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Quantitative Types for the Linear Substitution Calculus
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.
Cited literature [40 references]
https://hal.inria.fr/hal-01402078
Contributor : Hal Ifip <>
Submitted on : Thursday, November 24, 2016 - 11:08:59 AM
Last modification on : Friday, March 27, 2020 - 3:59:15 AM
Long-term archiving on: : Tuesday, March 21, 2017 - 4:36:29 AM
Contributor : Hal Ifip <>
Submitted on : Thursday, November 24, 2016 - 11:08:59 AM
Last modification on : Friday, March 27, 2020 - 3:59:15 AM
Long-term archiving on: : Tuesday, March 21, 2017 - 4:36:29 AM
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