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arXiv · 2407.14253

Strong Nominal Semantics for Fixed-Point Constraints

Ali K. Caires-Santos·Maribel Fernández·Daniele Nantes-Sobrinho
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Abstract

Nominal algebra includes $\alpha$-equality and freshness constraints on nominal terms endowed with a nominal set semantics that facilitates reasoning about languages with binders. Nominal unification is decidable and unitary, however, its extension with equational axioms such as Commutativity (which has a finitary first-order unification type) is no longer finitary unless permutation fixed-point constraints are used. In this paper, we extend the notion of nominal algebra by introducing fixed-point constraints and provide a sound semantics using strong nominal sets. We show, by providing a counter-example, that the class of nominal sets is not a sound denotation for this extended nominal algebra. To recover soundness we propose two different formulations of nominal algebra, one obtained by restricting to a class of fixed-point contexts that are in direct correspondence with freshness contexts and another obtained by using a different set of derivation rules.

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Ali K. Caires-Santos, Maribel Fernández, Daniele Nantes-Sobrinho. 2024-07-19. Strong Nominal Semantics for Fixed-Point Constraints. https://doi.org/10.46298/entics.14777

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