Quantitative Types for Intuitionistic Calculi

Delia Kesner (1) , Daniel Ventura (2)

1 PPS - Preuves, Programmes et Systèmes
2 Instituto de Informática

We define quantitative type systems for two intuitionistic term languages. While the first language in natural deduction style is already known in the literature, the second one is one of the contributions of the paper, and turns out to be a natural computational interpretation of sequent calculus style by means of a non-idempotent type discipline. The type systems are able to characterize linear-head, weak and strong normalization sets of terms. All such characterizations are given by means of combinatorial arguments, i.e. there is a measure based on type derivations which is decreasing with respect to the different reduction relations considered in the paper.

Mots clés: Non-idempotent intersection types; natural deduction; sequence calculus; linear-head reduction; weak normalization; strong normalization

Domaines: Langage de programmation [cs.PL]

Delia Kesner, Daniel Ventura. Quantitative Types for Intuitionistic Calculi. 2014. ⟨hal-00980868⟩