Deriving SN from PSN: a general proof technique

Details Deriving SN from PSN: a general proof technique Deriving SN from PSN: a general proof technique

2009-09-28

arxiv.org/abs/0909.5045v1

TR-LACL (2006) 1-50

Computer Science

Logic in Computer Science

Scientific paper

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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