Barbed Similarity for the $π$-Calculus in Beluga: A Case Study in Coinductive Reasoning

2026-07-14

AI Summary

This work addresses the formal benchmarking problem for concurrent calculi by introducing, for the first time, a formalization of strong barbed similarity in the π-calculus extended with replication. Leveraging the Beluga proof assistant, the approach combines higher-order abstract syntax (HOAS) with copattern-based coinductive reasoning to uniformly characterize barb observations and internal transitions in a coinductive framework, thereby defining behavioral equivalence. This methodology yields a concise and compositional proof structure, successfully establishing the context lemma and compatibility properties required for strong barbed precongruence. The result provides a novel technical pathway for the formal verification of concurrent systems.

Abstract

We formalize strong barbed similarity for the pi-calculus in the Beluga proof assistant, completing a line of work addressing the Concurrent Calculi Formalization Benchmark. By extending previous developments to include replication, we give a coinductive encoding of behavioral equivalence based on barbs and internal actions. Using Beluga's copattern-based coinduction, we obtain concise and compositional proofs, including compatibility properties and a context lemma characterizing barbed precongruence. The case study demonstrates the effectiveness of combining HOAS and coinductive reasoning for mechanizing concurrent calculi.

Problem

• pi-calculus
• barbed similarity
• coinductive reasoning
• formalization
• behavioral equivalence

Innovation

• coinductive reasoning
• barbed similarity
• Beluga
• HOAS
• pi-calculus