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Add DistributedReplicatedLog example.
The property `IsSync` in `DistributedReplicatedLog.tla` does not hold; the node with the longest log may forever append a value before the other nodes can catch up. TLC finds the following (valid) counterexample (for three nodes): ```tla Error: Temporal properties were violated. Error: The following behavior constitutes a counter-example: State 1: <Initial predicate> cLogs = (n1 :> <<>> @@ n2 :> <<>> @@ n3 :> <<>>) State 2: <Extend(n2) line 35, col 5 to line 38, col 49 of module DistributedReplicatedLog> cLogs = (n1 :> <<>> @@ n2 :> <<v>> @@ n3 :> <<>>) State 3: <Extend(n2) line 35, col 5 to line 38, col 49 of module DistributedReplicatedLog> cLogs = (n1 :> <<>> @@ n2 :> <<v, v>> @@ n3 :> <<>>) State 4: <Copy(n3) line 26, col 9 to line 32, col 96 of module DistributedReplicatedLog> cLogs = (n1 :> <<>> @@ n2 :> <<v, v>> @@ n3 :> <<v>>) Back to state 2: <Copy(n1) line 26, col 9 to line 32, col 96 of module DistributedReplicatedLog> ``` Signed-off-by: Markus Alexander Kuppe <[email protected]>
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‎README.md

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| [Software-Defined Perimeter](specifications/SDP_Verification) | Luming Dong, Zhi Niu | | | | ✔ | |
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| [Simplified Fast Paxos](specifications/SimplifiedFastPaxos) | Lim Ngian Xin Terry, Gaurav Gandhi | | | | ✔ | |
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| [Checkpoint Coordination](specifications/CheckpointCoordination) | Andrew Helwer | | | | ✔ | |
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| [Finitizing Monotonic Systems](specifications/FiniteMonotonic) | Andrew Helwer | | | | ✔ | |
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| [Finitizing Monotonic Systems](specifications/FiniteMonotonic) | Andrew Helwer, Stephan Merz, Markus Kuppe | | ✔ | | ✔ | |
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| [Multi-Car Elevator System](specifications/MultiCarElevator) | Andrew Helwer | | | | ✔ | |
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| [Nano Blockchain Protocol](specifications/NanoBlockchain) | Andrew Helwer | | | | ✔ | |
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| [The Readers-Writers Problem](specifications/ReadersWriters) | Isaac DeFrain | | | | ✔ | |

‎manifest.json

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"tlaLanguageVersion": 2,
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"features": [],
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"models": []
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},
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{
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"path": "specifications/FiniteMonotonic/MCDistributedReplicatedLog.tla",
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"communityDependencies": ["FiniteSetsExt"],
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"tlaLanguageVersion": 2,
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"features": [],
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"models": [
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{
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"path": "specifications/FiniteMonotonic/MCDistributedReplicatedLog.cfg",
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"runtime": "00:00:05",
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"size": "small",
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"mode": "exhaustive search",
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"features": [
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"liveness", "view"
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],
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"result": "success",
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"distinctStates": 37,
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"totalStates": 271,
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"stateDepth": 4
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}
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]
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},
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{
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"path": "specifications/FiniteMonotonic/DistributedReplicatedLog.tla",
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"communityDependencies": ["SequencesExt", "FiniteSetsExt"],
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"tlaLanguageVersion": 2,
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"features": [],
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"models": []
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}
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]
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},

‎specifications/FiniteMonotonic/DistributedReplicatedLog.tla

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This spec was inspired by https://github.com/microsoft/CCF/blob/main/tla/consensus/abs.tla.
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This spec has a machine-closed fairness constraint, which differs from the the CRDT and
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ReplicatedLog examples. However, this spec assumes that a server can consistently read the
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state of all other servers, which is clearly not a realistic assumption for a real
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distributed system. A real system would rely on some messaging protocol to determine the
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lag between servers (compare Raft).
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---- MODULE DistributedReplicatedLog ----
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EXTENDS Sequences, SequencesExt, Integers, FiniteSets, FiniteSetsExt
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CONSTANT Lag, Servers, Values
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ASSUME Lag \in Nat /\ IsFiniteSet(Servers)
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VARIABLE cLogs
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vars == <<cLogs>>
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TypeOK ==
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/\ cLogs \in [Servers -> Seq(Values)]
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Init ==
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/\ cLogs \in [Servers -> {<< >>}]
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Copy(i) ==
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\E j \in Servers:
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/\ Len(cLogs[j]) > Len(cLogs[i])
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/\ \* Sync some prefix up to prefix = suffix of the unsynced suffix.
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LET L == (Len(cLogs[j]) - Len(cLogs[i]))
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\* Force to proportionally to the lag L copy more.
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\* Lag: 1 -> 0..L, 2 -> 1..L, 3 -> 2..L
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IN \E l \in L-1 .. L:
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cLogs' = [cLogs EXCEPT ![i] = @ \o SubSeq(cLogs[j], Len(@) + 1, Len(@) + l)]
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Extend(i) ==
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/\ \A j \in Servers:
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Len(cLogs[j]) \leq Len(cLogs[i])
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/\ \E s \in BoundedSeq(Values, Lag - Max({Len(cLogs[i]) - Len(cLogs[j]) : j \in Servers})):
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cLogs' = [cLogs EXCEPT ![i] = @ \o s]
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Next ==
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\E i \in Servers:
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\/ Copy(i)
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\/ Extend(i)
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Spec ==
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/\ Init
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/\ [][Next]_vars
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/\ \A s \in Servers: WF_vars(Extend(s)) /\ WF_vars(Copy(s))
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----
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\* Invariants
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Abs(n) ==
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IF n < 0 THEN -n ELSE n
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BoundedLag ==
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\A i, j \in Servers: Abs(Len(cLogs[i]) - Len(cLogs[j])) <= Lag
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THEOREM Spec => []BoundedLag
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----
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\* Liveness
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AllExtending ==
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\A s \in Servers: []<><<IsStrictPrefix(cLogs[s], cLogs'[s])>>_cLogs
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THEOREM Spec => AllExtending
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InSync ==
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\* TLC correctly verifies that InSync is not a property of the system because
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\* followers are permitted to copy only a prefix of the missing suffix.
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\A i, j \in Servers : []<>(cLogs[i] = cLogs[j])
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====

‎specifications/FiniteMonotonic/MCDistributedReplicatedLog.cfg

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SPECIFICATION
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Spec
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CONSTANTS
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Servers = {n1, n2, n3}
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Values = {v}
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Lag = 3
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INVARIANTS
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TypeOK
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BoundedLag
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PROPERTIES
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AllExtending
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InSync
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VIEW
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DropCommonPrefix
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CHECK_DEADLOCK
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TRUE

‎specifications/FiniteMonotonic/MCDistributedReplicatedLog.tla

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---- MODULE MCDistributedReplicatedLog ----
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EXTENDS DistributedReplicatedLog, FiniteSetsExt
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ASSUME
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\* LongestCommonPrefix in View for a single server would always shorten the
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\* log to <<>>, reducing the state-space to a single state.
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Cardinality(Servers) > 1
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----
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\* Combining the following conditions makes the state space finite:
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\* 1) The divergence of any two logs is bounded (See Extend action)
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\*
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\* 2) Terms is a *finite* set.
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ASSUME IsFiniteSet(Values)
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\*
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\* 3) The longest common prefix of all logs is discarded.
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DropCommonPrefix ==
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LET commonPrefixBound == Len(LongestCommonPrefix(Range(cLogs)))
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Drop(seq, idx) == SubSeq(seq, idx + 1, Len(seq))
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IN [ s \in Servers |-> Drop(cLogs[s], commonPrefixBound) ]
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====

‎specifications/FiniteMonotonic/README.md

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Specs & models include:
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- `CRDT.tla`: the spec of a basic grow-only counter CRDT
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- `ReplicatedLog.tla`: the "spec of a basic append-only replicated log
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- `ReplicatedLog.tla`: the spec of a basic append-only replicated log
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- `DistributedReplicatedLog.tla`: a spec of a distributed replicated log that demonstrates how the technique can be used to find violations of a liveness property (`Insync`).

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