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# A Proof of Weak Termination of the Simply-Typed {$\lambda\sigma$}-Calculus

Abstract : We show that reducing any simply-typed $\lambda\sigma$-term by applying the rules in $\sigma$ eagerly always terminates, by a translation to the simply-typed $\lambda$-calculus, and similarly for $\lambda\sigma_\lift$-terms with $\sigma_\lift$-eager rewrites. This holds even with term and substitution meta-variables. In fact, every reduction terminates provided that $(\beta)$-redexes are only contracted under so-called safe contexts. The previous results follow because in $\sigma$, resp. $\sigma_{\lift}$-normal forms, all contexts around terms of sort $T$ are safe.
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https://hal.inria.fr/inria-00073601
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Submitted on : Wednesday, May 24, 2006 - 1:17:40 PM
Last modification on : Thursday, February 3, 2022 - 11:16:54 AM
Long-term archiving on: : Sunday, April 4, 2010 - 11:51:41 PM

### Identifiers

• HAL Id : inria-00073601, version 1

### Citation

Jean Goubault-Larrecq. A Proof of Weak Termination of the Simply-Typed {$\lambda\sigma$}-Calculus. [Research Report] RR-3090, INRIA. 1997. ⟨inria-00073601⟩

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