feat(FLP): distributed algorithms for solving the consensus problem - #556
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benbrastmckie
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Jun 14, 2026
…eanprover#556) This is the first PR of the formalization of Völzer's proof of the famous result in distributed computing, first proved by Fischer, Lynch and Paterson, that distributed consensus is impossible in the presence of even a single crash fault. * `Algorithm.lean` defines the "syntax" of a distributed algorithm for solving the consensus problem and proves some basic properties. * `Consensus.lean` defines what it means for a distributed algorithm to solve the consensus problem in a fault-tolerant way and proves some basic properties. * README.md is for the overall project and mentions Lean files which will be PR-ed later. * references.bib is updated to add the papers by FLP and Völzer. Zulip discussion: [#CSLib > Impossibility of distributed consensus](https://leanprover.zulipchat.com/#narrow/channel/513188-CSLib/topic/Impossibility.20of.20distributed.20consensus/with/592462001) [#CSLib: PR reviews > leanprover#556: consensus](https://leanprover.zulipchat.com/#narrow/channel/605128-CSLib.3A-PR-reviews/topic/.23556.3A.20consensus/with/598654217)
dtumad
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Jul 13, 2026
… fairness properties (leanprover#612) This PR contains some technical machineries for reasoning about diamond and fairness properties about the distributed algorithms introduced in leanprover#556: * `CanReachVia.lean` defines the notion of reachability via a subset of processes and proves some of its properties, including some diamond properties. * `FairScheduler.lean` contains a technical machinery for constructing fair executions, which will be used in formalizing some arguments which were either only hinted at or completely glossed over in Völzer's paper. Zulip discussion: https://leanprover.zulipchat.com/#narrow/channel/513188-CSLib/topic/Impossibility.20of.20distributed.20consensus/with/592462001
intgrah
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Jul 14, 2026
… fairness properties (leanprover#612) This PR contains some technical machineries for reasoning about diamond and fairness properties about the distributed algorithms introduced in leanprover#556: * `CanReachVia.lean` defines the notion of reachability via a subset of processes and proves some of its properties, including some diamond properties. * `FairScheduler.lean` contains a technical machinery for constructing fair executions, which will be used in formalizing some arguments which were either only hinted at or completely glossed over in Völzer's paper. Zulip discussion: https://leanprover.zulipchat.com/#narrow/channel/513188-CSLib/topic/Impossibility.20of.20distributed.20consensus/with/592462001
fmontesi
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Jul 22, 2026
… fairness properties (#612) This PR contains some technical machineries for reasoning about diamond and fairness properties about the distributed algorithms introduced in #556: * `CanReachVia.lean` defines the notion of reachability via a subset of processes and proves some of its properties, including some diamond properties. * `FairScheduler.lean` contains a technical machinery for constructing fair executions, which will be used in formalizing some arguments which were either only hinted at or completely glossed over in Völzer's paper. Zulip discussion: https://leanprover.zulipchat.com/#narrow/channel/513188-CSLib/topic/Impossibility.20of.20distributed.20consensus/with/592462001
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This is the first PR of the formalization of Völzer's proof of the famous result in distributed computing, first proved by Fischer, Lynch and Paterson, that distributed consensus is impossible in the presence of even a single crash fault.
Algorithm.leandefines the "syntax" of a distributed algorithm for solving the consensus problem and proves some basic properties.Consensus.leandefines what it means for a distributed algorithm to solve the consensus problem in a fault-tolerant way and proves some basic properties.Zulip discussion:
#CSLib > Impossibility of distributed consensus
#CSLib: PR reviews > #556: consensus