Parallelism in Soft Linear Logic

Author Paulin Jacobé de Naurois

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

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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)


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
  • Implicit Complexity
  • Typing
  • Linear Logic
  • Functional Programming


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