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A Deterministic Lazy Narrowing Calculus
 Journal of Symbolic Computation
, 1998
"... In this paper we study the nondeterminism between the inference rules of the lazy narrowing calculus lnc (Middeldorp et al., 1996). We show that all nondeterminism can be removed without losing the important completeness property by restricting the underlying term rewriting systems to leftlinear ..."
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Cited by 23 (4 self)
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In this paper we study the nondeterminism between the inference rules of the lazy narrowing calculus lnc (Middeldorp et al., 1996). We show that all nondeterminism can be removed without losing the important completeness property by restricting the underlying term rewriting systems to leftlinear con uent constructor systems and interpreting equality as strict equality. For the subclass of orthogonal constructor systems the resulting narrowing calculus is shown to have the nice property that solutions computed by di erent derivations starting from the same goal are incomparable. 1.
On Reducing the Search Space of HigherOrder Lazy Narrowing
, 1999
"... Higherorder lazy narrowing is a general method for solving Eunification problems in theories presented as sets of rewrite rules. In this paper we study the possibility to improve the search for normalized solutions of a higherorder lazy narrowing calculus LN. We introduce a new calculus, LNff, ob ..."
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Cited by 9 (5 self)
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Higherorder lazy narrowing is a general method for solving Eunification problems in theories presented as sets of rewrite rules. In this paper we study the possibility to improve the search for normalized solutions of a higherorder lazy narrowing calculus LN. We introduce a new calculus, LNff, obtained by extending LN and define an equation selection strategy Sn such that LNff with strategy Sn is complete. The main advantages of using LNff with strategy Sn instead of LN include the possibility to restrict the application of outermost narrowing at variable position, and the computation of more specific solutions because of additional inference rules for solving exex equations. We also show that for orthogonal pattern rewrite systems we can adopt an eager variable elimination strategy that makes the calculus LNff with strategy Sn even more deterministic.
HigherOrder Lazy Narrowing Calculus: A Computation Model for a Higherorder Functional Logic Language
 In Proceedings of Sixth International Joint Conference, ALP '97  HOA '97, LNCS 1298
, 1997
"... this paper we present a computation model for a higherorder functional and logic programming. Although investigations of computation models for higherorder functional logic languages are under way[13, 9, 8, 20, 22], implemented functional logic languages like KLEAF[6] and Babel[18] among others, a ..."
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Cited by 8 (4 self)
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this paper we present a computation model for a higherorder functional and logic programming. Although investigations of computation models for higherorder functional logic languages are under way[13, 9, 8, 20, 22], implemented functional logic languages like KLEAF[6] and Babel[18] among others, are all based on firstorder models of computation. Firstorder narrowing has been used as basic computation mechanism. The lack of higherorderness is exemplified by the following prototypical program
Standardization and Evaluation in Combinatory Reduction Systems
, 2000
"... A rewrite system has standardization i for any rewrite sequence there is an equivalent one which contracts the redexes in a standard order. Standardization is extremely useful for finding normalizing strategies and proving that a rewrite system for a programming language is sound with respect to the ..."
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Cited by 4 (1 self)
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A rewrite system has standardization i for any rewrite sequence there is an equivalent one which contracts the redexes in a standard order. Standardization is extremely useful for finding normalizing strategies and proving that a rewrite system for a programming language is sound with respect to the language's operational semantics. Although for some rewrite systems the standardorder can be simple, e.g., lefttoright or outermostfirst, many systems need a more delicate order. There are abstract notions of standard order which always apply, but proofs (often quite dicult) are required that the rewrite system satis es a number of axioms and not much guidance is provided for finding a concrete order that satisfies the abstract definition. This paper gives a framework based on combinatory reduction systems (CRS's) which is general enough to handle many programming languages. If the CRS is orthogonal and fully extended and a good redex ordering can be found, then a standard order is obtain...
Higherorder Lazy Narrowing Calculus: a Solver for HigherOrder Equations
 in Proc. 8th Intâ€™l Conf. Computer Aided Systems (EuroCAST 2001), LNCS
, 2001
"... This paper introduces a higherorder lazy narrowing calculus (HOLN for short) that solves higherorder equations over the domain of simply typed #terms. HOLN is an extension and refinement of Prehofer's higherorder narrowing calculus LN using the techniques developed in the refinement of a fir ..."
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Cited by 1 (0 self)
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This paper introduces a higherorder lazy narrowing calculus (HOLN for short) that solves higherorder equations over the domain of simply typed #terms. HOLN is an extension and refinement of Prehofer's higherorder narrowing calculus LN using the techniques developed in the refinement of a firstorder lazy narrowing calculus LNC.
Two Applications of Standardization and Evaluation in Combinatory Reduction Systems
, 2000
"... We present two worked applications of a general framework that can be used to support reasoning about the operational equality relation defined by a programming language semantics. The framework, based on Combinatory Reduction Systems, facilitates the proof of standardization theorems for programmin ..."
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Cited by 1 (1 self)
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We present two worked applications of a general framework that can be used to support reasoning about the operational equality relation defined by a programming language semantics. The framework, based on Combinatory Reduction Systems, facilitates the proof of standardization theorems for programming calculi. The importance of standardization theorems to programming language semantics was shown by Plotkin [Plo75]: standardization together with confluence guarantee that two terms equated in the calculus are semantically equal. We apply the framework to the λ_νcalculus and to an untyped version of the λ^CILcalculus. The latter is a basis for an intermediate language being used in a compiler.