Abstract. This paper gives an overviewof the Maude 2.0 system. We emphasize the full generality with which rewriting logic and membership equational logic are supported, operational semantics issues, the new built-in modules, the more general Full Maude module algebra, the new META-LEVEL module, the LTL model checker, and newimplementation techniques yielding substantial performance improvements in rewriting modulo. We also comment on Maude’s formal tool environment and on applications. 1

Abstract. Formal semantic definitions of concurrent languages, when specified in a well-suited semantic framework and supported by generic and efficient formal tools, can be the basis of powerful software analysis tools. Such tools can be obtained for free from the semantic definitions; in our experience in just the few weeks required to define a language’s semantics even for large languages like Java. By combining, yet distinguishing, both equations and rules, rewriting logic semantic definitions unify both the semantic equations of equational semantics (in their higher-order denotational version or their first-order algebraic counterpart) and the semantic rules of SOS. Several limitations of both SOS and equational semantics are thus overcome within this unified framework. By using a high-performance implementation of rewriting logic such as Maude, a language’s formal specification can be automatically transformed into an efficient interpreter. Furthermore, by using Maude’s breadth first search command, we also obtain for free a semi-decision procedure for finding failures of safety properties; and by using Maude’s LTL model checker, we obtain, also for free, a decision procedure for LTL properties of finite-state programs. These possibilities, and the competitive performance of the analysis tools thus obtained, are illustrated by means of a concurrent Caml-like language; similar experience with Java (source and JVM) programs is also summarized. 1

Abstract The rewriting calculus, also called ρ-calculus, is a framework embedding λ-calculus and rewriting capabilities, by allowing abstraction not only on variables but also on patterns. The higher-order mechanisms of the λ-calculus and the pattern matching facilities of the rewriting are then both available at the same level. Many type systems for the λ-calculus can be generalized to the ρ-calculus: in this paper, we study extensively a first-order ρ-calculus à la Church, called ρ stk The type system of ρ stk � allows one to type (object oriented flavored) fixpoints, leading to an expressive and safe calculus. In particular, using pattern matching, one can encode and typecheck term rewriting systems in a natural and automatic way. Therefore, we can see our framework as a starting point for the theoretical basis of a powerful typed rewriting-based language.

Abstract. Abstraction reduces the problem of whether an infinite state system satisfies version. The most common abstractions are quotients of the original system. We present a simple method of defining quotient abstractions by means of equations collapsing the set of states. Our method yields the minimal quotient system together with a set of proof obligations that guarantee its executability and can be discharged with tools such as those in the Maude formal environment.

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journal = {Journal of Symbolic Computation}, year = 2005, volume = 40, number = 1, pages = {831-873}, note = {Special issue on Reduction Strategies in Rewriting and Programming}, editor = {Bernhard Gramlich and Salvador Lucas},

Abstract. Computational systems are often represented by means of Kripke structures, and related using simulations. We propose rewriting logic as a flexible and executable framework in which to formally specify these mathematical models, and introduce a particular and elegant way of representing simulations in it: theoroidal maps. A categorical viewpoint is very natural in the study of these structures and we show how to organize Kripke structures in categories that afterwards are lifted to the rewriting logic’s level. We illustrate the use of theoroidal maps with two applications: predicate abstraction and the study of fairness constraints. 1

Abstract. We demonstrate how access control models and policies can be represented by using term rewriting systems, and how rewriting may be used for evaluating access requests and for proving properties of an access control policy. We focus on two kinds of access control models: discretionary models, based on access control lists (ACLs), and rolebased access control (RBAC) models. For RBAC models, we show that we can specify several variants, including models with role hierarchies, and constraints and support for security administrator review querying. 1

Abstract. For narrowing to be an efficient evaluation mechanism, several lazy narrowing strategies have been proposed, although typically for the restricted case of left-linear constructor systems. These assumptions, while reasonable for functional programming applications, are too restrictive for a much broader range of applications to which narrowing can be fruitfully applied, including applications where rules have a non-equational meaning either as transitions in a concurrent system or as inferences in a logical system. In this paper, we propose an efficient lazy narrowing strategy called natural narrowing which can be applied to general term rewriting systems with no restrictions whatsoever. An important consequence of this generalization is the wide range of applications that can now be efficiently supported by narrowing. We highlight a few such applications including symbolic model checking, theorem proving, programming languages, and partial evaluation. What thus emerges is a general and efficient unified mechanism based on narrowing, that seamlessly integrates a very wide range of applications in programming and proving. 1

Abstract: This paper presents a modular rewriting semantics (MRS) specification for Reppy’s Concurrent ML (CML), based on Peter Mosses ’ modular structural operational semantics specification for CML. A modular rewriting semantics specification for a programming language is a rewrite theory in rewriting logic written using techniques that support the modular development of the specification in the precise sense that every module extension is conservative. We show that the MRS of CML can be used to interpret CML programs using the rewrite engine of the Maude system, a highperformance implementation of rewriting logic, and to verify CML programs using Maude’s built-in LTL model checker. It is assumed that the reader is familiar with basic concepts of structural operational semantics and algebraic specifications.