An arithmetical proof of the strong normalization for the λ-calculus with recursive equations on types

Authors:
René David;Karim Nour
Affiliations:
Université de Savoie, Le Bourget du Lac, France;Université de Savoie, Le Bourget du Lac, France
Venue:
TLCA'07 Proceedings of the 8th international conference on Typed lambda calculi and applications
Year:
2007

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Abstract

We give an arithmetical proof of the strong normalization of the λ-calculus (and also of the λµ-calculus) where the type system is the one of simple types with recursive equations on types. The proof using candidates of reducibility is an easy extension of the one without equations but this proof cannot be formalized in Peano arithmetic. The strength of the system needed for such a proof was not known. Our proof shows that it is not more than Peano arithmetic.