Verifying Reachability-Logic Properties on Rewriting-Logic Specifications

Abstract

Abstract. Reachability Logic is a recently introduced formalism, which is currently used for defining the operational semantics of programming languages and for stating properties about program executions. In this paper we show how Reachability Logic can be adapted for stating properties of transition systems described by Rewriting-Logic specifications. We propose an automatic procedure for verifying Rewriting-Logic specifications against Reachability-Logic properties. We prove the soundness of the procedure and illustrate it by verifying a communication protocol specified in Maude.

Unification in Matching Logic

“…Matching Logic [22,24] started as a logic over a particular case of constrained terms [23,26,9,25,27,5,14], but now it is developed as a solid program logic framework. Here we recall from [22] the particular definitions and notions of ML that we use in this paper.…”

“…Matching Logic [22] (hereafter shorthanded as ML) is a novel framework which is currently used for specifying programming languages semantics [11,12,19,8] and for reasoning about programs [23,10,9,26,27,14,5]. The logic is inspired from the domain of programming language semantics and it aims to use the operational semantics of a programming language as a basis for both execution and verification of programs.…”

“…ConclusionsPrevious verification efforts with ML[23,26,25,27,5,14,10,17,20,9] were based on unification. However, unification was always considered a trusted component.In this paper we finally tackle down this issue by proposing a sound method for unification which involves a syntactic unification algorithm.…”

Generalized Rewrite Theories and Coherence Completion

“…Closely related work falls into three categories: (i) the already-mentioned symbolic reasoning techniques for rewrite theories, e.g., [10,2,22,1,12,16,25,17,24]; (ii) executability techniques for standard rewrite theories, including [27,8]; and (iii) variant-based symbolic computation, including [5,11,20,23], and also [7], where a limited form of "equational coherence completion" was introduced. In relation to all the work in (i)-(iii), the main contributions of this paper are: (1) a new notion of generalized rewrite theory, of rewriting in a generalized rewrite theory, and an initial model semantics for such theories; (2) new symbolic executability requirements, including a new notion of coherence that is a substantial generalization of the standard notions in [27,8]; and (3) new automatable theory transformations both to ensure ground coherence of generalized rewrite theories by coherence completion, and to make symbolic executability applicable to a widest possible class of such theories.…”

“…Symbolic methods are used to reason about concurrent systems specified by rewrite theories in many ways, including: (i) cryptographic protocol verification, e.g., [10], (ii) logical LTL model checking, e.g., [2], (iii) rewriting modulo SMT and related approaches, e.g., [22,1], (iv) inductive theorem proving and program verification, e.g., [12,16], and (v) reachability logic theorem proving, e.g., [25,17,24]. One key issue is that the rewrite theories used in several of these approaches go beyond the standard notion of rewrite theory in, say [3], and also beyond the executability requirements in, say, [8].…”