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Lazy narrowing: Strong completeness and eager variable elimination

Aart Middeldorp, Satoshi Okui, Tetsuo Ida
1996 Theoretical Computer Science  
. $[19, 18] $ for the lazy narrowing calculus $\mathrm{L}\mathrm{N}\mathrm{C}$ .  ...  Because narrowing is a rather complicated operation, several authors studied calculi in which narrowing is replaced by more simple inference rules.  ...  version of the eager variable elimination strategy is complete for left-linear confluent TRSs.  ... 
doi:10.1016/0304-3975(96)00071-0 fatcat:csqbkmjo65eitdlfj7euhyn2gq

Lazy narrowing: Strong completeness and eager variable elimination (extended abstract) [chapter]

Satoshi Okui, Aart Middeldorp, Tetsuo Ida
1995 Lecture Notes in Computer Science  
\u prove completeness of the calculus and we establish an interesting connection between its strong completeness and the completeness of basic narrowing.  ...  We also address the eager variable elimination problem.  ...  We address the eager variable elimination problem for non-terminating TRSs. We prove completeness of a slightly restricted version of eager variable elimination in the case of orthogonal TRSs.  ... 
doi:10.1007/3-540-59293-8_209 fatcat:mvlwpy4ufnf6dn3ezolyxrqf6e

A Deterministic Lazy Narrowing Calculus

Aart Middeldorp, Satoshi Okui
1998 Journal of symbolic computation  
In this paper we study the non-determinism between the inference rules of the lazy narrowing calculus lnc (Middeldorp et al., 1996) .  ...  We show that all non-determinism can be removed without losing the important completeness property by restricting the underlying term rewriting systems to left-linear confluent constructor systems and  ...  and Culture of Japan, and by the Okawa Foundation for Information and Telecommunications.  ... 
doi:10.1006/jsco.1997.0197 fatcat:slg36be7azc2di5uzbc56ekhme

New completeness results for lazy conditional narrowing

Mircea Marin, Aart Middeldorp
2004 Proceedings of the 6th ACM SIGPLAN international conference on Principles and practice of declarative programming - PPDP '04  
We show the completeness of the lazy conditional narrowing calculus (LCNC) with leftmost selection for the class of deterministic conditional rewrite systems (CTRSs).  ...  Deterministic CTRSs permit extra variables in the right-hand sides and conditions of their rewrite rules.  ...  Variable Elimination Eager variable elimination is the problem of identifying sufficient criteria which guarantee that the eager application of inference rule [v] preserves completeness.  ... 
doi:10.1145/1013963.1013979 dblp:conf/ppdp/MarinM04 fatcat:njruej4qqra4jbzsqtk6lhthz4

Lazy narrowing with parametric order sorted types [chapter]

J. M. Almendros-Jiménez, A. Gil-Luezas
1997 Lecture Notes in Computer Science  
The aim of the present work is to provide the previous one with the incorporation of a typed lazy narrowing calculus for goal solving which combines lazy uni cation, sharing and type checking at run-time  ...  Furthermore, we state soundness and completeness results of the goal solving procedure w.r.t. the typed rewriting calculi presented in 2] which were proved to be also sound and complete w.r.t. the notion  ...  X = c( X); X : X ; S X=c( X)]2X 1 e 1 ; : : :; X n e n ; c( X) : X ; X 1 : X1 ; : : :; X n : Xn ; N X=c( X)] (EVE) Eager Variable Elimination S2e X; X : X ; N !  ... 
doi:10.1007/bfb0027009 fatcat:qlrhgde2u5dfnmrkv723oo6xxy

Lazy unification with simplification [chapter]

Michael Hanus
1994 Lecture Notes in Computer Science  
We show soundness and completeness of our method for equational theories represented by ground confluent and terminating rewrite systems which is a reasonable class w.r.t, functional logic programming.  ...  This paper presents an improvement of the proposed lazy unification methods by incorporating simplification into the unification process.  ...  The research described in this paper was supported in part by the German Ministry for Research and Technology (BMFT) under grant ITS 9103 and by the ESPRIT Basic Research Working Group 6028 (Construction  ... 
doi:10.1007/3-540-57880-3_18 fatcat:dqkwgzzpo5e57ntrs3rgyxapei

Specialization of lazy functional logic programs

M. Alpuente, M. Falaschi, P. Julián, G. Vidal
1997 Proceedings of the 1997 ACM SIGPLAN symposium on Partial evaluation and semantics-based program manipulation - PEPM '97  
However, the results inherited by [2, 3] mainly regard the termination of the PE method, while the (strong) soundness and completeness results must be restated for the lazy strategy.  ...  This phase is essential also for other non-lazy narrowing strategies, like innermost narrowing, and our method can be easily extended to these strategies.  ...  We have used the simplification and eager variable elimination [38] rules in order to get better specialization.  ... 
doi:10.1145/258993.259015 dblp:conf/pepm/AlpuenteFJV97 fatcat:2yypd4tzyffdvehqaz223gcxze

Specialization of lazy functional logic programs

M. Alpuente, M. Falaschi, P. Julián, G. Vidal
1997 SIGPLAN notices  
However, the results inherited by [2, 3] mainly regard the termination of the PE method, while the (strong) soundness and completeness results must be restated for the lazy strategy.  ...  This phase is essential also for other non-lazy narrowing strategies, like innermost narrowing, and our method can be easily extended to these strategies.  ...  We have used the simplification and eager variable elimination [38] rules in order to get better specialization.  ... 
doi:10.1145/258994.259015 fatcat:mpf7yjkd3zarfiz4muxsbdslem

Rules + strategies for transforming lazy functional logic programs

Marı́a Alpuente, Moreno Falaschi, Ginés Moreno, Germán Vidal
2004 Theoretical Computer Science  
This work introduces a transformation methodology for functional logic programs based on needed narrowing, the optimal and complete operational principle for modern declarative languages which integrate  ...  We provide correctness results for the transformation system w.r.t. the set of computed values and answer substitutions and show that the prominent properties of needed narrowing-namely, the optimality  ...  We thank the anonymous referees for their accurate and useful remarks and suggestions, which helped to improve our paper.  ... 
doi:10.1016/j.tcs.2003.10.033 fatcat:2kq2qdesszeyxbvodwzrphouhe

Extending constructive negation for partial functions in lazy functional-logic languages [chapter]

Juan José Moreno-Navarro
1996 Lecture Notes in Computer Science  
In this paper the mechanism of Default Rules for narrowingbased languages proposed in 24] is adapted to lazy narrowing. Every partial de nition of a function can be completed with a default rule.  ...  Lazy narrowing semantics are extended with the technique of constructive negation 4, 5, 27].  ...  (Idea): The proof proceeds by using the T operator, combining the completeness of lazy narrowing and the completeness proof of 27].  ... 
doi:10.1007/3-540-60983-0_15 fatcat:66f3bhxubzdhhnndp6ypukjfyu

Conditional narrowing without conditions

Sergio Antoy, Bernd Brassel, Michael Hanus
2003 Proceedings of the 5th ACM SIGPLAN international conference on Principles and practice of declaritive programming - PPDP '03  
This is achieved by a transformation of conditional term rewriting systems (CTRS) into unconditional ones which is sound and complete w.r.t. the semantics of the original CTRS.  ...  Our notion of weakly orthogonal conditional rewrite system extends a notion of Bergstra and Klop and covers a large part of programs de£ned by conditional equations.  ...  Clearly, a termination requirement is too strong for practical programming since it inhibits the formulation of some programs (e.g., interpreters). 1 Needed narrowing [5] is a sound, complete, and  ... 
doi:10.1145/888251.888255 dblp:conf/ppdp/AntoyBH03 fatcat:n3734tg5rjeh5cq7pnfnjo4h6a

Specialization of Functional Logic Programs Based on Needed Narrowing [article]

Maria Alpuente, Michael Hanus, Salvador Lucas, German Vidal
2004 arXiv   pre-print
Needed narrowing is an optimal evaluation strategy which constitutes the basis of modern (narrowing-based) lazy functional logic languages.  ...  We provide correctness results for partial evaluation based on needed narrowing and show that the nice properties of this strategy are essential for the specialization process.  ...  correctness is only proved for an eager narrowing strategy.  ... 
arXiv:cs/0403011v1 fatcat:xrdmm5652fdlzfstopsv4s2f5y

Narrowing-driven partial evaluation of functional logic programs [chapter]

M. Alpuente, M. Falaschi, G. Vidal
1996 Lecture Notes in Computer Science  
Languages that integrate functional and logic programming with a complete operational semantics are based on narrowing, a unification-based goal-solving mechanism which subsumes the reduction principle  ...  We study the semantic properties of the transformation and the conditions under which the technique terminates, is sound and complete, and is also generally applicable to a wide class of programs.  ...  We have shown how a core PE procedure whose behaviour does not depend on the eager or lazy nature of the narrower can be defined.  ... 
doi:10.1007/3-540-61055-3_28 fatcat:kc32ey7d55dj7ajdl2y5rwah44

A Narrowing-based Instantiation Rule for Rewriting-based Fold/Unfold Transformations

Ginés Moreno
2003 Electronical Notes in Theoretical Computer Science  
More exactly, we propose a complete fold/unfold based transformation system for optimizing lazy functional programs.  ...  As a consequence, our correct/complete technique avoids redundant rules and preserves the natural structure of programs.  ...  I am also grateful to the anonymous referees for their accurate and useful remarks and suggestions, which helped to improve this paper.  ... 
doi:10.1016/s1571-0661(04)80698-4 fatcat:rp2pffq6ercvjnbcdwtpuwym2y

Rewriting and narrowing for constructor systems with call-time choice semantics [article]

Francisco J. López-Fraguas, Enrique Martin-Martin, Juan Rodríguez-Hortalá, Jaime Sánchez-Hernández
2012 arXiv   pre-print
After that, we provide a notion of let-narrowing which is adequate for call-time choice as proved by soundness and completeness results of let-narrowing with respect to let-rewriting.  ...  Moreover, we relate those let-rewriting and let-narrowing relations (and hence CRWL) with ordinary term rewriting and narrowing (..) To appear in Theory and Practice of Logic Programming (TPLP).  ...  This implicitly applied strategy can be seen as a translation to let-narrowing of lazy narrowing (Moreno-Navarro and Rodríguez-Artalejo 1992; Alpuente et al. 2003) .  ... 
arXiv:1209.2617v2 fatcat:g7irofitz5f2dh36sqtdl65lly
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