# Taking Linear Logic Apart

## TL;DR

This paper introduces HCP-, a simplified version of Hypersequent Classical Processes, providing reduction semantics and proving key properties, thereby bridging the gap between linear logic-based process calculi and practical concurrent programming.

## Contribution

HCP- extends HCP by adding reduction semantics and removing delayed actions, aligning process behavior with linear logic principles and prior calculi like CP.

## Key findings

- HCP- supports the same communication protocols as CP.
- HCP- has proven progress, preservation, and termination.
- HCP- effectively models deadlock-free concurrent processes.

## Abstract

Process calculi based on logic, such as $\pi$DILL 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 $\pi$-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.