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Quantitative Types for Intuitionistic Calculi

By Delia Kesner and Daniel Ventura


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

Topics: Non-idempotent intersection types, natural deduction, sequence calculus, linear-head reduction, weak normalization, strong normalization, [ INFO.INFO-PL ] Computer Science [cs]/Programming Languages [cs.PL]
Publisher: HAL CCSD
Year: 2014
OAI identifier: oai:HAL:hal-00980868v1
Provided by: Hal-Diderot

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