Abstract
The impossibility of distributed consensus with one faulty process is a result with important consequences for real world distributed systems e.g., commits in replicated databases. Since proofs are not immune to faults and even plausible proofs with a profound formalism can conclude wrong results, we validate the fundamental result named FLP after Fischer, Lynch and Paterson by using the interactive theorem prover Isabelle/HOL. We present a formalization of distributed systems and the aforementioned consensus problem. Our proof is based on Hagen Völzer’s paper A constructive proof for FLP. In addition to the enhanced confidence in the validity of Völzer’s proof, we contribute the missing gaps to show the correctness in Isabelle/HOL. We clarify the proof details and even prove fairness of the infinite execution that contradicts consensus. Our Isabelle formalization may serve as a starting point for similar proofs of properties of distributed systems.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
Bertot, Y., Castéran, P.: Interactive Theorem Proving and Program Development: Coq’Art: The Calculus of Inductive Constructions. Texts in Theoretical Computer Science An EATCS Series. Springer, Heidelberg (2013)
Bisping, B., Brodmann, P.D., Jungnickel, T., Rickmann, C., Seidler, H., Stüber, A., Wilhelm-Weidner, A., Peters, K., Nestmann, U.: A Constructive Proof for FLP. Archive of Formal Proofs (2016). http://isa-afp.org/entries/FLP.shtml. Formal proof development
Buckley, G.N., Silberschatz, A.: An effective implementation for the generalized input-output construct of CSP. ACM Trans. Program. Lang. Syst. (TOPLAS) 5(2), 223–235 (1983)
Constable, R.L.: Effectively Nonblocking Consensus Procedures can Execute Forever - a Constructive Version of FLP. Tech. Rep. 11513, Cornell University (2011)
Constable, R.L., Allen, S.F., Bromley, H.M., Cleaveland, W.R., Cremer, J.F., Harper, R.W., Howe, D.J., Knoblock, T.B., Mendler, N.P., Panangaden, P., Sasaki, J.T., Smith, S.F.: Implementig Mathematics with the Nuprl Proof Development System. Prentice-Hall, Upper Saddle River (1986)
Fischer, M.J., Lynch, N.A., Paterson, M.S.: Impossibility of distributed consensus with one faulty process. J. ACM (JACM) 32(2), 374–382 (1985)
Kammüller, F., Wenzel, M., Paulson, L.C.: Locales - a sectioning concept for Isabelle. In: Bertot, Y., Dowek, G., Hirschowitz, A., Paulin, C., Théry, L. (eds.) TPHOLs 1999. LNCS, vol. 1690, pp. 149–165. Springer, Heidelberg (1999)
Küfner, P., Nestmann, U., Rickmann, C.: Formal verification of distributed algorithms. In: Baeten, J.C.M., Ball, T., de Boer, F.S. (eds.) TCS 2012. LNCS, vol. 7604, pp. 209–224. Springer, Heidelberg (2012)
Kumar, D., Silberschatz, A.: A counter-example to an algorithm for the generalized input-output construct of CSP. Inform. Proc. Lett. 61(6), 287 (1997)
Lamport, L.: The part-time parliament. ACM Trans. Comput. Syst. (TOCS) 16(2), 133–169 (1998)
Nipkow, T., Paulson, L.C., Wenzel, M. (eds.): Isabelle/HOL: A Proof Assistant for Higher-Order Logic. LNCS, vol. 2283. Springer, Heidelberg (2002)
Ongaro, D., Ousterhout, J.: In Search of an Understandable Consensus Algorithm. In: Proceedings of USENIX, pp. 305–320 (2014)
Völzer, H.: A constructive proof for FLP. Inform. Proc. Lett. 92(2), 83–87 (2004)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this paper
Cite this paper
Bisping, B. et al. (2016). Mechanical Verification of a Constructive Proof for FLP. In: Blanchette, J., Merz, S. (eds) Interactive Theorem Proving. ITP 2016. Lecture Notes in Computer Science(), vol 9807. Springer, Cham. https://doi.org/10.1007/978-3-319-43144-4_7
Download citation
DOI: https://doi.org/10.1007/978-3-319-43144-4_7
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-43143-7
Online ISBN: 978-3-319-43144-4
eBook Packages: Computer ScienceComputer Science (R0)