arXiv subjects

Gabriele Cecilia

Publications and source records attributed to Gabriele Cecilia.

3 recordsLinked to original sources

arXiv2026

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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arXiv2025

A Formalization of the Reversible Concurrent Calculus CCSKP in Beluga

Reversible concurrent calculi are abstract models for concurrent systems in which any action can potentially be undone. Over the last few decades, different formalisms have been developed and their mathematical properties have been explored; however, none have been machine-checked within a proof assistant. This paper presents the first Beluga formalization of the Calculus of Communicating Systems with Keys and Proof labels (CCSKP), a reversible extension of CCS. Beyond the syntax and semantics of the calculus, the encoding covers state-of-the-art results regarding three relations over proof labels -- namely, dependence, independence and connectivity -- which offer new insights into the notions of causality and concurrency of events. As is often the case with formalizations, our encoding introduces adjustments to the informal proof and makes explicit details which were previously only sketched, some of which reveal to be less straightforward than initially assumed. We believe this work lays the foundations for future reversible concurrent calculi formalizations.

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arXiv2024

A Beluga Formalization of the Harmony Lemma in the $π$-Calculus

The "Harmony Lemma", as formulated by Sangiorgi & Walker, establishes the equivalence between the labelled transition semantics and the reduction semantics in the $π$-calculus. Despite being a widely known and accepted result for the standard $π$-calculus, this assertion has never been rigorously proven, formally or informally. Hence, its validity may not be immediately apparent when considering extensions of the $π$-calculus. Contributing to the second challenge of the Concurrent Calculi Formalization Benchmark -- a set of challenges tackling the main issues related to the mechanization of concurrent systems -- we present a formalization of this result for the fragment of the $π$-calculus examined in the Benchmark. Our formalization is implemented in Beluga and draws inspiration from the HOAS formalization of the LTS semantics popularized by Honsell et al. In passing, we introduce a couple of useful encoding techniques for handling telescopes and lexicographic induction.

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