Isomorphisms of simple inductive types through extensional rewriting

• Autores: David Chemouil
• Localización: Mathematical structures in computer science, ISSN 0960-1295, Vol. 15, Nº 5, 2005, págs. 875-915
• Idioma: inglés
• DOI: 10.1017/s0960129505004950
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• Resumen

  • We study isomorphisms of inductive types (that is, recursive types satisfying a condition of strict positivity) in an extensional simply typed $\lambda$-calculus with product and unit types. We first show that the calculus enjoys strong normalisation and confluence. Then we extend it with new conversion rules ensuring that all inductive representations of the product and unit types are isomorphic, and such that the extended reduction remains convergent. Finally, we define the notion of a faithful copy of an inductive type and a corresponding conversion relation that also preserves the good properties of the calculus.