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arXiv · 2607.12652

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

Lea Trogni·Gabriele Cecilia·Alberto Momigliano
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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.

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Lea Trogni, Gabriele Cecilia, Alberto Momigliano. 2026-07-14. Barbed Similarity for the $\pi$-Calculus in Beluga: A Case Study in Coinductive Reasoning. https://doi.org/10.4204/eptcs.448.1

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