Theoretical Computer Science
A completeness result for E-unification algorithms based on conditional narrowing
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Theoretical Computer Science - Second Conference on Rewriting Techniques and Applications, Bordeaux, May 1987
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Foundations of Equational Logic Programming
Handbook of theoretical computer science (vol. B)
A proof theory for general unification
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Handbook of logic in computer science (vol. 2)
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TAPSOFT '95 Selected papers from the 6th international joint conference on Theory and practice of software development
Term rewriting and all that
A deterministic lazy narrowing calculus
Journal of Symbolic Computation
Journal of the ACM (JACM)
Solving Higher-Order Equations: From Logic to Programming
Solving Higher-Order Equations: From Logic to Programming
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ESOP '94 Proceedings of the 5th European Symposium on Programming: Programming Languages and Systems
On Reducing the Search Space of Higher-Order Lazy Narrowing
FLOPS '99 Proceedings of the 4th Fuji International Symposium on Functional and Logic Programming
Level-Confluence of Conditional Rewrite Systems with Extra Variables in Right-Hand Sides
RTA '95 Proceedings of the 6th International Conference on Rewriting Techniques and Applications
Canonical Forms and Unification
Proceedings of the 5th Conference on Automated Deduction
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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.