Isomorphisms of simple inductive types through extensional rewriting - Archive ouverte HAL Access content directly
Journal Articles Mathematical Structures in Computer Science Year : 2005

Isomorphisms of simple inductive types through extensional rewriting

Abstract

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.

Dates and versions

hal-00782793 , version 1 (30-01-2013)

Identifiers

Cite

David Chemouil. Isomorphisms of simple inductive types through extensional rewriting. Mathematical Structures in Computer Science, 2005, 15 (5), pp.875-915. ⟨10.1017/S0960129505004950⟩. ⟨hal-00782793⟩
97 View
0 Download

Altmetric

Share

Gmail Facebook X LinkedIn More