Logic for computer science: foundations of automatic theorem proving
Logic for computer science: foundations of automatic theorem proving
The set of unifiers in typed &lgr;-calculus as regular expression
Proc. of the first international conference on Rewriting techniques and applications
Introduction to combinators and &lgr;-calculus
Introduction to combinators and &lgr;-calculus
Natural deduction as higher-order resolution
Journal of Logic Programming
Complete sets of unifiers and matchers in equational theories
Theoretical Computer Science
A higher-order logic as the basis for logic programming
A higher-order logic as the basis for logic programming
Higher-order unification with dependent function types
RTA-89 Proceedings of the 3rd international conference on Rewriting Techniques and Applications
Journal of the ACM (JACM)
A Complete Mechanization of Second-Order Type Theory
Journal of the ACM (JACM)
An Efficient Unification Algorithm
ACM Transactions on Programming Languages and Systems (TOPLAS)
Higher-Order Logic Programming
Proceedings of the Third International Conference on Logic Programming
Specifying Theorem Provers in a Higher-Order Logic Programming Language
Proceedings of the 9th International Conference on Automated Deduction
Length of proofs and unification theory (second-order, complexity proofs)
Length of proofs and unification theory (second-order, complexity proofs)
Complete sets of transformations for general unification
Complete sets of transformations for general unification
Some uses of higher-order logic in computational linguistics
ACL '86 Proceedings of the 24th annual meeting on Association for Computational Linguistics
A mechanization of type theory
IJCAI'73 Proceedings of the 3rd international joint conference on Artificial intelligence
Functional and constraint logic programming
Constraints in computational logics
Higher Order Unification 30 Years Later
TPHOLs '02 Proceedings of the 15th International Conference on Theorem Proving in Higher Order Logics
Stratified Context Unification Is in PSPACE
CSL '01 Proceedings of the 15th International Workshop on Computer Science Logic
Higher-Order Positive Set Constraints
CSL '02 Proceedings of the 16th International Workshop and 11th Annual Conference of the EACSL on Computer Science Logic
Reducing Search Space in Solving Higher-Order Equations
Progress in Discovery Science, Final Report of the Japanese Discovery Science Project
Higher-order unification and matching
Handbook of automated reasoning
Higher-order narrowing with definitional trees
Journal of Functional Programming
Decidability of bounded second order unification
Information and Computation
Deciding security of protocols against off-line guessing attacks
Proceedings of the 12th ACM conference on Computer and communications security
Matching modulo superdevelopments application to second-order matching
LPAR'06 Proceedings of the 13th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
A structured set of higher-order problems
TPHOLs'05 Proceedings of the 18th international conference on Theorem Proving in Higher Order Logics
A functional logic language based on higher order narrowing
FP'95 Proceedings of the 1995 international conference on Functional Programming
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In this paper, we reexamine the problem of general higher-order unification and develop an approach based on the method of transformations on systems of terms which has its roots in Herbrand's thesis, and which was developed by Martelli and Montanari in the context of first-order unification. This method provides an abstract and mathematically elegant means of analyzing the invariant properties of unification in various settings by providing a clean separation of the logical issues from the specification of procedural information. Our major contribution is three-fold. First, we have extended the Herbrand-Martelli-Montanari method of transformations on systems to higher-order unification and pre-unification; second, we have used this formalism to provide a more direct proof of the completeness of a method for higher-order unification than has previously been available; and, finally, we have shown the completeness of the strategy of eager variable elimination. In addition, this analysis provides another justification of the design of Huet's procedure, and shows how its basic principles work in a more general setting. Finally, it is hoped that this presentation might form a good introduction to higher-order unification for those readers unfamiliar with the field.