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Abstract : We define two non-idempotent intersection type systems for the linear substitution calculus, a calculus with partial substitutions acting at a distance that is a computational interpretation of linear logic proof-nets. The calculus naturally express linear-head reduction, a notion of evaluation of proof nets that is strongly related to abstract machines. We show that our first (resp. second) quantitave type system characterizes linear-head, head and weak (resp. strong) normalizing sets of terms. All such characterizations are given by means of combinatorial arguments, i.e. there is a measure based on type derivations which decreases with respect to each reduction relation considered in the paper.
https://hal.inria.fr/hal-01402078 Contributor : Hal IfipConnect in order to contact the contributor Submitted on : Thursday, November 24, 2016 - 11:08:59 AM Last modification on : Saturday, June 25, 2022 - 8:57:44 PM Long-term archiving on: : Tuesday, March 21, 2017 - 4:36:29 AM
Delia Kesner, Daniel Ventura. Quantitative Types for the Linear Substitution Calculus. 8th IFIP International Conference on Theoretical Computer Science (TCS), Sep 2014, Rome, Italy. pp.296-310, ⟨10.1007/978-3-662-44602-7_23⟩. ⟨hal-01402078⟩