Parallel needed reduction for pure interaction nets

TL;DR

This paper introduces a parallel needed reduction method for pure interaction nets that achieves constant-time steps without sacrificing parallelism, improving efficiency over traditional linear-depth reductions.

Contribution

It refines the weak interaction calculus to enable constant-time parallel needed reduction without free ports, enhancing reduction efficiency.

Findings

Constant-time per step reduction for pure interaction nets

Refined calculus reveals actual reduction costs

Parallel needed reduction maintains efficiency without free ports

Abstract

Reducing interaction nets without any specific strategy benefits from constant time per step. On the other hand, a canonical reduction step for weak reduction to interface normal form is linear by depth of terms. In this paper, we refine the weak interaction calculus to reveal the actual cost of its reduction. As a result, we obtain a notion of needed reduction that can be implemented in constant time per step without allowing any free ports and without sacrificing parallelism.