A Deterministic Lazy Narrowing Calculus

Middeldorp, Aart; Okui, Satoshi

doi:10.1006/jsco.1997.0197

Cited by 21 publications

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References 17 publications

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“…In a later paper [MO95], more results on removing non-determinism from the LNC calculus have been obtained, assuming the left-most selection strategy. The previous result on eager variable elimination for left-most LNC has been extended to the class of left-linear confluent TRSs.…”

Section: Theorem 3 Completeness Of Clnc Assume An Initial Goal G Fomentioning

confidence: 98%

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Functional and Constraint Logic Programming

Rodríguez-Artalejo

2001

Constraints in Computational Logics

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Dpto. Sistemas Informáticos y Programación, UCM, Madrid IntroductionStarting at a seminal paper published by J. Jaffar and J.L. Lassez in 1987 [JL87], Constraint Logic Programming (CLP) has developed as a powerful programming paradigm which supports a clean combination of logic (in the form of Horn clauses) and domain-specific methods for constraint satisfaction, simplification and optimization. The well established mathematical foundations of logic programming [Llo87, Apt90] have been succesfully extended to CLP [JMMS96]. Simultaneously, practical applications of CLP have arisen in many fields. Good introductions to the theory, implementation issues and programming applications of CLP languages can be found in [JM94,MS98]. On the other hand, the combination of logic programming with other declarative programming paradigms (especially functional programming) has been widely investigated during the last decade, leading to useful insights for the design of more expressive declarative languages. The first attempt to combine functional and logic languages was done by J.A. Robinson and E.E. Sibert when proposing the language LOGLISP [RS82]. Some other early proposals for the design of functional + logic languages are described in [De86]. A more recent survey of the operational principles and implementation techniques used for the integration of functions into logic programming can be found in [Han94b].Declarative programming, in the wide sense, should provide a logical semantics for programs. Nevertheless, many of the early proposals for the integration of functional and logic programming had no clear logical basis. Among the logically well-founded approaches, most proposals (as e.g. [JLM84, GM87, Höl89]) have suggested to use equational logic. This allows to represent programs as sets of oriented equations, also known as rewrite rules, whose computational use can rely on a well established theory [DJ90,Klo92,BN98]. Goals (also called queries) for a functional logic program can be represented as systems of equations, and narrowing (a natural combination of rewriting and unification, originally proposed as a theorem proving tool [Sla74, Lan75, Fay79, Hul80]) can be used as a goal solving mechanism.

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Section: Theorem 3 Completeness Of Clnc Assume An Initial Goal G Fomentioning

confidence: 98%

“…The left-most outside-in narrowing calculus OINC from [IN97] is quite similar to LNC and it has a variant S-OINC tailored to strict equality, which is close to LNC d ; see [MO95] for a more detailed comparison. A conditional extension LCNC of LNC has been presented in [HM97].…”

Section: Theorem 3 Completeness Of Clnc Assume An Initial Goal G Fomentioning

confidence: 98%

Functional and Constraint Logic Programming

Rodríguez-Artalejo

2001

Constraints in Computational Logics

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“…For instance, flattening is introduced in [23] (where it is called unfolding); subsumption is used in many different contexts (e.g., [4,1]); (constructor) decomposition rules are used in different narrowing calculi (see, e.g., [18]); finally, splitting is considered when proving compositionality results (e.g., [3]) and in the partial evaluation of logic programs [9]. The relevance of the notion of extended narrowing tree is that, thanks to the use of the rules of flattening, constructor decomposition, 7 and splitting, one can always produce a tree with finitely many non-variant nodes.…”

Section: Construction Of Finite Narrowing Treesmentioning

confidence: 99%

A Finite Representation of the Narrowing Space

Nishida

Vidal

2014

Logic-Based Program Synthesis and Transformation

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Abstract. Narrowing 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 graph that still represents all the narrowing derivations. Furthermore, we introduce a novel, compact equational representation of the (possibly infinite) answers computed by narrowing for a given initial term. Both the finite graphs and the equational representation of the computed answers might be useful in a number of areas, like program comprehension, static analysis, program transformation, etc.

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“…En definitiva se intenta liberar al programador de describir detalladamente la secuencia de acciones que debe realizar la máquina para obtener el resultado buscado, como es habitual en los tradicionales lenguajes imperativos, en los cuales el programador no sólo tiene que especificar las restricciones, sino que además tiene que definir cómo se resolverán esas relaciones. varias propuestas, pero uno de los mecanismos más estudiados y extendidos es la "reescritura con unificación" o, más comúnmente, narrowing (estrechamiento) [88,138].…”

Section: Programación Declarativaunclassified

Declarative Constraint Programming

Fernández¹

2006

Int. Artif.

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ResumenRecientemente, esta revista ha publicado una excelente monografía, [65], dedicada a los problemas de satisfacción con restricciones. La monografía cubre muchos de los aspectos relacionados con estos problemas pero obvia unárea tradicionalmente muy importante en la comunidad de las restricciones como es la integración de restricciones en los lenguajes de programación declarativos (especialmente los lógicos).Este artículo describe el estado-del-arte de la programación declarativa con restricciones (PDC) con especiaĺ enfasis en la integración de restricciones en los lenguajes de programación lógicos. El artículo está dirigido tanto a personas con conocimientos de PDC como a aquellos interesados en conocerla, y cubre sus orígenes históricos, los fundamentos teóricos y las instancias más populares dependientes del dominio de computación.Palabras clave: Satisfacción de Restricciones, Programación Lógica, Programación Funcional, Resolutor. IntroducciónRecientemente, esta revista ha publicado una estupenda monografía [65] enfocada sobre los problemas de satisfacción con restricciones (CSP, Constraint Satisfaction Problem) y en la cual se abordan las técnicas clásicas empleadas para su resolución y, más particularmente, otras técnicas usadas sobreáreas específicas de aplicación (tales como la diagnosis, las bases de datos o la recuperación de información). La monografía cubre muchos de los aspectos relacionados con los CSPs pero obvia unárea muy importante como es la integración de restricciones en los lenguajes declarativos (especialmente los lógicos). En realidad, la programación lógica con restricciones (CLP, Constraint Logic Programming) [110,179] es uno de los campos de investigación más activos en la comunidad de las restricciones puesto que está directamente relacionado con el modelado (a alto nivel) de soluciones a los problemas de satisfacción con restricciones; más aún, como ya fue apuntado en [54][capítulo 15], uno no puede (ni debe) asumir que todas las restricciones estarán disponibles al comienzo del proceso de búsqueda de las soluciones y el usuario podría querer construir el CSP a resolver de forma incremental y "representar las restricciones a través de fórmu-las pertenecientes a un cierto lenguaje de programación en vez de representaréstas mediante conjuntos de tuplas de valores". Este aspecto no fue considerado en [65], yésa es precisamente la razón que ha generado este artículo.Este artículo describe el estado-del-arte de la programación declarativa con restricciones, con especialénfasis en la programación lógica con restricciones ya que la naturaleza relacional de las restricciones hace que los lenguajes que guardan algún componente lógico sean más adecuados para la integración de las mismas.

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A Deterministic Lazy Narrowing Calculus

Cited by 21 publications

References 17 publications

Functional and Constraint Logic Programming

Functional and Constraint Logic Programming

A Finite Representation of the Narrowing Space

Declarative Constraint Programming

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