Arithmetical Proofs of Strong Normalization Results for Symmetric λ-calculi

Issue title: Typed Lambda Calculi and Applications 2005, Selected Papers

Article type: Research Article

Authors: David, René | Nour, Karim

Affiliations: Laboratoire de Mathématiques, Université de Savoie, 73376 Le Bourget du Lac. France. E-mail: {david,nour}@univ-savoie.fr

Abstract: We give arithmetical proofs of the strong normalization of two symmetric λ-calculi corresponding to classical logic. The first one is the λ¯μμ˜-calculus introduced by Curien & Herbelin. It is derived via the Curry-Howard correspondence from Gentzen's classical sequent calculus LK in order to have a symmetry on one side between "program" and "context" and on other side between "call-by-name" and "callby-value". The second one is the symmetric λμ-calculus. It is the λμ-calculus introduced by Parigot in which the reduction rule μ', which is the symmetric of μ, is added. These results were already known but the previous proofs use candidates of reducibility where the interpretation of a type is defined as the fix point of some increasing operator and thus, are highly non arithmetical.

Journal: Fundamenta Informaticae, vol. 77, no. 4, pp. 489-510, 2007