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.
@InProceedings{jacobedenaurois:LIPIcs.CSL.2022.26, author = {Jacob\'{e} de Naurois, Paulin}, title = {{Parallelism in Soft Linear Logic}}, booktitle = {30th EACSL Annual Conference on Computer Science Logic (CSL 2022)}, pages = {26:1--26:16}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-218-1}, ISSN = {1868-8969}, year = {2022}, volume = {216}, editor = {Manea, Florin and Simpson, Alex}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2022.26}, URN = {urn:nbn:de:0030-drops-157468}, doi = {10.4230/LIPIcs.CSL.2022.26}, annote = {Keywords: Implicit Complexity, Typing, Linear Logic, Functional Programming} }
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