Technical Reports (CIS)
Document Type
Technical Report
Subject Area
GRASP
Date of this Version
February 1989
Abstract
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.
Recommended Citation
Wayne Snyder and Jean H. Gallier, "Higher Order Unification Revisited: Complete Sets of Transformations", . February 1989.
Date Posted: 06 December 2007
Comments
University of Pennsylvania Department of Computer and Information Science Technical Report No. MS-CIS-89-11.