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