On Automated Lemma Generation for Separation Logic with Inductive Definitions

Separation Logic with inductive definitions is a well-known approach for deductive verification of programs that manipulate dynamic data structures. Deciding verification conditions in this context is usually based on user-provided lemmas relating the inductive definitions. We propose a novel approach for generating these lemmas automatically which is based on simple syntactic criteria and deterministic strategies for applying them. Our approach focuses on iterative programs, although it can be applied to recursive programs as well, and specifications that describe not only the shape of the data structures, but also their content or their size. Empirically, we find that our approach is powerful enough to deal with sophisticated benchmarks, e.g., iterative procedures for searching, inserting, or deleting elements in sorted lists, binary search tress, red-black trees, and AVL trees, in a very efficient way

Automated verification of shape, size and bag properties.

In recent years, separation logic has emerged as a contender for formal reasoning of heap-manipulating imperative programs. Recent works have focused on specialised provers that are mostly based on fixed sets of predicates. To improve expressivity, we have proposed a prover that can automatically handle user-defined predicates. These shape predicates allow programmers to describe a wide range of data structures with their associated size properties. In the current work, we shall enhance this prover by providing support for a new type of constraints, namely bag (multi-set) constraints. With this extension, we can capture the reachable nodes (or values) inside a heap predicate as a bag constraint. Consequently, we are able to prove properties about the actual values stored inside a data structure

An Entailment Checker for Separation Logic with Inductive Definitions An Entailment Checker for Separation Logic with Inductive Definitions

International audienceIn this paper, we present Inductor, a checker for entailments between mutually recursive predicates, whose inductive definitions contain ground constraints belonging to the quantifier-free fragment of Separation Logic. Our tool implements a proof-search method for a cyclic proof system that we have shown to be sound and complete, under certain semantic restrictions involving the set of constraints in a given inductive system. Dedicated decision procedures from the DPLL(T)-based SMT solver CVC4 are used to establish the satisfiability of Separation Logic formu-lae. Given inductive predicate definitions, an entailment query, and a proof-search strategy, Inductor uses a compact tree structure to explore all derivations enabled by the strategy. A successful result is accompanied by a proof, while an unsuccessful one is supported by a counterexample

An Entailment Checker for Separation Logic with Inductive Definitions

In this paper, we present Inductor, a checker for entailments between mutually recursive predicates, whose inductive definitions contain ground constraints belonging to the quantifier-free fragment of Separation Logic. Our tool implements a proof-search method for a cyclic proof system that we have shown to be sound and complete, under certain semantic restrictions involving the set of constraints in a given inductive system. Dedicated decision procedures from the DPLL(T)-based SMT solver CVC4 are used to establish the satisfiability of Separation Logic formulae. Given inductive predicate definitions, an entailment query, and a proof-search strategy, Inductor uses a compact tree structure to explore all derivations enabled by the strategy. A successful result is accompanied by a proof, while an unsuccessful one is supported by a counterexample