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Types as Resources for Classical Natural Deduction

Authors Delia Kesner, Pierre Vial

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LIPIcs.FSCD.2017.24.pdf
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Delia Kesner
Pierre Vial

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Delia Kesner and Pierre Vial. Types as Resources for Classical Natural Deduction. In 2nd International Conference on Formal Structures for Computation and Deduction (FSCD 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 84, pp. 24:1-24:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017) https://doi.org/10.4230/LIPIcs.FSCD.2017.24

Abstract

We define two resource aware typing systems for the lambda-mu-calculus based on non-idempotent intersection and union types. The
non-idempotent approach provides very simple combinatorial arguments - based on decreasing measures of type derivations - to characterize head and strongly normalizing terms. Moreover, typability provides upper bounds for the length of head-reduction sequences and  maximal reduction sequences.

Subject Classification

Keywords
  • lambda-mu-calculus
  • classical logic
  • intersection types
  • normalization

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