Source-Tracking Unification [chapter]

Venkatesh Choppella, Christopher T. Haynes
2003 Lecture Notes in Computer Science  
We propose a path-based framework for deriving and simplifying source-tracking information for firstorder term unification in the empty theory. Such a framework is useful for diagnosing unification-based systems, including debugging of type errors in programs and the generation of success and failure proofs in logic programming. The objects of source-tracking are deductions in the logic of term unification. The semantics of deductions are paths over a unification graph whose labels form the
more » ... ix language of a semi-Dyck set. Based on this idea of unification paths, two algorithms for generating proofs are presented: the first uses context-free labeled shortest-path algorithms to generate optimal (shortest) proofs in time O(n 3 ) for a fixed signature, where n is the number of vertices of the unification graph. The second algorithm integrates easily with standard unification algorithms, entailing an overhead of only a constant factor, but generates non-optimal proofs. These non-optimal proofs may be further simplified by group rewrite rules.
doi:10.1007/978-3-540-45085-6_39 fatcat:56ievgbgqnfcxhbo5hx56bd66m