Quantitative Types for the Linear Substitution Calculus

@inproceedings{Kesner2014QuantitativeTF,
  title={Quantitative Types for the Linear Substitution Calculus},
  author={Delia Kesner and Daniel Lima Ventura},
  booktitle={IFIP TCS},
  year={2014}
}
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… 

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