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Isomorphisms of simple inductive types through extensional rewriting

Published online by Cambridge University Press:  04 October 2005

DAVID CHEMOUIL
Affiliation:
IRIT, Université Paul Sabatier, 118 route de Narbonne, 31062 Toulouse, France Email: chemouil@irit.fr

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.

Type
Paper
Copyright
2005 Cambridge University Press

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