A Proof of Strong Normalisation using Domain Theory

Thierry Coquand (1) , Arnaud Spiwack (2, 3)

1 Division of Computing Science
2 LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau]
3 TYPICAL - Types, Logic and computing

U. Berger, significantly simplified Tait's normalisation proof for bar recursion, replacing Tait's introduction of infinite terms by the construction of a domain having the property that a term is strongly normalizing if its semantics is not bottom. The goal of this paper is to show that, using ideas from the theory of intersection types and Martin-Löf's domain interpretation of type theory, we can in turn simplify U. Berger's argument in the construction of such a domain model. We think that our domain model can be used to give modular proofs of strong normalization for various type theory. As an example, we show in some details how it can be used to prove strong normalization for Martin-Löf dependent type theory extended with bar recursion, and with some form of proof-irrelevance.

Domaines: Logique en informatique [cs.LO]; Langage de programmation [cs.PL]

Thierry Coquand, Arnaud Spiwack. A Proof of Strong Normalisation using Domain Theory. LICS 2006, Aug 2006, Seatle, United States. 10 p., ⟨10.1109/LICS.2006.8⟩. ⟨inria-00432490⟩