Unification and matching algorithms are essential components of logic and functional programming languages and theorem provers. Nominal extensions have been developed to deal with syntax involving binding operators: nominal unification takes into account α-equivalence; however, it does not take into account non-capturing substitutions, which are not primitive in nominal syntax. We consider an extension of nominal syntax with non-capturing substitutions and show that matching is decidable and finitary but unification is undecidable. We provide a matching algorithm and characterise problems for which matching is unitary, giving rise to expressive and efficient rewriting systems.
CITATION STYLE
Domínguez, J., & Fernández, M. (2019). Nominal Syntax with Atom Substitutions: Matching, Unification, Rewriting. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 11651 LNCS, pp. 64–79). Springer Verlag. https://doi.org/10.1007/978-3-030-25027-0_5
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