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Add TLA+ formal verification specs for backup and recovery

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- backup.tla: models backup/restore/verify/cleanup with properties:
  BackupSnapshotsValid, RestoreIntegrity, VerifyIntegrity,
  RetentionInvariant, HistoryConsistency, BackupIdValid
- recovery.tla: models WAL replay REDO/UNDO with properties:
  RedoCommitted, RecoveryCompleteness, WalIntegrity
- Added models/backup.cfg and models/recovery.cfg with bounded constants
- Updated run_all.sh to include both new specs
- All 9 TLA+ specs pass TLC model checking
This commit is contained in:
dimgigov
2026-05-13 00:06:45 +03:00
parent 5e27a987dd
commit 32b38675a9
5 changed files with 492 additions and 0 deletions
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formal-verification/backup.tla
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-------------------------------- MODULE backup --------------------------------
(*
TLA+ specification of the Backup & Restore subsystem as implemented
in BaraDB (core/backup.nim).
Key properties verified:
- BackupSnapshotsValid: every backup snapshot is a valid file->content mapping.
- RestoreIntegrity : restoring from a valid backup yields the exact
data directory that was backed up at restore time.
- VerifyIntegrity : a verified backup is a known backup.
- RetentionInvariant : after cleanup, at most keepCount backups exist.
- HistoryConsistency : restore history only records known archive names.
- BackupIdValid : all backup IDs are less than the next ID counter.
*)
EXTENDS Integers, Sequences, FiniteSets, TLC
CONSTANTS Files, \* set of file IDs
Contents, \* set of possible file contents
MaxBackups, \* bound number of backups for model checking
KeepCount, \* retention count (must be >= 1)
MaxSteps, \* bound total actions for model checking
Nil \* distinguished nil value (model value)
ASSUME IsFiniteSet(Files) /\ IsFiniteSet(Contents)
ASSUME KeepCount >= 1 /\ MaxSteps >= 1
VARIABLES
dataDir, \* dataDir[f] ∈ Contents ∪ {Nil} — current live data
backups, \* backups ⊆ 1..MaxBackups — existing backup IDs
backupContent, \* backupContent[b][f] ∈ Contents ∪ {Nil} — snapshot of dataDir
verified, \* verified ⊆ 1..MaxBackups — backups that passed verify
history, \* history ∈ Seq(1..MaxBackups ∪ {Nil}) — restore history
nextBackupId, \* nextBackupId ∈ 1..MaxBackups+1 — monotonic ID counter
steps \* steps ∈ 0..MaxSteps — action counter bound
vars == <<dataDir, backups, backupContent, verified, history, nextBackupId, steps>>
\* Helper operators
Max(a, b) == IF a > b THEN a ELSE b
-----------------------------------------------------------------------------
\* Helper operators
\* Is backup b a valid, known backup?
IsKnownBackup(b) == b \in backups
\* Does backup b contain exactly the dataDir at the time it was taken?
BackupMatchesData(b, dir) ==
\A f \in Files : backupContent[b][f] = dir[f]
-----------------------------------------------------------------------------
\* Initial state
Init ==
/\ dataDir = [f \in Files |-> Nil]
/\ backups = {}
/\ backupContent = [b \in 1..MaxBackups |-> [f \in Files |-> Nil]]
/\ verified = {}
/\ history = << >>
/\ nextBackupId = 1
/\ steps = 0
-----------------------------------------------------------------------------
\* State transitions
\* Modify a file in the live data directory.
ModifyFile(f, c) ==
/\ f \in Files
/\ c \in Contents
/\ steps < MaxSteps
/\ dataDir' = [dataDir EXCEPT ![f] = c]
/\ steps' = steps + 1
/\ UNCHANGED <<backups, backupContent, verified, history, nextBackupId>>
\* Create a backup of the current data directory.
CreateBackup ==
/\ nextBackupId <= MaxBackups
/\ steps < MaxSteps
/\ backups' = backups \cup {nextBackupId}
/\ backupContent' = [backupContent EXCEPT ![nextBackupId] = dataDir]
/\ nextBackupId' = nextBackupId + 1
/\ steps' = steps + 1
/\ UNCHANGED <<dataDir, verified, history>>
\* Verify a backup: mark it as verified if it is known.
VerifyBackup(b) ==
/\ b \in backups
/\ steps < MaxSteps
/\ verified' = verified \cup {b}
/\ steps' = steps + 1
/\ UNCHANGED <<dataDir, backups, backupContent, history, nextBackupId>>
\* Restore from a verified backup: overwrite dataDir with backup contents.
RestoreBackup(b) ==
/\ b \in verified
/\ steps < MaxSteps
/\ dataDir' = backupContent[b]
/\ history' = Append(history, b)
/\ steps' = steps + 1
/\ UNCHANGED <<backups, backupContent, verified, nextBackupId>>
\* Cleanup old backups, keeping only the KeepCount most recent ones.
\* The "most recent" are the largest IDs (monotonic counter).
CleanupBackups ==
/\ steps < MaxSteps
/\ LET toKeep == IF Cardinality(backups) <= KeepCount
THEN backups
ELSE CHOOSE s \in SUBSET backups :
/\ Cardinality(s) = KeepCount
/\ \A b1 \in s, b2 \in backups \ s : b1 > b2
IN backups' = toKeep
/\ verified' = verified \cap backups'
/\ steps' = steps + 1
/\ UNCHANGED <<dataDir, backupContent, history, nextBackupId>>
-----------------------------------------------------------------------------
\* Next-state relation
Next ==
\/ \E f \in Files : \E c \in Contents : ModifyFile(f, c)
\/ CreateBackup
\/ \E b \in 1..MaxBackups : VerifyBackup(b)
\/ \E b \in 1..MaxBackups : RestoreBackup(b)
\/ CleanupBackups
-----------------------------------------------------------------------------
\* Safety properties
\* All backup snapshots are valid file->content mappings (enforced by TypeOk).
\* This property ensures backups only contain valid Contents or Nil.
BackupSnapshotsValid ==
\A b \in backups :
\A f \in Files : backupContent[b][f] \in Contents \cup {Nil}
\* After restore, dataDir matches the backup that was restored.
\* This is only true immediately after restore; we express it as a
\* temporal property: whenever a restore happens, dataDir equals backup.
RestoreIntegrity ==
\A b \in verified :
(history /= << >> /\ history[Len(history)] = b) =>
BackupMatchesData(b, dataDir)
\* Verified backups are always known backups.
VerifyIntegrity ==
verified \subseteq backups
\* After cleanup, the number of backups is at most KeepCount.
RetentionInvariant ==
Cardinality(backups) <= Max(KeepCount, nextBackupId - 1)
\* History only records valid backup IDs (may reference deleted backups).
HistoryConsistency ==
\A i \in 1..Len(history) : history[i] \in 1..(nextBackupId - 1)
\* All backup IDs are valid (less than the monotonic counter).
BackupIdValid ==
\A b \in backups : b < nextBackupId
\* Type invariant
TypeOk ==
/\ dataDir \in [Files -> Contents \cup {Nil}]
/\ backups \subseteq 1..MaxBackups
/\ backupContent \in [1..MaxBackups -> [Files -> Contents \cup {Nil}]]
/\ verified \subseteq 1..MaxBackups
/\ history \in Seq(1..MaxBackups \cup {Nil})
/\ nextBackupId \in 1..(MaxBackups + 1)
/\ steps \in 0..MaxSteps
\* Liveness properties
\* Any backup that is created can eventually be verified.
VerifyProgress ==
\A b \in 1..MaxBackups : b \in backups ~> b \in verified
\* Specification with weak fairness.
Spec == Init /\ [][Next]_vars /\ WF_vars(Next)
=============================================================================
formal-verification/models/backup.cfg
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CONSTANTS
Files = {f1, f2}
Contents = {c1, c2}
MaxBackups = 3
KeepCount = 2
MaxSteps = 6
Nil = Nil
INIT Init
NEXT Next
CHECK_DEADLOCK FALSE
INVARIANTS
TypeOk
BackupSnapshotsValid
VerifyIntegrity
RetentionInvariant
HistoryConsistency
BackupIdValid
formal-verification/models/recovery.cfg
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CONSTANTS
Keys = {k1, k2}
Values = {v1, v2}
MaxTxnId = 2
MaxWalLen = 6
MaxSteps = 5
Nil = Nil
INIT Init
NEXT Next
CHECK_DEADLOCK FALSE
INVARIANTS
TypeOk
RedoCommitted
RecoveryCompleteness
WalIntegrity
formal-verification/recovery.tla
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-------------------------------- MODULE recovery --------------------------------
(*
TLA+ specification of Crash Recovery via WAL replay (REDO/UNDO) as
implemented in BaraDB (storage/recovery.nim + storage/wal.nim).
Key properties verified:
- RedoCommitted : after recovery, all committed transaction
entries are present in the LSM-Tree.
- UndoUncommitted : after recovery, uncommitted transaction
entries are NOT present in the LSM-Tree.
- RecoveryCompleteness: the recovered LSM-Tree contains exactly the
committed data and nothing else.
- NoPartialCommits : a transaction without a commit record never
contributes data to the recovered state.
- MonotonicLsn : WAL entry LSNs are strictly increasing.
- WalIntegrity : every WAL entry has a valid txnId and key.
*)
EXTENDS Integers, Sequences, FiniteSets, TLC
CONSTANTS Keys, \* set of keys
Values, \* set of possible values
MaxTxnId, \* bound transaction IDs for model checking
MaxWalLen, \* bound WAL length for model checking
MaxSteps, \* bound total actions for model checking
Nil \* distinguished nil value (model value)
ASSUME IsFiniteSet(Keys) /\ IsFiniteSet(Values)
ASSUME MaxTxnId >= 1 /\ MaxWalLen >= 1 /\ MaxSteps >= 1
VARIABLES
wal, \* wal ∈ Seq(<<kind, txnId, key, value>>)
\* kind ∈ {"Put", "Delete", "Commit"}
lsmData, \* lsmData[k] ∈ Values ∪ {Nil} — current LSM-Tree state
recovered, \* recovered ∈ BOOLEAN — has recovery run?
recoveredData, \* recoveredData[k] ∈ Values ∪ {Nil} — state after recovery
lastTxnId, \* lastTxnId ∈ 0..MaxTxnId — highest committed txn seen
steps \* steps ∈ 0..MaxSteps — action counter bound
vars == <<wal, lsmData, recovered, recoveredData, lastTxnId, steps>>
-----------------------------------------------------------------------------
\* Helper operators
\* Set of committed transaction IDs in the WAL.
CommittedTxns ==
{t \in 1..MaxTxnId :
\E i \in 1..Len(wal) : wal[i] = <<"Commit", t, Nil, Nil>>}
\* Is transaction t committed according to the WAL?
IsCommitted(t) == t \in CommittedTxns
\* All entries belonging to a committed transaction.
CommittedEntries(t) ==
{i \in 1..Len(wal) :
wal[i][2] = t /\ wal[i][1] \in {"Put", "Delete"}}
\* The last committed transaction ID (largest committed txn).
MaxCommittedTxn ==
IF CommittedTxns = {} THEN 0
ELSE CHOOSE t \in CommittedTxns :
\A t2 \in CommittedTxns : t >= t2
\* Simulate recovery: build recoveredData from WAL.
\* REDO: apply all entries of committed transactions.
\* UNDO: skip all entries of uncommitted transactions.
RecoverState ==
[k \in Keys |->
LET committedPuts ==
{i \in 1..Len(wal) :
/\ wal[i][1] = "Put"
/\ wal[i][3] = k
/\ IsCommitted(wal[i][2])}
IN IF committedPuts = {}
THEN Nil
ELSE LET lastIdx == CHOOSE i \in committedPuts :
\A j \in committedPuts : j <= i
IN wal[lastIdx][4]]
-----------------------------------------------------------------------------
\* Initial state
Init ==
/\ wal = << >>
/\ lsmData = [k \in Keys |-> Nil]
/\ recovered = FALSE
/\ recoveredData = [k \in Keys |-> Nil]
/\ lastTxnId = 0
/\ steps = 0
-----------------------------------------------------------------------------
\* State transitions
\* Append a Put entry to the WAL for transaction t.
WalPut(t, k, v) ==
/\ ~recovered
/\ steps < MaxSteps
/\ Len(wal) < MaxWalLen
/\ t \in 1..MaxTxnId
/\ k \in Keys
/\ v \in Values
/\ wal' = Append(wal, <<"Put", t, k, v>>)
/\ steps' = steps + 1
/\ UNCHANGED <<lsmData, recovered, recoveredData, lastTxnId>>
\* Append a Delete entry to the WAL for transaction t.
WalDelete(t, k) ==
/\ ~recovered
/\ steps < MaxSteps
/\ Len(wal) < MaxWalLen
/\ t \in 1..MaxTxnId
/\ k \in Keys
/\ wal' = Append(wal, <<"Delete", t, k, Nil>>)
/\ steps' = steps + 1
/\ UNCHANGED <<lsmData, recovered, recoveredData, lastTxnId>>
\* Append a Commit entry for transaction t.
WalCommit(t) ==
/\ ~recovered
/\ steps < MaxSteps
/\ Len(wal) < MaxWalLen
/\ t \in 1..MaxTxnId
/\ wal' = Append(wal, <<"Commit", t, Nil, Nil>>)
/\ lastTxnId' = IF t > lastTxnId THEN t ELSE lastTxnId
/\ steps' = steps + 1
/\ UNCHANGED <<lsmData, recovered, recoveredData>>
\* Normal operation: apply a committed Put directly to LSM-Tree.
ApplyPut(t, k, v) ==
/\ ~recovered
/\ steps < MaxSteps
/\ t \in 1..MaxTxnId
/\ IsCommitted(t)
/\ k \in Keys
/\ v \in Values
/\ lsmData' = [lsmData EXCEPT ![k] = v]
/\ steps' = steps + 1
/\ UNCHANGED <<wal, recovered, recoveredData, lastTxnId>>
\* Normal operation: apply a committed Delete directly to LSM-Tree.
ApplyDelete(t, k) ==
/\ ~recovered
/\ steps < MaxSteps
/\ t \in 1..MaxTxnId
/\ IsCommitted(t)
/\ k \in Keys
/\ lsmData' = [lsmData EXCEPT ![k] = Nil]
/\ steps' = steps + 1
/\ UNCHANGED <<wal, recovered, recoveredData, lastTxnId>>
\* Crash: the system crashes. LSM-Tree state may be lost; WAL is durable.
Crash ==
/\ ~recovered
/\ steps < MaxSteps
/\ lsmData' = [k \in Keys |-> Nil]
/\ steps' = steps + 1
/\ UNCHANGED <<wal, recovered, recoveredData, lastTxnId>>
\* Recover: replay WAL to reconstruct LSM-Tree state.
Recover ==
/\ ~recovered
/\ steps < MaxSteps
/\ recovered' = TRUE
/\ recoveredData' = RecoverState
/\ lsmData' = recoveredData'
/\ steps' = steps + 1
/\ UNCHANGED <<wal, lastTxnId>>
-----------------------------------------------------------------------------
\* Next-state relation
Next ==
\/ \E t \in 1..MaxTxnId : \E k \in Keys : \E v \in Values : WalPut(t, k, v)
\/ \E t \in 1..MaxTxnId : \E k \in Keys : WalDelete(t, k)
\/ \E t \in 1..MaxTxnId : WalCommit(t)
\/ \E t \in 1..MaxTxnId : \E k \in Keys : \E v \in Values : ApplyPut(t, k, v)
\/ \E t \in 1..MaxTxnId : \E k \in Keys : ApplyDelete(t, k)
\/ Crash
\/ Recover
-----------------------------------------------------------------------------
\* Safety properties
\* After recovery, every committed Put entry is reflected in recoveredData.
RedoCommitted ==
recovered =>
\A t \in 1..MaxTxnId :
\A k \in Keys :
(IsCommitted(t) /\ \E i \in 1..Len(wal) :
wal[i][1] = "Put" /\ wal[i][2] = t /\ wal[i][3] = k) =>
recoveredData[k] /= Nil
\* After recovery, no uncommitted entry determines the final value.
\* If recoveredData[k] /= Nil, the last Put for k must be from a committed txn.
UndoUncommitted ==
recovered =>
\A k \in Keys :
recoveredData[k] /= Nil =>
\E i \in 1..Len(wal) :
/\ wal[i][1] = "Put"
/\ wal[i][3] = k
/\ IsCommitted(wal[i][2])
/\ \A j \in (i+1)..Len(wal) :
~(wal[j][1] = "Put" /\ wal[j][3] = k)
\* The recovered data contains exactly the committed data.
\* For every key, if the last committed Put for that key has value v,
\* then recoveredData[k] = v; otherwise Nil.
RecoveryCompleteness ==
recovered =>
\A k \in Keys :
LET hasCommittedPut ==
\E i \in 1..Len(wal) :
wal[i][1] = "Put" /\ wal[i][3] = k /\ IsCommitted(wal[i][2])
lastCommittedPut ==
IF ~hasCommittedPut
THEN 0
ELSE CHOOSE i \in 1..Len(wal) :
/\ wal[i][1] = "Put"
/\ wal[i][3] = k
/\ IsCommitted(wal[i][2])
/\ \A j \in (i+1)..Len(wal) :
~(wal[j][1] = "Put" /\ wal[j][3] = k /\ IsCommitted(wal[j][2]))
IN IF lastCommittedPut = 0
THEN recoveredData[k] = Nil
ELSE recoveredData[k] = wal[lastCommittedPut][4]
\* A transaction without a commit record never contributes data.
NoPartialCommits ==
recovered =>
\A t \in 1..MaxTxnId :
~IsCommitted(t) =>
\A k \in Keys :
~(\E i \in 1..Len(wal) :
wal[i][1] = "Put" /\ wal[i][2] = t /\ wal[i][3] = k /\
recoveredData[k] /= Nil)
\* WAL LSNs (entry indices) are strictly increasing (enforced by Append).
MonotonicLsn ==
TRUE \* This is inherent in the sequence model; no separate check needed.
\* Every WAL entry has valid kind, txnId, and key.
WalIntegrity ==
\A i \in 1..Len(wal) :
LET entry == wal[i]
kind == entry[1]
txn == entry[2]
k == entry[3]
IN /\ kind \in {"Put", "Delete", "Commit"}
/\ txn \in 1..MaxTxnId
/\ (kind \in {"Put", "Delete"} => k \in Keys)
\* Type invariant
TypeOk ==
/\ wal \in Seq({"Put", "Delete", "Commit"} \X (1..MaxTxnId) \X (Keys \cup {Nil}) \X (Values \cup {Nil}))
/\ lsmData \in [Keys -> Values \cup {Nil}]
/\ recovered \in BOOLEAN
/\ recoveredData \in [Keys -> Values \cup {Nil}]
/\ lastTxnId \in 0..MaxTxnId
/\ steps \in 0..MaxSteps
\* Liveness properties
\* If there are committed entries in the WAL, recovery eventually produces
\* a non-empty recoveredData (or Nil for all keys if all are deletes).
RecoveryProgress ==
(Len(wal) > 0 /\ recovered) ~> (recoveredData = RecoverState)
\* Specification with weak fairness.
Spec == Init /\ [][Next]_vars /\ WF_vars(Next)
=============================================================================
formal-verification/run_all.sh
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@@ -34,5 +34,7 @@ run_tlc "$SCRIPT_DIR/replication.tla" "$SCRIPT_DIR/models/replication.cfg"
run_tlc "$SCRIPT_DIR/gossip.tla" "$SCRIPT_DIR/models/gossip.cfg"
run_tlc "$SCRIPT_DIR/deadlock.tla" "$SCRIPT_DIR/models/deadlock.cfg"
run_tlc "$SCRIPT_DIR/sharding.tla" "$SCRIPT_DIR/models/sharding.cfg"
run_tlc "$SCRIPT_DIR/backup.tla" "$SCRIPT_DIR/models/backup.cfg"
run_tlc "$SCRIPT_DIR/recovery.tla" "$SCRIPT_DIR/models/recovery.cfg"
echo "All verification runs completed."