Type-based termination of recursive definitions

Authors:
G. Barthe;M. J. Frade;E. Giménez;L. Pinto;T. Uustalu
Affiliations:
INRIA Sophia-Antipolis, 2004 route des Lucioles, BP 93, F-06902 Sophia-Antipolis Cedex, France;Dep. de Informática, Universidade do Minho, Campus de Gualtar, P-4710-057 Braga, Portugal;Trusted Logic, 5 rue du Bailliage, F-78000 Versailles, France and Instituto de Computación, Universidad de la República, Julio Herrera y Reissig 565, 11300 Montevideo, Uruguay;Dep. de Matemática, Universidade do Minho, Campus de Gualtar, P-4710-057 Braga, Portugal;Dep. de Informática, Universidade do Minho, Campus de Gualtar, P-4710-057 Braga, Portugal and Institute of Cybernetics, Akadeemia tee 21, EE-12618 Tallinn, Estonia
Venue:
Mathematical Structures in Computer Science
Year:
2004

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Abstract

This paper introduces $\lambda^\widehat$, a simply typed lambda calculus supporting inductive types and recursive function definitions with termination ensured by types. The system is shown to enjoy subject reduction, strong normalisation of typable terms and to be stronger than a related system $\lambda_{\mathcal{G}}$ in which termination is ensured by a syntactic guard condition. The system can, at will, be extended to support coinductive types and corecursive function definitions also.