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 Maude's 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

Reflection in conditional rewriting logic

AbstractWe recall general metalogical axioms for a reflective logic based on the notion of a universal theory, that is, a theory that can simulate the deductions of all other theories in a class of theories of interest, including itself. We then show that conditional rewriting logic is reflective, generalizing in two stages: first to the unsorted conditional case, and then to the many-sorted conditional case, the already known result for unconditional and unsorted rewriting logic (Reflection in Rewriting Logic: Metalogical Foundations and Metaprogramming Applications. CSLI Publications, 2000). This work should be seen as providing foundations for many useful applications of rewriting logic reflection. The results presented here have greatly influenced the design of the Maude language, which implements rewriting logic and supports its reflective capabilities, and have been used as a theoretical foundation for applications such as internal rewrite strategies, reflective design of theorem proving tools, module algebra and metaprogramming, and metareasoning in metalogical frameworks

Maude: specification and programming in rewriting logic

AbstractMaude 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 Maude's 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

Preface Volume 36

AbstractThis volume constitutes the proceedings of the Third International Workshop on Rewriting Logic and its Applications.Following the successful first and second International Workshops on Rewriting Logic and its Applications, held in Asilomar (California) in September 1996 and in Pont-à-Mousson (France) in September 1998 respectively, the third workshop takes place in Kanazawa (Japan) in September 18, 19, 20 (Mon, Tue, Wed), 2000.Kanazawa is one of the most beautiful old towns in Japan. The workshop site (Kanazawa City Cultural Hall) is located just in the downtown of Kanazawa and major sightseeing spots are easily accessible on foot. This setting helps to make the workshop intimate, enjoyable, and productive.Rewriting logic is a natural semantic framework for concurrency, parallelism, and communication in computing, and for the specification of a wide range of systems and languages. It also has good properties as a logical framework for representing many varieties of logics. A growing number of research efforts exploring the foundations and applications of rewriting logic in all these directions are being carried out worldwide, and several languages based on rewriting logic such as CafeOBJ, ELAN, and Maude are being designed and implemented.The goal of WRLA2000 is to bring together researchers, from all over the world so that they can present their recent works, discuss future research directions, and exchange ideas. In addition to the presentations of research results, the program includes invited presentations and system demonstrations.Technical focuses of WRLA2000 are placed on such topics as secure protocol specifications and verification, future language features, rewriting for behavioral specifications, architecture for supporting system. We hope the discussions at the workshop help each participant to understand the current status and future issues of rewriting logic and relating fields.The workshop is supported by honest efforts of many people and organizations. The authors who submitted papers provide us the primary possibility of having interesting and productive workshop. The program committee members and external reviewers worked hard to review and select papers for presentation. These makes it possible for us to have an attractive program. The local arrangement and publicity chairs take care of running of the workshop, and let us enjoy the workshop under nice conditions. Ishikawa Prefecture, Kanazawa City, JAIST, SRA, and MRI support the workshop financially. We want to thank all of them for making it possible for us to have this productive workshop.Kanazawa, Japan, September 2000Kokichi Futatsug

2D Dependency Pairs for Proving Operational Termination of CTRSs

The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-319-12904-4_11The notion of *operational termination* captures nonterminating computations due to subsidiary processes that are necessary to issue a *single* `main' step but which often remain `hidden' when the main computation sequence is observed. This highlights *two dimensions* of nontermination: one for the infinite sequencing of computation steps, and the other that concerns the proof of some single steps. For conditional term rewriting systems (CTRSs), we introduce a new *dependency pair framework* which exploits the *bidimensional* nature of conditional rewriting (rewriting steps + satisfaction of the conditions as reachability problems) to obtain a powerful and more expressive framework for proving operational termination of CTRSs.Lucas Alba, S.; Meseguer, J. (2014). 2D Dependency Pairs for Proving Operational Termination of CTRSs. En Rewriting Logic and Its Applications. Springer Verlag (Germany). 195-212. doi:10.1007/978-3-319-12904-4_11S19521

A Finite Representation of the Narrowing Space

The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-319-14125-1_4Narrowing basically extends rewriting by allowing free variables in terms and by replacing matching with unification. As a consequence, the search space of narrowing becomes usually infinite, as in logic programming. In this paper, we introduce the use of some operators that allow one to always produce a finite data structure that still represents all the narrowing derivations. Furthermore, we extract from this data structure a novel, compact equational representation of the (possibly infinite) answers computed by narrowing for a given initial term. Both the finite data structure and the equational representation of the computed answers might be useful in a number of areas, like program comprehension, static analysis, program transformation, etc.Nishida, N.; Vidal, G. (2013). A Finite Representation of the Narrowing Space. En Logic-Based Program Synthesis and Transformation. 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Basic completion strategies as another application of the Maude strategy language

The two levels of data and actions on those data provided by the separation between equations and rules in rewriting logic are completed by a third level of strategies to control the application of those actions. This level is implemented on top of Maude as a strategy language, which has been successfully used in a wide range of applications. First we summarize the Maude strategy language design and review some of its applications; then, we describe a new case study, namely the description of completion procedures as transition rules + control, as proposed by Lescanne.Comment: In Proceedings WRS 2011, arXiv:1204.531