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Communication Dans Un Congrès Année : 2024

From Rewrite Rules to Axioms in the λΠ-Calculus Modulo Theory

Résumé

The λΠ-calculus modulo theory is an extension of simply typed λ-calculus with dependent types and user-defined rewrite rules. We show that it is possible to replace the rewrite rules of a theory of the λΠ-calculus modulo theory by equational axioms, when this theory features the notions of proposition and proof, while maintaining the same expressiveness. To do so, we introduce in the target theory a heterogeneous equality, and we build a translation that replaces each use of the conversion rule by the insertion of a transport. At the end, the theory with rewrite rules is a conservative extension of the theory with axioms.
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Dates et versions

hal-04275229 , version 1 (08-11-2023)
hal-04275229 , version 2 (13-02-2024)

Identifiants

Citer

Valentin Blot, Gilles Dowek, Thomas Traversié, Théo Winterhalter. From Rewrite Rules to Axioms in the λΠ-Calculus Modulo Theory. FoSSaCS 2024 - 27th International Conference on Foundations of Software Science and Computation Structures, Apr 2024, Luxembourg City, Luxembourg. pp.3-23, ⟨10.1007/978-3-031-57231-9_1⟩. ⟨hal-04275229v2⟩
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