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SPECIFICATION AbsSpec | ||
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CONSTANTS | ||
NodeOne = n1 | ||
NodeTwo = n2 | ||
NodeThree = n3 | ||
Servers <- MCServers | ||
Terms <- MCTerms | ||
MaxLogLength <- MCMaxLogLength | ||
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INVARIANTS | ||
NoConflicts | ||
TypeOK | ||
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PROPERTIES | ||
AppendOnlyProp | ||
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---- MODULE MCabs ---- | ||
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EXTENDS abs | ||
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CONSTANTS NodeOne, NodeTwo, NodeThree | ||
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MCServers == {NodeOne, NodeTwo, NodeThree} | ||
MCTerms == 2..4 | ||
MCMaxLogLength == 7 | ||
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==== |
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---- MODULE abs ---- | ||
\* Abstract specification for a distributed consensus algorithm. | ||
\* Assumes that any node can atomically inspect the state of all other nodes. | ||
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EXTENDS Sequences, SequencesExt, Naturals, FiniteSets, FiniteSetsExt | ||
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CONSTANT Servers, Terms, MaxLogLength | ||
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\* Commit logs from each node | ||
\* Each log is append-only and the logs will never diverge. | ||
VARIABLE cLogs | ||
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TypeOK == | ||
/\ cLogs \in [Servers -> | ||
UNION {[1..l -> Terms] : l \in 0..MaxLogLength}] | ||
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StartTerm == Min(Terms) | ||
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InitialLogs == { | ||
<<>>, | ||
<<StartTerm, StartTerm>>, | ||
<<StartTerm, StartTerm, StartTerm, StartTerm>>} | ||
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Init == | ||
cLogs \in [Servers -> InitialLogs] | ||
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\* A node i can copy a ledger suffix from another node j. | ||
Copy(i) == | ||
\E j \in Servers : | ||
/\ Len(cLogs[j]) > Len(cLogs[i]) | ||
/\ \E l \in 1..(Len(cLogs[j]) - Len(cLogs[i])) : | ||
cLogs' = [cLogs EXCEPT ![i] = @ \o SubSeq(cLogs[j], Len(@) + 1, Len(@) + l)] | ||
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\* A node i with the longest log can extend its log upto length k. | ||
Extend(i, k) == | ||
/\ \A j \in Servers : Len(cLogs[j]) \leq Len(cLogs[i]) | ||
/\ \E l \in 0..(k - Len(cLogs[i])) : | ||
\E s \in [1..l -> Terms] : | ||
cLogs' = [cLogs EXCEPT ![i] = @ \o s] | ||
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ExtendToMax(i) == Extend(i, MaxLogLength) | ||
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\* The only possible actions are to append log entries. | ||
\* By construction there cannot be any conflicting log entries | ||
\* Log entries are copied if the node's log is not the longest. | ||
Next == | ||
\E i \in Servers : | ||
\/ Copy(i) | ||
\/ ExtendToMax(i) | ||
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AbsSpec == Init /\ [][Next]_cLogs | ||
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AppendOnlyProp == | ||
[][\A i \in Servers : IsPrefix(cLogs[i], cLogs'[i])]_cLogs | ||
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NoConflicts == | ||
\A i, j \in Servers : | ||
\/ IsPrefix(cLogs[i], cLogs[j]) | ||
\/ IsPrefix(cLogs[j], cLogs[i]) | ||
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==== |