Source-tracking unification

We propose a path-based framework for deriving and simplifying source-tracking information for first-order 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 failu...

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Bibliographic Details
Published in:Information and computation Vol. 201; no. 2; pp. 121 - 159
Main Authors: Choppella, Venkatesh, Haynes, Christopher T.
Format: Journal Article
Language:English
Published: San Diego, CA Elsevier Inc 01.01.2003
Elsevier
Subjects:
Algorithmics. Computability. Computer arithmetics
Algorithms
Applied sciences
Combinatorics
Combinatorics. Ordered structures
Computer science; control theory; systems
Debugging
Exact sciences and technology
Formal languages
Graph theory
Language theory and syntactical analysis
Logic programming
Mathematics
Path problems
Sciences and techniques of general use
Software
Software engineering
Term unification
Theoretical computing
Type inference
Type inference
Algorithms
Logic programming
Formal languages
Debugging
Term unification
Graph theory
Path problems
Formal language
Computer theory
Optimal algorithm
Deduction
Shortest path
Logical programming
Failures
Labelled graph
ISSN:0890-5401, 1090-2651
Online Access:Get full text
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Summary:We propose a path-based framework for deriving and simplifying source-tracking information for first-order 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 suffix 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.
ISSN:0890-5401
1090-2651
DOI:10.1016/j.ic.2004.10.013