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Mechanically verify the general confluence conjecture for the local language

Mechanically verify, within the Rocq formalization supporting the Quick Change choreographic calculus (Lambda-QC), that the required local-language property can be weakened from the diamond property to the following general confluence property: for all local terms e1, e2, and e3, if e1 reduces in zero or more steps to e2 and to e3, then there exists a term e4 such that both e2 and e3 reduce in zero or more steps to e4.

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Background

Lambda-QC assumes a diamond property for the small-step operational semantics of the underlying local language to ensure that multiply-located computations produce the same result. Although many deterministic or pure functional languages satisfy the diamond property, the authors argue that the assumption could be weakened to standard multi-step confluence (Church–Rosser), thereby broadening the class of admissible local languages.

They explicitly conjecture that this weaker property suffices and note that confluence may be mechanically established in Rocq, but they have not carried this out and leave it as future work.

References

We believe it can be weakened to the more general confluence statement that, if $e_1 \localsteps e_2$ and $e_1 \localsteps e_3$ then $e_2 \localsteps e_4$ and $e_3 \localsteps e_4$ for some~$e_4$, but we leave the challenge of mechanically verifying this conjecture to future work.

— Choreographic Quick Changes: First-Class Location (Set) Polymorphism (2506.10913 - Samuelson et al., 12 Jun 2025) in Section 3, System Model (Local Programs)