Abstract
This paper is concerned with the lazy conditional narrowing calculus LCNC. In an earlier paper we proved that this calculus is complete with respect to normalizable solutions for the class of confluent but not necessarily terminating conditional rewrite systems without so-called extra variables in the conditional parts of the rewrite rules. Unfortunately, the proof does not provide any useful complete selection function, hence in implementations we need to backtrack over the choice of equations in goals in order to guarantee that all solutions are enumerated. This is in contrast to the unconditional case where completeness with respect to the leftmost selection function is known. In this paper we close the gap by proving the completeness of lcnc with respect to the leftmost selection strategy for the above-mentioned class of conditional rewrite systems.
Acknowledgements
Taro Suzuki is partially supported by the Grant-in-Aid for Encouragement of Young Scientist 11780204. Aart Middeldorp is partially supported by the Grantin-Aids for Scientific Research B 12480066 and C(2) 11680338 of the Ministry of Education, Science, Sports and Culture of Japan.
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Suzuki, T., Middeldorp, A. (2001). A Complete Selection Function for Lazy Conditional Narrowing. In: Kuchen, H., Ueda, K. (eds) Functional and Logic Programming. FLOPS 2001. Lecture Notes in Computer Science, vol 2024. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44716-4_13
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