Published October 12, 2026 | Version 2
Preprint Open

Normalization Confluence for Registry-Governed Stream Processing

Authors/Creators

  • 1. Blackwell Systems

Description

Coordination-free convergence in distributed systems has been achieved through two structural regimes: operation commutativity (CRDTs) and invariant confluence (I-confluence). This paper identifies a third regime — normalization confluence — in which operations may be non-commutative and may violate application invariants, but convergence is restored through a compensation operator that normalizes states to validity.

We formalize this regime by introducing registry-governed stream processing, where an external registry of invariant predicates defines valid states and a compensation operator repairs violations. We construct a governance rewrite system and prove, via Newman's Lemma, that two structural conditions — well-founded compensation (WFC) and compensation commutativity (CC) — guarantee that all causality-respecting processing orders yield the same valid state. We prove both conditions are necessary: without WFC, compensation depth is unbounded; without CC, different orders reach different valid states.

Compensation commutativity is strictly weaker than operation commutativity: operations need not commute, only their compensated results. To make CC practically verifiable, we develop a verification calculus based on invariant footprints and decomposable repair that reduces the global CC obligation to local, per-event-pair checks, together with a product composition theorem for modular verification.

Notes

Version 2: corrected statements and an errata appendix; every result stated is mechanized axiom-free in the Coq development at https://github.com/blackwell-systems/normalization-confluence (see its CHANGELOG).

Files

normalization_confluence_2026.pdf

Files (325.4 kB)

Name Size
md5:c2eafd27f512fc461e15fc6720ca5917
212.0 kB Preview Download
md5:09272de904166840cbc83a617d32d776
113.4 kB Download

Additional details

Related works

Is cited by
Preprint: 10.5281/zenodo.18677400 (DOI)
Preprint: 10.5281/zenodo.23311468 (DOI)
Preprint: 10.5281/zenodo.23311489 (DOI)
Is documented by
https://blackwell-systems.github.io/normalization-confluence/ (URL)
Is supplemented by
Software: https://github.com/blackwell-systems/normalization-confluence (URL)

References

  • M. H. A. Newman, "On theories with a combinatorial definition of `equivalence'," Annals of Mathematics, vol. 43, no. 2, pp. 223-243, 1942.
  • M. Shapiro, N. Preguiça, C. Baquero, and M. Zawirski, "A comprehensive study of convergent and commutative replicated data types," INRIA Research Report RR-7506, 2011.
  • J. M. Hellerstein, "The declarative imperative: experiences and conjectures in distributed logic," SIGMOD Record, vol. 39, no. 1, pp. 5-19, 2010.
  • T. J. Ameloot, F. Neven, and J. Van den Bussche, "Relational transducers for declarative networking," Journal of the ACM, vol. 60, no. 2, pp. 1-38, 2013.
  • P. Bailis, A. Fekete, M. J. Franklin, A. Ghodsi, J. M. Hellerstein, and I. Stoica, "Coordination avoidance in database systems," Proc. VLDB Endowment, vol. 8, no. 3, pp. 185-196, 2014.
  • F. Baader and T. Nipkow, Term Rewriting and All That, Cambridge University Press, 1998.
  • W. Vogels, "Eventually consistent," Communications of the ACM, vol. 52, no. 1, pp. 40-44, 2009.
  • H. Garcia-Molina and K. Salem, "Sagas," Proc. ACM SIGMOD International Conference on Management of Data, pp. 249-259, 1987.
  • E. A. Lee and D. G. Messerschmitt, "Synchronous data flow," Proceedings of the IEEE, vol. 75, no. 9, pp. 1235-1245, 1987.
  • G. Kahn, "The semantics of a simple language for parallel programming," Information Processing, pp. 471-475, 1974.
  • T. Akidau, R. Bradshaw, C. Chambers, et al., "The Dataflow Model: A practical approach to balancing correctness, latency, and cost in massive-scale, unbounded, out-of-order data processing," Proc. VLDB Endowment, vol. 8, no. 12, pp. 1792-1803, 2015.
  • L. Lamport, "Time, clocks, and the ordering of events in a distributed system," Communications of the ACM, vol. 21, no. 7, pp. 558-565, 1978.
  • Dayna Blackwell, "Normalization Confluence in Federated Registry Networks," Zenodo, 2026. doi: 10.5281/zenodo.18677400.
  • P. Cousot and R. Cousot, "Abstract interpretation: a unified lattice model for static analysis of programs by construction or approximation of fixpoints," Proc. 4th ACM SIGACT-SIGPLAN Symp. on Principles of Programming Languages (POPL), pp. 238-252, 1977.
  • V. Balegas, S. Duarte, C. Ferreira, R. Rodrigues, N. Preguiça, M. Najafzadeh, and M. Shapiro, "Putting consistency back into eventual consistency," Proc. 10th European Conf. on Computer Systems (EuroSys), 2015.
  • V. Balegas, S. Duarte, C. Ferreira, R. Rodrigues, and N. Preguiça, "IPA: Invariant-preserving applications for weakly consistent replicated databases," Proc. VLDB Endowment, vol. 12, no. 4, 2018.
  • J. Meseguer, "Conditional rewriting logic as a unified model of concurrency," Theoretical Computer Science, vol. 96, no. 1, pp. 73-155, 1992.
  • F. Durán and J. Meseguer, "On the Church-Rosser and coherence properties of conditional order-sorted rewrite theories," Journal of Logic and Algebraic Programming, vol. 81, no. 7-8, pp. 816-850, 2012.
  • E. W. Dijkstra, "Self-stabilizing systems in spite of distributed control," Communications of the ACM, vol. 17, no. 11, pp. 643-644, 1974.
  • V. B. F. Gomes, M. Kleppmann, D. P. Mulligan, and A. R. Beresford, "Verifying strong eventual consistency in distributed systems," Proc. ACM on Programming Languages, vol. 1, no. OOPSLA, art. 109, 2017.