Lazy narrowing: Strong completeness and eager variable elimination

Middeldorp, Aart; Okui, Satoshi; Ida, Tetsuo

doi:10.1016/0304-3975(96)00071-0

Cited by 40 publications

(21 citation statements)

References 9 publications

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“…Moreover, for the case of orthogonal TRSs, [MOI96] proves the completeness of an outside-in narrowing strategy which extends the outer narrowing strategy from [You89]. Using this result, [MOI96] also proves the following: variable elimination for solved equations X ≈ t with X ∈ var(t) that are descendants of a parameter passing equation, can be performed eagerly without loss of completeness for left-most LNC, assuming an orthogonal TRS. This seems related to the CLNC rules (OB) and (IB), although CLNC works only with constructor-based rewrite rules.…”

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

confidence: 76%

“…A distinction is made between ordinary equations and parameter passing equations, somehow corresponding to the unsolved and delayed part of CLNC goals, respectively. However, [MOI96] works with inconditional TRSs and considers completeness w.r.t. normalized solutions and equational semantics.…”

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

confidence: 99%

“…[Höl89,Sny91]. In particular, [MOI96] investigates a lazy narrowing calculus LNC bearing some analogies to CLNC. Goals in LNC are systems of equations.…”

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

confidence: 99%

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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: 76%

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

confidence: 99%

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Functional and Constraint Logic Programming

Rodríguez-Artalejo

2001

Constraints in Computational Logics

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“…The non-determinism occurs when more than one rule can beapplied to a term, or when rules can beapplied in di erent places in a term. There are two kinds of non-determinism: don't care, and don't know MOI95].…”

Section: Equational Languages and Non-determinismmentioning

confidence: 99%

A model for I/O in equational languages with don't care non-determinism

Walters

Kamperman

1996

Recent Trends in Data Type Specification

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Existing models for I/O in side-e ect free languages focus on functional languages, which are usually based on a largely deterministic reduction strategy, allowing for a strict sequentialization of I/O operations. In concurrent logic programming languages a model is used which allows for don't care non-determinism the sequentialization of I/O is extensional rather than intensional. We apply this model to equational languages, which are closely related to functional languages, but exhibit don't care non-determinism. The semantics are formulated as constrained narrowing, a relation that contains the rewrite relation, and is contained in the narrowing relation.We p resent constrained narrowing and some of its properties a constructive method to transform conventional term rewriting systems to constrained narrowing systems and a discussion on requirements for a n implementation.

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“…Typical examples of narrowing calculi are LNC [15], LNC d [14], LCNC [8], LCNC [16], and LCNC d [13]. Higher-order versions of narrowing calculi are also known, e,g., LN [17], HOLN [11], and LN ff [12].…”

Section: Introductionmentioning

confidence: 99%

A rewrite-based computational model for functional logic programming

Marin¹,

Kutsia

Dundua³

EPiC Series in Computing

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Functional logic programming is an extension of the functional programming style with two important capabilities: to define nondeterministic operations with overlapping rules, and to use logic variables in both defining rules and expressions to evaluate. A suitable model for functional logic programs are conditional constructor-based term rewrite systems (CB-CTRSs), which can be transformed into an equivalent program in a simpler class of rewrite systems (the core language) where computations can be performed more efficiently.Recently, Antoy and Hanus proposed a translation of CB-CTRSs into an equivalent class of programs where computation can be performed efficiently by mere rewriting. Their computational model has the limitation of computing only ground answer substitutions for equations with strict semantics interpreted as joinability to a value. We propose two adjustments of their computational models, which are capable to compute non-ground answers.

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Lazy narrowing: Strong completeness and eager variable elimination

Cited by 40 publications

References 9 publications

Functional and Constraint Logic Programming

Functional and Constraint Logic Programming

A model for I/O in equational languages with don't care non-determinism

A rewrite-based computational model for functional logic programming

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