Equational logic as a programming language
Equational logic as a programming language
NARROWER: a new algorithm for unification and its application to logic programming
Proc. of the first international conference on Rewriting techniques and applications
A class of confluent term rewriting systems and unification
Journal of Automated Reasoning
A general complete E-unification procedure
on Rewriting techniques and applications
Automated Theorem-Proving for Theories with Simplifiers Commutativity, and Associativity
Journal of the ACM (JACM)
An Efficient Unification Algorithm
ACM Transactions on Programming Languages and Systems (TOPLAS)
Equational logic programming: an extension to equational programming
POPL '86 Proceedings of the 13th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
Incremental Construction of Unification Algorithms in Equational Theories
Proceedings of the 10th Colloquium on Automata, Languages and Programming
Improving Basic Narrowing Techniques
RTA '87 Proceedings of the 2nd International Conference on Rewriting Techniques and Applications
Canonical Forms and Unification
Proceedings of the 5th Conference on Automated Deduction
Proceedings of the 7th International Conference on Automated Deduction
POPL '94 Proceedings of the 21st ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Functional and constraint logic programming
Constraints in computational logics
Leftmost outside-in narrowing calculi
Journal of Functional Programming
A general framework for lazy functional logic programming with algebraic polymorphic types
Theory and Practice of Logic Programming
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Narrowing has been used as a mechanism for reasoning about equations and evaluatingequational logic programs, where enumeration of all narrowing derivations is often necessary in order to generate complete sets of solutions. In this paper, a special type of narrowing derivations, called outer narrowing derivations, is examined for the class of constructor-based term rewriting systems. It is shown that every narrowing derivation in this class is subsumed by an outer narrowing derivation. This result is applied to a matching problem in equational theories, i.e., whether an arbitrary term is E-matchable to a term composed of constructors and disjoint variables. It is shown that outer narrowing derivations generate complete and minimal sets of E-matchers. An E-matching procedure is presented which enumerates all and only outer narrowing derivations for the E-matching problem considered in this paper.