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. Springer. 54-71. doi:10.1007/978-3-319-14125-1_4S5471Albert, E., Vidal, G.: The Narrowing-Driven Approach to Functional Logic Program Specialization. New Generation Computing 20(1), 3–26 (2002)Alpuente, M., Falaschi, M., Vidal, G.: Partial Evaluation of Functional Logic Programs. ACM Transactions on Programming Languages and Systems 20(4), 768–844 (1998)Alpuente, M., Falaschi, M., Vidal, G.: Compositional Analysis for Equational Horn Programs. In: Rodríguez-Artalejo, M., Levi, G. (eds.) ALP 1994. LNCS, vol. 850, pp. 77–94. Springer, Heidelberg (1994)Antoy, S., Ariola, Z.: Narrowing the Narrowing Space. In: Hartel, P.H., Kuchen, H. (eds.) PLILP 1997. LNCS, vol. 1292, pp. 1–15. Springer, Heidelberg (1997)Arts, T., Giesl, J.: Termination of term rewriting using dependency pairs. Theoretical Computer Science 236(1–2), 133–178 (2000)Arts, T., Zantema, H.: Termination of Logic Programs Using Semantic Unification. In: Proietti, M. (ed.) LOPSTR 1995. LNCS, vol. 1048, pp. 219–233. Springer, Heidelberg (1996)Baader, F., Nipkow, T.: Term Rewriting and All That. Cambridge University Press (1998)Bae, K., Escobar, S., Meseguer, J.: Abstract Logical Model Checking of Infinite-State Systems Using Narrowing. In: Proceedings of the 24th International Conference on Rewriting Techniques and Applications. LIPIcs, vol. 21, pp. 81–96. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2013)De Schreye, D., Glück, R., Jørgensen, J., Leuschel, M., Martens, B., Sørensen, M.: Conjunctive partial deduction: foundations, control, algorihtms, and experiments. Journal of Logic Programming 41(2&3), 231–277 (1999)Escobar, S., Meadows, C., Meseguer, J.: A rewriting-based inference system for the NRL Protocol Analyzer and its meta-logical properties. Theoretical Computer Science 367(1–2), 162–202 (2006)Escobar, S., Meseguer, J.: Symbolic Model Checking of Infinite-State Systems Using Narrowing. In: Baader, F. (ed.) RTA 2007. LNCS, vol. 4533, pp. 153–168. 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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

Narrowing-based Optimization of Rewrite Theories

Partial evaluation has been never investigated in the context of rewrite theories that allow concurrent systems to be specified by means of rules, with an underlying equational theory being used to model system states as terms of an algebraic data type. In this paper, we develop a symbolic, narrowing-driven partial evaluation framework for rewrite theories that supports sorts, subsort overloading, rules, equations, and algebraic axioms. Our partial evaluation scheme allows a rewrite theory to be optimized by specializing the plugged equational theory with respect to the rewrite rules that define the system dynamics. This can be particularly useful for automatically optimizing rewrite theories that contain overly general equational theories which perform unnecessary computations involving matching modulo axioms, because some of the axioms may be blown away after the transformation. The specialization is done by using appropriate unfolding and abstraction algorithms that achieve significant specialization while ensuring the correctness and termination of the specialization. Our preliminary results demonstrate that our transformation can speed up a number of benchmarks that are difficult to optimize otherwise.This work has been partially supported by the EU (FEDER) and the Spanish MCIU under grant RTI2018094403-B-C32,andbyGeneralitatValencianaundergrantPROMETEO/2019/098. JuliaSapiñahasbeensupported by the Generalitat Valenciana APOSTD/2019/127 grantAlpuente Frasnedo, M.; Ballis, D.; Escobar Román, S.; Sapiña Sanchis, J. (2020). Narrowing-based Optimization of Rewrite Theories. Universitat Politècnica de València. http://hdl.handle.net/10251/14557

Normalisierung und partielle Auswertung von funktional-logischen Programmen

This thesis deals with the development of a normalization scheme and a partial evaluator for the functional logic programming language Curry. The functional logic programming paradigm combines the two most important fields of declarative programming, namely functional and logic programming. While functional languages provide concepts such as algebraic data types, higher-order functions or demanddriven evaluation, logic languages usually support a non-deterministic evaluation and a built-in search for results. Functional logic languages finally combine these two paradigms in an integrated way, hence providing multiple syntactic constructs and concepts to facilitate the concise notation of high-level programs. However, both the variety of syntactic constructs and the high degree of abstraction complicate the translation into efficient target programs. To reduce the syntactic complexity of functional logic languages, a typical compilation scheme incorporates a normalization phase to subsequently replace complex constructs by simpler ones until a minimal language subset is reached. While the individual transformations are usually simple, they also have to be correctly combined to make the syntactic constructs interact in the intended way. The efficiency of normalized programs can then be improved by means of different optimization techniques. A very powerful optimization technique is the partial evaluation of programs. Partial evaluation basically anticipates the execution of certain program fragments at compile time and computes a semantically equivalent program, which is usually more efficient at run time. Since partial evaluation is a fully automatic optimization technique, it can also be incorporated into the normal compilation scheme of programs. Nevertheless, this also requires termination of the optimization process, which establishes one of the main challenges for partial evaluation besides semantic equivalence. In this work we consider the language Curry as a representative of the functional logic programming paradigm. We develop a formal representation of the normalization process of Curry programs into a kernel language, while respecting the interference of different language constructs. We then define the dynamic semantics of this kernel language, before we subsequently develop a partial evaluation scheme and show its correctness and termination. Due to the previously described normalization process, this scheme is then directly applicable to arbitrary Curry programs. Furthermore, the implementation of a practical partial evaluator is sketched based on the partial evaluation scheme, and its applicability and usefulness is documented by a variety of typical partial evaluation examples

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

Towards Erlang Verification by Term Rewriting

The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-319-14125-1_7This paper presents a transformational approach to the verification of Erlang programs. We define a stepwise transformation from (first-order) Erlang programs to (non-deterministic) term rewrite systems that compute an overapproximation of the original Erlang program. In this way, existing techniques for term rewriting become available. Furthermore, one can use narrowing as a symbolic execution extension of rewriting in order to design a verification technique. We illustrate our approach with some examples, including a deadlock analysis of a simple Erlang program.Vidal Oriola, GF. (2013). Towards Erlang Verification by Term Rewriting. En Logic-Based Program Synthesis and Transformation. Springer. 109-126. doi:10.1007/978-3-319-14125-1_7S109126Albert, E., Arenas, P., Gómez-Zamalloa, M.: Symbolic Execution of Concurrent Objects in CLP. In: Russo, C., Zhou, N.-F. (eds.) PADL 2012. 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