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Reports (Research Report) Year : 1997

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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Dates and versions

inria-00073601 , version 1 (24-05-2006)

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  • HAL Id : inria-00073601 , version 1

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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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