On the Values of Reducibility Candidates

Colin Riba (1, 2)

1 LIP - Laboratoire de l'Informatique du Parallélisme
2 PLUME - Preuves et Langages

The straightforward elimination of union types is known to break subject reduction, and for some extensions of the lambda-calculus, to break strong normalization as well. Similarly, the straightforward elim- ination of implicit existential types breaks subject reduction. We propose elimination rules for union types and implicit existential quantification which use a form call-by-value issued from Girard's re- ducibility candidates. We show that these rules remedy the above men- tioned difficulties, for strong normalization and, for the existential quan- tification, for subject reduction as well. Moreover, for extensions of the lambda-calculus based on intuitionistic logic, we show that the obtained existential quantification is equivalent to its usual impredicative encoding w.r.t. provability in realizability models built from reducibility candidates and biorthogonals.

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

Colin Riba. On the Values of Reducibility Candidates. Typed Lambda Calculi and Applications, 9th International Conference, TLCA 2009, Jul 2009, Brasilia, Brazil. pp 264-278, ⟨10.1007/978-3-642-02273-9_20⟩. ⟨hal-00800668⟩