Guided Unfoldings for Finding Loops in Standard Term Rewriting

In this paper, we reconsider the unfolding-based technique that we have introduced previously for detecting loops in standard term rewriting. We improve it by guiding the unfolding process, using distinguished positions in the rewrite rules. This results in a depth-first computation of the unfoldings, whereas the original technique was breadth-first. We have implemented this new approach in our tool NTI and compared it to the previous one on a bunch of rewrite systems. The results we get are promising (better times, more successful proofs).Comment: Pre-proceedings paper presented at the 28th International Symposium on Logic-Based Program Synthesis and Transformation (LOPSTR 2018), Frankfurt am Main, Germany, 4-6 September 2018 (arXiv:1808.03326

Inspecting Maude Variants with GLINTS

[EN] This paper introduces GLINTS, a graphical tool for exploring variant narrowing computations in Maude. The most recent version of Maude, version 2.7.1, provides quite sophisticated unification features, including order-sorted equational unification for convergent theories modulo axioms such as associativity, commutativity, and identity. This novel equational unification relies on built-in generation of the set of variants of a term t, i.e., the canonical form of t sigma for a computed substitution sigma. Variant generation relies on a novel narrowing strategy called folding variant narrowing that opens up new applications in formal reasoning, theorem proving, testing, protocol analysis, and model checking, especially when the theory satisfies the finite variant property, i.e., there is a finite number of most general variants for every term in the theory. However, variant narrowing computations can be extremely involved and are simply presented in text format by Maude, often being too heavy to be debugged or even understood. The GLINTS system provides support for (i) determining whether a given theory satisfies the finite variant property, (ii) thoroughly exploring variant narrowing computations, (iii) automatic checking of node embedding and closedness modulo axioms, and (iv) querying and inspecting selected parts of the variant trees.This work has been partially supported by EU (FEDER) and Spanish MINECO grant TIN 2015-69175-C4-1-R and by Generalitat Valenciana PROMETEO-II/2015/013. Angel Cuenca-Ortega is supported by SENESCYT, Ecuador (scholarship program 2013), and Julia Sapina by FPI-UPV grant SP2013-0083. Santiago Escobar is supported by the Air Force Office of Scientific Research under award number FA9550-17-1-0286.Alpuente Frasnedo, M.; Cuenca-Ortega, A.; Escobar Román, S.; Sapiña-Sanchis, J. (2017). Inspecting Maude Variants with GLINTS. Theory and Practice of Logic Programming. 17(5-6):689-707. https://doi.org/10.1017/S147106841700031XS689707175-

A partial evaluation methodology for optimizing rewrite theories incrementally

Partial evaluation (PE) is a branch of computer science that achieves code optimization via specialization. This article describes a PE methodology for optimizing rewrite theories that encode concurrent as well as nondeterministic systems by means of the Maude language. The main advantages of the proposed methodology can be summarized as follows: • An automatic program optimization technique for rewrite theories featuring several PE criteria that support the specialization of a broad class of rewrite theories. • An incremental partial evaluation modality that allows the key specialization components to be encapsulated at the desired granularity level to facilitate progressive refinements of the specialization. • All executability theory requirements are preserved by the PE transformation. Also the transformation ensures the semantic equivalence between the original rewrite theory and the specialized theory under rather mild conditions

Basic Narrowing Revisited

In this paper we study basic narrowing as a method for solving equations in the initial algebra specified by a ground confluent and terminating term rewriting system. Since we are interested in equation solving, we don’t study basic narrowing as a reduction relation on terms but consider immediately its reformulation as an equation solving rule. This reformulation leads to a technically simpler presentation and reveals that the essence of basic narrowing can be captured without recourse to term unification. We present an equation solving calculus that features three classes of rules. Resolution rules, whose application is don’t care nondeterministic, are the basic rules and suffice for a complete solution procedure. Failure rules detect inconsistent parts of the search space. Simplification rules, whose application is don’t care nondeterministic, enhance the power of the failure rules and reduce the number of necessary don’t know steps. Three of the presented simplification rules are new. The rewriting rule allows for don’t care nondeterministic rewriting and thus yields a marriage of basic and normalizing narrowing. The safe blocking rule is specific to basic narrowing and is particulary useful in conjunction with the rewriting rule. Finally, the unfolding rule allows for a variety of search strategies that reduce the number of don’t know alternatives that need to be explored

A Partial Evaluation Framework for Order-sorted Equational Programs modulo Axioms

[EN] Partial evaluation is a powerful and general program optimization technique with many successful applications. Existing PE schemes do not apply to expressive rule-based languages like Maude, CafeOBJ, OBJ, ASF+SDF, and ELAN, which support: 1) rich type structures with sorts, subsorts, and overloading; and 2) equational rewriting modulo various combinations of axioms such as associativity, commutativity, and identity. In this paper, we develop the new foundations needed and illustrate the key concepts by showing how they apply to partial evaluation of expressive programs written in Maude. Our partial evaluation scheme is based on an automatic unfolding algorithm that computes term variants and relies on high-performance order-sorted equational least general generalization and order-sorted equational homeomorphic embedding algorithms for ensuring termination. We show that our partial evaluation technique is sound and complete for convergent rewrite theories that may contain various combinations of associativity, commutativity, and/or identity axioms for different binary operators. We demonstrate the effectiveness of Maude's automatic partial evaluator, Victoria, on several examples where it shows significant speed-ups. (C) 2019 Elsevier Inc. All rights reserved.This work has been partially supported by the EU (FEDER) and the Spanish MCIU under grant RTI2018-094403-B-C32, by Generalitat Valenciana under grant PROMETEO/2019/098, and by NRL under contract number N00173-17-1-G002. Angel Cuenca-Ortega has been supported by the SENESCYT, Ecuador (scholarship program 2013).Alpuente Frasnedo, M.; Cuenca-Ortega, AE.; Escobar Román, S.; Meseguer, J. (2020). A Partial Evaluation Framework for Order-sorted Equational Programs modulo Axioms. Journal of Logical and Algebraic Methods in Programming. 110:1-36. https://doi.org/10.1016/j.jlamp.2019.100501S13611

On Unfolding Completeness for Rewriting Logic Theories

Many transformation systems for program optimization, program synthesis, and program specialization are based on fold/unfold transformations. In this paper, we investigate the semantic properties of a narrowing-based unfolding transformation that is useful to transform rewriting logic theories. We also present a transformation methodology that is able to determine whether an unfolding transformation step would cause incompleteness and avoid this problem by completing the transformed rewrite theory with suitable extra rules. More precisely, our methodology identifies the sources of incompleteness and derives a set of rules that are added to the transformed rewrite theory in order to preserve the semantics of the original theory.Alpuente Frasnedo, M.; Baggi, M.; Ballis, D.; Falaschi, M. (2010). On Unfolding Completeness for Rewriting Logic Theories. http://hdl.handle.net/10251/863

A term rewrite system framework for code carrying theory

Picci, P. (2011). A term rewrite system framework for code carrying theory. http://hdl.handle.net/10251/11146.Archivo delegad

Rule-based Methodologies for the Specification and Analysis of Complex Computing Systems

Desde los orígenes del hardware y el software hasta la época actual, la complejidad de los sistemas de cálculo ha supuesto un problema al cual informáticos, ingenieros y programadores han tenido que enfrentarse. Como resultado de este esfuerzo han surgido y madurado importantes áreas de investigación. En esta disertación abordamos algunas de las líneas de investigación actuales relacionada con el análisis y la verificación de sistemas de computación complejos utilizando métodos formales y lenguajes de dominio específico. En esta tesis nos centramos en los sistemas distribuidos, con un especial interés por los sistemas Web y los sistemas biológicos. La primera parte de la tesis está dedicada a aspectos de seguridad y técnicas relacionadas, concretamente la certificación del software. En primer lugar estudiamos sistemas de control de acceso a recursos y proponemos un lenguaje para especificar políticas de control de acceso que están fuertemente asociadas a bases de conocimiento y que proporcionan una descripción sensible a la semántica de los recursos o elementos a los que se accede. También hemos desarrollado un marco novedoso de trabajo para la Code-Carrying Theory, una metodología para la certificación del software cuyo objetivo es asegurar el envío seguro de código en un entorno distribuido. Nuestro marco de trabajo está basado en un sistema de transformación de teorías de reescritura mediante operaciones de plegado/desplegado. La segunda parte de esta tesis se concentra en el análisis y la verificación de sistemas Web y sistemas biológicos. Proponemos un lenguaje para el filtrado de información que permite la recuperación de informaciones en grandes almacenes de datos. Dicho lenguaje utiliza información semántica obtenida a partir de ontologías remotas para re nar el proceso de filtrado. También estudiamos métodos de validación para comprobar la consistencia de contenidos web con respecto a propiedades sintácticas y semánticas. Otra de nuestras contribuciones es la propuesta de un lenguaje que permite definir y comprobar automáticamente restricciones semánticas y sintácticas en el contenido estático de un sistema Web. Finalmente, también consideramos los sistemas biológicos y nos centramos en un formalismo basado en lógica de reescritura para el modelado y el análisis de aspectos cuantitativos de los procesos biológicos. Para evaluar la efectividad de todas las metodologías propuestas, hemos prestado especial atención al desarrollo de prototipos que se han implementado utilizando lenguajes basados en reglas.Baggi ., M. (2010). Rule-based Methodologies for the Specification and Analysis of Complex Computing Systems [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/8964Palanci

Rule-Based Software Verification and Correction

The increasing complexity of software systems has led to the development of sophisticated formal Methodologies for verifying and correcting data and programs. In general, establishing whether a program behaves correctly w.r.t. the original programmer s intention or checking the consistency and the correctness of a large set of data are not trivial tasks as witnessed by many case studies which occur in the literature. In this dissertation, we face two challenging problems of verification and correction. Specifically, verification and correction of declarative programs, and the verification and correction of Web sites (i.e. large collections of semistructured data). Firstly, we propose a general correction scheme for automatically correcting declarative, rule-based programs which exploits a combination of bottom-up as well as topdown inductive learning techniques. Our hybrid hodology is able to infer program corrections that are hard, or even impossible, to obtain with a simpler,automatic top-down or bottom-up learner. Moreover, the scheme will be also particularized to some well-known declarative programming paradigm: that is, the functional logic and the functional programming paradigm. Secondly, we formalize a framework for the automated verification of Web sites which can be used to specify integrity conditions for a given Web site, and then automatically check whether these conditions are fulfilled. We provide a rule-based, formal specification language which allows us to define syntactic as well as semantic properties of the Web site. Then, we formalize a verification technique which detects both incorrect/forbidden patterns as well as lack of information, that is, incomplete/missing Web pages. Useful information is gathered during the verification process which can be used to repair the Web site. So, after a verification phase, one can also infer semi-automatically some possible corrections in order to fix theWeb site. The methodology is based on a novel rewritBallis, D. (2005). Rule-Based Software Verification and Correction [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/194