Taking Linear Logic Apart
Abstract
Process calculi based on logic, such as $\pi$DILL and CP, provide a foundation for deadlockfree concurrent programming. However, in previous work, there is a mismatch between the rules for constructing proofs and the term constructors of the $\pi$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.
 Publication:

arXiv eprints
 Pub Date:
 April 2019
 arXiv:
 arXiv:1904.06848
 Bibcode:
 2019arXiv190406848K
 Keywords:

 Computer Science  Logic in Computer Science;
 Computer Science  Programming Languages;
 D.3.1;
 D.3.2;
 F.3.2;
 F.4.1
 EPrint:
 In Proceedings LinearityTLLA 2018, arXiv:1904.06159