decision technique, providing a fully automated framework for the verification of quantitative properties expressed as pre-and post-conditions on programs working on lists and integer counters.

Domaines: Logique en informatique [cs.LO]

Marius Bozga, Radu Iosif, Swann Perarnau. Quantitative Separation Logic and Programs with Lists. The 4th International Joint Conference on Automated Reasoning (IJCAR 2008), Aug 2008, Sydney, Australia. pp.34-49, ⟨10.1007/978-3-540-71070-7_4⟩. ⟨hal-01418913⟩