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.
Document type :
Preprints, Working Papers, ...
Complete list of metadatas

https://hal.archives-ouvertes.fr/hal-00004358
Contributor : Stéphane Graham-Lengrand <>
Submitted on : Saturday, March 5, 2005 - 2:13:48 AM
Last modification on : Friday, January 4, 2019 - 5:32:58 PM
Long-term archiving on : Tuesday, June 2, 2015 - 1:20:17 PM

Files

Identifiers

  • HAL Id : hal-00004358, version 2

Collections

Citation

Stéphane Lengrand. Induction principles as the foundation of the theory of normalisation: Concepts and Techniques. 2005. ⟨hal-00004358v2⟩

Share

Metrics

Record views

479

Files downloads

64