feat(FLP): distributed algorithms for solving the consensus problem#556
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ctchou wants to merge 1 commit into
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feat(FLP): distributed algorithms for solving the consensus problem#556ctchou wants to merge 1 commit into
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Rebased on the current |
| the reception of message `m` and `none` denotes a stuttering step. -/ | ||
| abbrev Action (P M : Type*) := Option (Message P M) | ||
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| /-- `Dest ps x` means that if `x ≠ none`, then `x = some m` with `m.dest ∈ ps`. -/ |
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Here you meant to write DestIn.
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| /-- Given `inp : P → Bool`, the initial state of the algorithm `a` contains a single message | ||
| carrying the boolean value `inp p` to each process `p`, where the initial internal state is | ||
| `a.init p` and no decision has been made. The assumption `[Fintyep P]` is made because |
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Fintyep -> Fintype.
| its `out` field, it is not allowed to "change its mind" later. -/ | ||
| def Algorithm.recvMsg (a : Algorithm P M S) (m : Message P M) (s : State P M S) : State P M S := | ||
| let p := m.dest | ||
| { msgs := s.msgs.erase m + a.send m (s.proc p) |
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What if m wasn't contained in s.msgs to begin with? I see that is handled by Algorithm.LTS correctly, but a comment explaining this would be useful for future readers.
| /-- The global state of the distributed algorithm. -/ | ||
| structure State (P M S : Type*) where | ||
| /-- A multiset containing all messages that are in-flight (namely, they have been sent but | ||
| not yet received. Note that being a multiset implies that the messages are not ordered. -/ |
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close parens here?
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| /-- The stuttering step does not change the global state. -/ | ||
| theorem tr_none {s s' : State P M S} (h : a.LTS.Tr s none s') : s = s' := by | ||
| grind [Algorithm.LTS] |
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I think the iff here might be nicer?
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| namespace Cslib.FLP | ||
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| open Function Set Sum Multiset |
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Function is unused here.
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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.Zulip discussion:
#CSLib > Impossibility of distributed consensus