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arXiv · 2506.05835

Nominal Equational Rewriting and Narrowing

Mauricio Ayala-Rincón·Maribel Fernández·Daniele Nantes-Sobrinho·Daniella Santaguida
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Abstract

Narrowing is a well-known technique that adds to term rewriting mechanisms the required power to search for solutions to equational problems. Rewriting and narrowing are well-studied in first-order term languages, but several problems remain to be investigated when dealing with languages with binders using nominal techniques. Applications in programming languages and theorem proving require reasoning modulo alpha-equivalence considering structural congruences generated by equational axioms, such as commutativity. This paper presents the first definitions of nominal rewriting and narrowing modulo an equational theory. We establish a property called nominal E-coherence and demonstrate its role in identifying normal forms of nominal terms. Additionally, we prove the nominal E-Lifting theorem, which ensures the correspondence between sequences of nominal equational rewriting steps and narrowing, crucial for developing a correct algorithm for nominal equational unification via nominal equational narrowing. We illustrate our results using the equational theory for commutativity.

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Mauricio Ayala-Rincón, Maribel Fernández, Daniele Nantes-Sobrinho, Daniella Santaguida. 2025-06-06. Nominal Equational Rewriting and Narrowing. https://doi.org/10.4204/eptcs.421.5

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