Induction principles as the foundation of the theory of normalisation: Concepts and Techniques

Abstract : This technical report presents a constructive theory of normalisation based on induction principles, using second-order quantification. Standard techniques are established constructively, such as proving strong normalisation by (possibly non-deterministic) simulation, the termination of lexicographic reductions and multi-set reductions. Two new techniques are then presented to derive strong normalisation: the first one applies to any rewrite system but is classical, the second one applies more specifically to lambda-calculi, especially with explicit substitutions, and is still intuitionistic. The former gives short proofs of PSN for lambda x and lambda bar, the latter gives a proof of PSN for lambdalxr, which is a new result.
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Pré-publication, Document de travail
Early 2005. Chapter 0 of my thesis. 2005
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https://hal.archives-ouvertes.fr/hal-00004358
Contributeur : Stéphane Graham-Lengrand <>
Soumis le : samedi 5 mars 2005 - 02:13:48
Dernière modification le : mardi 11 octobre 2016 - 13:55:42
Document(s) archivé(s) le : mardi 2 juin 2015 - 13:20:17

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  • HAL Id : hal-00004358, version 2

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Stéphane Lengrand. Induction principles as the foundation of the theory of normalisation: Concepts and Techniques. Early 2005. Chapter 0 of my thesis. 2005. <hal-00004358v2>

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