Operational Termination of Conditional Rewriting with Built-in Numbers and Semantic Data Structures

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Abstract

While ordinary conditional rewrite systems are more elegant than unconditional ones, they still have limited expressive power since semantic data structures, such as sets or multisets, cannot be modeled elegantly. Extending our work presented at RTA 2008 [Falke, S. and D. Kapur, Dependency pairs for rewriting with built-in numbers and semantic data structures, in: A. Voronkov, editor, Proceedings of the 19th Conference on Rewriting Techniques and Applications (RTA '08), Lecture Notes in Computer Science 5117 (2008), pp. 94–109], the present paper defines a class of conditional rewrite systems that allows the use of semantic data structures and supports built-in natural numbers, including constraints taken from Presburger arithmetic. The framework is both expressive and natural. Rewriting is performed using a combination of normalized equational rewriting with recursive evaluation of conditions and validity checking of instantiated constraints.

Termination is one of the most important properties of any kind of rewriting. For conditional systems, it is not sufficient to only show well-foundedness of the rewrite relation, but it also has to be ensured that evaluation of the conditions terminates. These properties are captured by the notion of operational termination. In this work, we show that operational termination for the class of conditional rewrite systems discussed above can be reduced to (regular) termination of unconditional systems using a syntactic transformation. Powerful methods for showing termination of unconditional systems are presented in [Falke, S. and D. Kapur, Dependency pairs for rewriting with built-in numbers and semantic data structures, in: A. Voronkov, editor, Proceedings of the 19th Conference on Rewriting Techniques and Applications (RTA '08), Lecture Notes in Computer Science 5117 (2008), pp. 94–109].

Keywords

Conditional term rewriting
operational termination
semantic data structures

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Partially supported by NSF grant CCF-0541315.