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

Stéphane Lengrand

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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Dates and versions

hal-00004358 , version 1 (04-03-2005)
hal-00004358 , version 2 (05-03-2005)

Identifiers

  • 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. 2005. ⟨hal-00004358v2⟩
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