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\* Copyright 2019 MongoDB, Inc.
\*
\* This work is licensed under:
\* - Creative Commons Attribution-3.0 United States License
\* http://creativecommons.org/licenses/by/3.0/us/
--------------------------------- MODULE RaftMongoWithRaftReconfig --------------------------------
\* This is the formal specification for the Raft consensus algorithm in MongoDB.
\* It allows reconfig using the protocol for single server membership changes described in Raft.
\* Note that we did not choose to implement the protocol for single server membership changes
\* described in Raft. This specification was for exploratory purposes only.
EXTENDS Naturals, FiniteSets, Sequences, TLC
\* The set of server IDs
CONSTANTS Server
\* Server states.
\* Candidate is not used, but this is fine.
CONSTANTS Follower, Candidate, Leader
\* A reserved value.
CONSTANTS Nil
----
\* Global variables
\* Servers in a given config version.
\* e.g. << {S1, S2}, {S1, S2, S3} >>
VARIABLE configs
\* The set of log entries that have been acknowledged as committed, i.e.
\* "immediately committed" entries. It does not include "prefix committed"
\* entries, which are allowed to roll back on minority nodes.
VARIABLE committedEntries
----
\* The following variables are all per server (functions with domain Server).
\* The server's term number.
VARIABLE currentTerm
\* The server's state (Follower, Candidate, or Leader).
VARIABLE state
serverVars == <<currentTerm, state>>
\* A Sequence of log entries. The index into this sequence is the index of the
\* log entry. Unfortunately, the Sequence module defines Head(s) as the entry
\* with index 1, so be careful not to use that!
VARIABLE log
logVars == <<log, committedEntries>>
\* End of per server variables.
----
\* All variables; used for stuttering (asserting state hasn't changed).
vars == <<serverVars, logVars, configs>>
----
\* Helpers
\* The term of the last entry in a log, or 0 if the log is empty.
GetTerm(xlog, index) == IF index = 0 THEN 0 ELSE xlog[index].term
LogTerm(i, index) == GetTerm(log[i], index)
LastTerm(xlog) == GetTerm(xlog, Len(xlog))
\* Return the minimum value from a set, or undefined if the set is empty.
Min(s) == CHOOSE x \in s : \A y \in s : x <= y
\* Return the maximum value from a set, or undefined if the set is empty.
Max(s) == CHOOSE x \in s : \A y \in s : x >= y
\* The config version in the node's last entry.
GetConfigVersion(i) == log[i][Len(log[i])].configVersion
\* Gets the node's first entry with a given config version.
GetConfigEntry(i, configVersion) == LET configEntries == {index \in 1..Len(log[i]) :
log[i][index].configVersion = configVersion}
IN Min(configEntries)
\* The servers that are in the same config as i.
ServerViewOn(i) == configs[GetConfigVersion(i)]
\* The set of all quorums. This just calculates simple majorities, but the only
\* important property is that every quorum overlaps with every other.
Quorum(me) == {sub \in SUBSET(ServerViewOn(me)) : Cardinality(sub) * 2 > Cardinality(ServerViewOn(me))}
----
\* Define initial values for all variables
InitServerVars == /\ currentTerm = [i \in Server |-> 0]
/\ state = [i \in Server |-> Follower]
InitLogVars == /\ log = [i \in Server |-> << [term |-> 0, configVersion |-> 1] >>]
/\ committedEntries = {[term |-> 0, index |-> 1]}
InitConfigs == configs = << Server >>
Init == /\ InitServerVars
/\ InitLogVars
/\ InitConfigs
----
\* Message handlers
\* i = recipient, j = sender, m = message
AppendOplog(i, j) ==
/\ state[i] = Follower \* Disable primary catchup and draining
/\ j \in ServerViewOn(i) \* j is in the config of i.
/\ Len(log[i]) < Len(log[j])
/\ LastTerm(log[i]) = LogTerm(j, Len(log[i]))
/\ log' = [log EXCEPT ![i] = Append(log[i], log[j][Len(log[i]) + 1])]
/\ UNCHANGED <<serverVars, committedEntries, configs>>
CanRollbackOplog(i, j) ==
/\ j \in ServerViewOn(i) \* j is in the config of i.
/\ Len(log[i]) > 0
/\ \* The log with later term is more up-to-date
LastTerm(log[i]) < LastTerm(log[j])
/\
\/ Len(log[i]) > Len(log[j])
\* There seems no short-cut of OR clauses, so I have to specify the negative case
\/ /\ Len(log[i]) <= Len(log[j])
/\ LastTerm(log[i]) /= LogTerm(j, Len(log[i]))
RollbackOplog(i, j) ==
/\ CanRollbackOplog(i, j)
\* Rollback 1 oplog entry
/\ LET new == [index2 \in 1..(Len(log[i]) - 1) |-> log[i][index2]]
IN log' = [log EXCEPT ![i] = new]
/\ UNCHANGED <<serverVars, committedEntries, configs>>
\* The set of nodes in my config that has log[me][logIndex] in their oplog
Agree(me, logIndex) ==
{ node \in ServerViewOn(me) :
/\ Len(log[node]) >= logIndex
/\ LogTerm(me, logIndex) = LogTerm(node, logIndex) }
NotBehind(me, j) == \/ LastTerm(log[me]) > LastTerm(log[j])
\/ /\ LastTerm(log[me]) = LastTerm(log[j])
/\ Len(log[me]) >= Len(log[j])
\* ACTION
\* i = the new primary node.
BecomePrimaryByMagic(i, ayeVoters) ==
/\ \A j \in ayeVoters : /\ i \in ServerViewOn(j)
/\ NotBehind(i, j)
/\ currentTerm[j] <= currentTerm[i]
/\ ayeVoters \in Quorum(i)
/\ state' = [index \in Server |-> IF index \notin ayeVoters
THEN state[index]
ELSE IF index = i THEN Leader ELSE Follower]
/\ currentTerm' = [index \in Server |-> IF index \in (ayeVoters \union {i})
THEN currentTerm[i] + 1
ELSE currentTerm[index]]
/\ UNCHANGED <<logVars, configs>>
\* ACTION
\* Leader i receives a client request to add v to the log.
ClientWrite(i) ==
/\ state[i] = Leader
/\ LET entry == [term |-> currentTerm[i], configVersion |-> GetConfigVersion(i)]
newLog == Append(log[i], entry)
IN log' = [log EXCEPT ![i] = newLog]
/\ UNCHANGED <<serverVars, committedEntries, configs>>
\* ACTION
\* Commit the latest log entry on a primary.
AdvanceCommitPoint ==
\E leader \in Server : \E acknowledgers \in SUBSET Server :
/\ state[leader] = Leader
/\ acknowledgers \subseteq Agree(leader, Len(log[leader]))
/\ acknowledgers \in Quorum(leader)
\* If we comment out the following line, a replicated log entry from old primary will voilate the safety.
\* [ P (2), S (), S ()]
\* [ S (2), S (), P (3)]
\* [ S (2), S (2), P (3)] !!! the log from term 2 shouldn't be considered as committed.
/\ LogTerm(leader, Len(log[leader])) = currentTerm[leader]
\* If an acknowledger has a higher term, the leader would step down.
/\ \A j \in acknowledgers : currentTerm[j] <= currentTerm[leader]
/\ committedEntries' = committedEntries \union {[term |-> LastTerm(log[leader]), index |-> Len(log[leader])]}
/\ UNCHANGED <<serverVars, log, configs>>
UpdateTermThroughHeartbeat(i, j) ==
/\ j \in ServerViewOn(i) \* j is in the config of i.
/\ currentTerm[j] > currentTerm[i]
/\ currentTerm' = [currentTerm EXCEPT ![i] = currentTerm[j]]
/\ state' = [state EXCEPT ![i] = IF ~(state[i] = Leader) THEN state[i] ELSE Follower]
/\ UNCHANGED <<logVars, configs>>
Reconfig(i, newConfig) ==
/\ state[i] = Leader
/\ i \in newConfig
\* Only support single node addition/removal.
/\ Cardinality(ServerViewOn(i) \ newConfig) + Cardinality(newConfig \ ServerViewOn(i)) <= 1
\* The config entry must be committed.
/\ LET configEntry == GetConfigEntry(i, GetConfigVersion(i))
IN [term |-> log[i][configEntry].term, index |-> configEntry] \in committedEntries
\* The primary must have committed an entry in its current term.
/\ \E entry \in committedEntries : entry.term = currentTerm[i]
/\ configs' = Append(configs, newConfig)
/\ LET entry == [term |-> currentTerm[i], configVersion |-> Len(configs) + 1]
newLog == Append(log[i], entry)
IN log' = [log EXCEPT ![i] = newLog]
/\ UNCHANGED <<serverVars, committedEntries>>
----
AppendOplogAction ==
\E i,j \in Server : AppendOplog(i, j)
RollbackOplogAction ==
\E i,j \in Server : RollbackOplog(i, j)
BecomePrimaryByMagicAction ==
\E i \in Server : \E ayeVoters \in SUBSET(Server) : BecomePrimaryByMagic(i, ayeVoters)
ClientWriteAction ==
\E i \in Server : ClientWrite(i)
UpdateTermThroughHeartbeatAction ==
\E i,j \in Server : UpdateTermThroughHeartbeat(i, j)
ReconfigAction ==
\E i \in Server : \E newConfig \in SUBSET(Server) : Reconfig(i, newConfig)
----
\* Defines how the variables may transition.
Next ==
\* --- Replication protocol
\/ AppendOplogAction
\/ RollbackOplogAction
\/ BecomePrimaryByMagicAction
\/ ClientWriteAction
\/ AdvanceCommitPoint
\/ ReconfigAction
\/ UpdateTermThroughHeartbeatAction
Liveness ==
/\ SF_vars(AppendOplogAction)
/\ SF_vars(RollbackOplogAction)
\* A new primary should eventually write one entry.
/\ WF_vars(\E i \in Server : LastTerm(log[i]) # currentTerm[i] /\ ClientWrite(i))
\* /\ WF_vars(ClientWriteAction)
\* The specification must start with the initial state and transition according
\* to Next.
Spec == Init /\ [][Next]_vars /\ Liveness
\* RollbackCommitted and NeverRollbackCommitted are not actions.
\* They are used for verification.
RollbackCommitted(i) ==
/\ [term |-> LastTerm(log[i]), index |-> Len(log[i])] \in committedEntries
/\ \E j \in Server: CanRollbackOplog(i, j)
NeverRollbackCommitted ==
\A i \in Server: ~RollbackCommitted(i)
TwoPrimariesInSameTerm ==
\E i, j \in Server :
/\ i # j
/\ currentTerm[i] = currentTerm[j]
/\ state[i] = Leader
/\ state[j] = Leader
NoTwoPrimariesInSameTerm == ~TwoPrimariesInSameTerm
===============================================================================
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