# An arithmetical proof of the strong normalization for the $\lambda$-calculus with recursive equations on types

Abstract : We give an arithmetical proof of the strong normalization of the $\lambda$-calculus (and also of the $\lambda\mu$-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.
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Conference papers
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Cited literature [43 references]

https://hal.archives-ouvertes.fr/hal-00382263
Contributor : Karim Nour <>
Submitted on : Thursday, May 7, 2009 - 4:16:47 PM
Last modification on : Thursday, January 11, 2018 - 6:12:26 AM
Document(s) archivé(s) le : Thursday, June 10, 2010 - 10:55:10 PM

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tlca_07.pdf
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### Identifiers

• HAL Id : hal-00382263, version 1
• ARXIV : 0905.1032

### Citation

René David, Karim Nour. An arithmetical proof of the strong normalization for the $\lambda$-calculus with recursive equations on types. Typed Lambda Calculi and Applications, Jun 2007, Paris, France. pp.84-101. ⟨hal-00382263⟩

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