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Deriving SN from PSN: a general proof technique

Abstract : In the framework of explicit substitutions there is two termination properties: preservation of strong normalization (PSN), and strong normalization (SN). Since there are not easily proved, only one of them is usually established (and sometimes none). We propose here a connection between them which helps to get SN when one already has PSN. For this purpose, we formalize a general proof technique of SN which consists in expanding substitutions into "pure" lambda-terms and to inherit SN of the whole calculus by SN of the "pure" calculus and by PSN. We apply it successfully to a large set of calculi with explicit substitutions, allowing us to establish SN, or, at least, to trace back the failure of SN to that of PSN.
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Contributor : Emmanuel Polonowski <>
Submitted on : Tuesday, September 29, 2009 - 10:16:33 AM
Last modification on : Wednesday, September 4, 2019 - 1:52:06 PM

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  • HAL Id : hal-00420464, version 1
  • ARXIV : 0909.5045



Emmanuel Polonowski. Deriving SN from PSN: a general proof technique. 2006. ⟨hal-00420464⟩



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