Taking Linear Logic Apart

Wen Kokke
(University of Edinburgh)
Fabrizio Montesi
(University of Southern Denmark)
Marco Peressotti
(University of Southern Denmark)

Process calculi based on logic, such as πDILL and CP, provide a foundation for deadlock-free concurrent programming. However, in previous work, there is a mismatch between the rules for constructing proofs and the term constructors of the π-calculus: the fundamental operator for parallel composition does not correspond to any rule of linear logic.

Kokke et al. (2019) introduced Hypersequent Classical Processes (HCP), which addresses this mismatch using hypersequents (collections of sequents) to register parallelism in the typing judgements. However, the step from CP to HCP is a big one. As of yet, HCP does not have reduction semantics, and the addition of delayed actions means that CP processes interpreted as HCP processes do not behave as they would in CP.

We introduce HCP-, a variant of HCP with reduction semantics and without delayed actions. We prove progress, preservation, and termination, and show that HCP- supports the same communication protocols as CP.

In Thomas Ehrhard, Maribel Fernández, Valeria de Paiva and Lorenzo Tortora de Falco: Proceedings Joint International Workshop on Linearity & Trends in Linear Logic and Applications (Linearity-TLLA 2018), Oxford, UK, 7-8 July 2018, Electronic Proceedings in Theoretical Computer Science 292, pp. 90–103.
Published: 15th April 2019.

ArXived at: https://dx.doi.org/10.4204/EPTCS.292.5 bibtex PDF

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