Unification and Matching in Hierarchical Combinations of Syntactic Theories

Serdar Erbatur 1 Deepak Kapur 2 Andrew Marshall 3 Paliath Narendran 4 Christophe Ringeissen 5
1 LMU - Ludwig-Maximilians-Universität München
2 The University of New Mexico [Albuquerque]
3 University of Mary Washington
4 University at Albany [SUNY]
5 CASSIS - Combination of approaches to the security of infinite states systems
FEMTO-ST - Franche-Comté Électronique Mécanique, Thermique et Optique - Sciences et Technologies (UMR 6174), Inria Nancy - Grand Est, LORIA - FM - Department of Formal Methods
Abstract : We investigate a hierarchical combination approach to the unification problem in non-disjoint unions of equational theories. In this approach, the idea is to extend a base theory with some additional axioms given by rewrite rules in such way that the unification algorithm known for the base theory can be reused without loss of completeness. Additional techniques are required to solve a combined problem by reducing it to a problem in the base theory. In this paper we show that the hierarchical combination approach applies successfully to some classes of syntactic theories, such as shallow theories since the required unification algorithms needed for the combination algorithm can always be obtained. We also consider the matching problem in syntactic extensions of a base theory. Due to the more restricted nature of the matching problem, we obtain several improvements over the unification problem.
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Submitted on : Tuesday, September 29, 2015 - 2:34:24 PM
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Serdar Erbatur, Deepak Kapur, Andrew Marshall, Paliath Narendran, Christophe Ringeissen. Unification and Matching in Hierarchical Combinations of Syntactic Theories. Frontiers of Combining Systems - 10th International Symposium, FroCoS 2015, Sep 2015, Wroclaw, Poland. pp.291--306, ⟨10.1007/978-3-319-24246-0_18⟩. ⟨hal-01206669⟩

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