NARROWER: a new algorithm for unification and its application to logic programming
Proc. of the first international conference on Rewriting techniques and applications
Logic programming: functions, relations, and equations
Logic programming: functions, relations, and equations
Logic programming with equations
Journal of Logic Programming
Unification in combinations of collapse-free regular theories
Journal of Symbolic Computation
Computable values can be classical
POPL '87 Proceedings of the 14th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
Simplifying conditional term rewriting systems: Unification, termination and confluence
Journal of Symbolic Computation
Unification in a combination of arbitrary disjoint equational theories
Journal of Symbolic Computation
Complete sets of transformations for general E-unification
Theoretical Computer Science - Second Conference on Rewriting Techniques and Applications, Bordeaux, May 1987
Foundations of Equational Logic Programming
Foundations of Equational Logic Programming
CADE-10 Proceedings of the tenth international conference on Automated deduction
Unification modulo an equality theory for equational logic programming
Journal of Computer and System Sciences
Kernel-LEAF: a logic plus functional language
Journal of Computer and System Sciences
Rewriting, and equational unification: the higher-order cases (extended abstract)
RTA-91 Proceedings of the 4th international conference on Rewriting techniques and applications
Modular higher-order E-unification
RTA-91 Proceedings of the 4th international conference on Rewriting techniques and applications
Logic programming in the LF logical framework
Logical frameworks
Handbook of logic in artificial intelligence and logic programming
Polymorphic Rewriting Conserves Algebraic Strong Normalization and Confluence
ICALP '89 Proceedings of the 16th International Colloquium on Automata, Languages and Programming
Compiling Logic Programs with Equality
PLILP '90 Proceedings of the 2nd International Workshop on Programming Language Implementation and Logic Programming
Linear Unification of Higher-Order Patterns
TAPSOFT '93 Proceedings of the International Joint Conference CAAP/FASE on Theory and Practice of Software Development
Unification in Conditional Equational Theories
EUROCAL '85 Research Contributions from the European Conference on Computer Algebra-Volume 2
BABEL: A Functional and Logic Programming Language based on Constructor Discipline and Narrowing
Proceedings of the International Workshop on Algebraic and Logic Programming
Counterexamples to Completeness Results for Basic Narrowing (Extended Abstract)
Proceedings of the Third International Conference on Algebraic and Logic Programming
Canonical Forms and Unification
Proceedings of the 5th Conference on Automated Deduction
Associative-Commutative Unification
Proceedings of the 7th International Conference on Automated Deduction
A Combinatory Logic Approach to Higher-order E-unification (Extended Abstract)
CADE-11 Proceedings of the 11th International Conference on Automated Deduction: Automated Deduction
Higher Order Unification 30 Years Later
TPHOLs '02 Proceedings of the 15th International Conference on Theorem Proving in Higher Order Logics
Higher-order unification and matching
Handbook of automated reasoning
Towards the uniform implementation of declarative languages
Computer Languages
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Higher-order equational logic programming is a paradigm which combines first-order equational and higher-order logic programming, where higher-order logic programming is based on a subclass of simply typed &lgr;-terms, called higher-order patterns. Central to the notion of higher-order equational logic programming is the so-called higher-order equational unification. This paper extends several important classes of first-order equational unification algorithms to the higher-order setting: only problems of the extensions are discussed and first-order equational unifications are viewed as black boxes whenever possible.We first extend narrowing and show that the completeness of many higher-order narrowing strategies reduces to that of their underlying first-order counterparts. Then we propose an algorithm or higher-order equational unification of free higher-order patterns in an arbitrary equational theory. Finally a general approach to extend first-order unification combination algorithms is sketched informally. The termination property of the above higher-order extensions is considered in a uniform way.