Steven Eker

Maude: specification and programming in rewriting logic

Maude is a high-level language and a high-performance system supporting executable specification and declarative programming in rewriting logic. Since rewriting logic contains equational logic, Maude also supports equational specification and programming in its sublanguage of functional modules and theories. The underlying equational logic chosen for Maude is membership equational logic, that has sorts, subsorts, operator overloading, and partiality definable by membership and equality conditions. Rewriting logic is reflective, in the sense of being able to express its own metalevel at the object level. Reflection is systematically exploited in Maude endowing the language with powerful metaprogramming capabilities, including both user-definable module operations and declarative strategies to guide the deduction process. This paper explains and illustrates with examples the main concepts of Maudes language design, including its underlying logic, functional, system and object-oriented modules, as well as parameterized modules, theories, and views. We also explain how Maude supports reflection, metaprogramming and internal strategies. The paper outlines the principles underlying the Maude system implementation, including its semicompilation techniques. We conclude with some remarks about applications, work on a formal environment for Maude, and a mobile language extension of Maude.

The maude 2.0 system

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 new implementation techniques yielding substantial performance improvements in rewriting modulo. We also comment on Maudes formal tool environment and on applications.

Principles of Maude

Abstract This paper introduces the basic concepts of the rewriting logic language Maude and discusses its implementation. Maude is a wide-spectrum language supporting formal specification, rapid prototyping, and parallel programming. Maudes rewriting logic paradigm includes the functional and object-oriented paradigms as sublanguages. The fact that rewriting logic is reflective leads to novel metaprogramming capabilities that can greatly increase software reusability and adaptability. Control of the rewriting computation is achieved through internal strategy languages defined inside the logic. Maudes rewrite engine is designed with the explicit goal of being highly extensible and of supporting rapid prototyping and formal methods applications, but its semi-compilation techniques allow it to meet those goals with good performance.

The Maude LTL Model Checker

Abstract The Maude LTL model checker supports on-the-fly explicit-state model checking of concurrent systems expressed as rewrite theories with performance comparable to that of current tools of that kind, such as SPIN. This greatly expands the range of applications amenable to model checking analysis. Besides traditional areas well supported by current tools, such as hardware and communication protocols, many new applications in areas such as rewriting logic models of cell biology, or next-generation reflective distributed systems can be easily specified and model checked with our tool.

PATHWAY LOGIC: SYMBOLIC ANALYSIS OF BIOLOGICAL SIGNALING

The genomic sequencing of hundreds of organisms including homo sapiens, and the exponential growth in gene expression and proteomic data for many species has revolutionized research in biology. However, the computational analysis of these burgeoning datasets has been hampered by the sparse successes in combinations of data sources, representations, and algorithms. Here we propose the application of symbolic toolsets from the formal methods community to problems of biological interest, particularly signaling pathways, and more specifically mammalian mitogenic and stress responsive pathways. The results of formal symbolic analysis with extremely efficient representations of biological networks provide insights with potential biological impact. In particular, novel hypotheses may be generated which could lead to wet lab validation of new signaling possibilities. We demonstrate the graphic representation of the results of formal analysis of pathways, including navigational abilities, and describe the logical underpinnings of the approach. In summary, we propose and provide an initial description of an algebra and logic of signaling pathways and biologically plausible abstractions that provide the foundation for the application of high-powered tools such as model checkers to problems of biological interest.

The Maude System

Maude is a high-performance language and system supporting both equational and rewriting logic computation for a wide range of applications, including development of theorem proving tools, language prototyping, executable specification and analysis of concurrent and distributed systems, and logical framework applications in which other logics are represented, translated, and executed. Maude’s functional modules are theories in membership equational logic [8,1], a Horn logic whose atomic sentences are either equalities t = t′ or membership assertions of the form t : s, stating that a term t has a certain sort s. Such a logic extends OBJ3’s [4] order-sorted equational logic and supports sorts, subsorts, subsort polymorphic overloading of operators, and definition of partial functions with equationally defined domains. Maude’s functional modules are assumed to be Church-Rosser; they are executed by the Maude engine according to the rewriting techniques and operational semantics developed in [1]. Membership equational logic is a sublogic of rewriting logic [6]. A rewrite theory is a pair (T, R) with T a membership equational theory, and R a collection of labeled and possibly conditional rewrite rules involving terms in the signature of T . Maude’s system modules are rewrite theories in exactly this sense. The rewrite rules r : t −→ t′ in R are not equations. Computationally, they are interpreted as local transition rules in a possibly concurrent system. Logically, they are interpreted as inference rules in a logical system. This makes rewriting logic both a general semantic framework to specify concurrent systems and languages [7], and a general logical framework to represent and execute different logics [5]. Rewriting in (T, R) happens modulo the equational axioms in T . Maude supports rewriting modulo different combinations of associativity, commutativity, identity, and idempotency axioms. The rules in R need not be Church-Rosser and need not be terminating. Many different rewriting paths are then possible; therefore, the choice of appropriate strategies is crucial for executing rewrite theories. In Maude, such strategies are not an extra-logical part of the language.

Pathway Logic: Executable Models of Biological Networks

Abstract In this paper we describe the use of the rewriting logic based Maude tool to model and analyze mammalian signaling pathways. We discuss the representation of the underlying biological concepts and events and describe the use of the new search and model checking capabilities of Maude 2.0 to analyze the modeled network. We also discuss the use of Maudes reflective capability for meta modeling and analyzing the models themselves. The idea of symbolic biological experiments opens up an exciting new world of challenging applications for formal methods in general and for rewriting logic based formalisms in particular.

Building Equational Proving Tools by Reflection in Rewriting Logic

Publisher Summary This chapter explains the design and use of two proving tools such as inductive theorem prover and a Church-Rosser checker. It uses these tools to prove theorems about equational specifications with initial algebra semantics and to check whether such specifications satisfy the Church-Rosser property. These tools have been developed as part of the Cafe project, and can also be used on their own to prove properties of equational specifications in Maude. An important feature of these tools is that they are written entirely in Maude and are in fact executable specifications in rewriting logic of the formal inference systems that they implement. This chapter also gives a brief review of membership equational logic, rewriting logic, and Maude, including reflective features and the related topic of strategies. After summarizing the reflective design of the tools, the chapter explains each of the tools, including its inference system and its corresponding Maude implementation, with examples and concluding remarks.

Maude as a Formal Meta-tool

Given the different perspectives from which a complex software system has to be analyzed, the multiplicity of formalisms is unavoidable. This poses two important technical challenges: how to rigorously meet the need to interrelate formalisms, and how to reduce the duplication of effort in tool and specification building across formalisms. These challenges could be answered by adequate formal meta-tools that, when given the specification of a formal inference system, generate an efficient inference engine, and when given a specification of two formalisms and a translation, generate an actual translator between them. Similarly, module composition operations that are logic-independent, but that at present require costly implementation efforts for each formalism, could be provided for logics in general by module algebra generator meta-tools. The foundations of meta-tools of this kind can be based on a metatheory of general logics. Their actual design and implementation can be based on appropriate logical frameworks having efficient implementations. This paper explains how the reflective logical framework of rewriting logic can be used, in conjunction with an efficient reflective implementation such as the Maude language, to design formal meta-tools such as those described above. The feasibility of these ideas and techniques has been demonstrated by a number of substantial experiments in which new formal tools and new translations between formalisms, efficient enough to be used in practice, have been generated.

The maude LTL model checker and its implementation

A model checker typically supports two different levels of specification: (1) a system specification level, in which the concurrent system to be analyzed is formalized; and (2) a property specification level, in which the properties to be model checked—for example, temporal logic formulae—are specified. The Maude LTL model checker has been designed with the goal of combining a very expressive and general system specification language (Maude [1]) with an advanced on-the-fly explicit-state LTL model checking engine.