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Rewrite systems on free data structures have limited expressive power since semantic data structures like sets or multisets cannot be modeled elegantly. In this work the authors define a class of rewrite systems that allows the use of semantic data structures. Additionally, built-in natural numbers, including (dis)equality, ordering, and divisibility constraints, are supported. The rewrite mechanism is a combination of normalized equational rewriting with evaluation of conditions and validity checking of instantiated constraints. The framework is highly expressive and allows modeling of algorithms in a natural way.
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