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Parallelism in Soft Linear Logic

Author Paulin Jacobé de Naurois

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Author Details

Paulin Jacobé de Naurois
  • CNRS, Université Paris 13, Sorbonne Paris Cité, LIPN, UMR 7030, F-93430 Villetaneuse, France

Funding

  • Jacobé de Naurois, Paulin: ANR project ELICA - ANR-14-CE25-0005.

Cite AsGet BibTex

Paulin Jacobé de Naurois. Parallelism in Soft Linear Logic. In 30th EACSL Annual Conference on Computer Science Logic (CSL 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 216, pp. 26:1-26:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)
https://doi.org/10.4230/LIPIcs.CSL.2022.26

Abstract

We extend the Soft Linear Logic of Lafont with a new kind of modality, called parallel. Contractions on parallel modalities are only allowed in the cut and the left ⊸ rules, in a controlled, uniformly distributive way. We show that SLL, extended with this parallel modality, is sound and complete for PSPACE. We propose a corresponding typing discipline for the λ-calculus, extending the STA typing system of Gaboardi and Ronchi, and establish its PSPACE soundness and completeness. The use of the parallel modality in the cut-rule drives a polynomial-time, parallel call-by-value evaluation strategy of the terms.

Subject Classification

ACM Subject Classification
  • Theory of computation → Linear logic
  • Theory of computation → Complexity theory and logic
Keywords
  • Implicit Complexity
  • Typing
  • Linear Logic
  • Functional Programming

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References

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