Abstract
We propose a practical path-based framework for deriving and simplifying source-tracking information for term unification in the empty theory. Such a framework is useful for debugging unification-based systems, including the diagnosis of ill-typed programs and the generation of success and failure proofs in logic programming.
The objects of source-tracking are deductions in the logic of unification. The semantics of deductions are paths over a unification graph whose labels form the language of suffixes of a semi-Dyck set. Based on this framework, two algorithms for generating proofs are presented: the first uses context-free shortest-path algorithms to generate optimal (shortest) proofs in time O(n 3), 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.
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Choppella, V., Haynes, C.T. (2003). Source-Tracking Unification. In: Baader, F. (eds) Automated Deduction – CADE-19. CADE 2003. Lecture Notes in Computer Science(), vol 2741. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-45085-6_39
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DOI: https://doi.org/10.1007/978-3-540-45085-6_39
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