An Arithmetical Proof of the Strong Normalization for the λ-Calculus with Recursive Equations on Types

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.KeywordsClassical LogicIntuitionistic LogicOrder TypeRecursive EquationTyping RuleThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.