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48 lines
2.0 KiB
Plaintext
48 lines
2.0 KiB
Plaintext
--------------------- MODULE DistributedTransactionProofs -------------------
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EXTENDS DistributedTransaction, TLAPS
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THEOREM SpecTypeOK == Spec => TypeOK
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PROOF OMITTED
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LEMMA NextInv ==
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Next =>
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/\ next_ts' = next_ts + 1 \/ UNCHANGED next_ts
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/\ \E reqs : SendReqs(reqs) \/ UNCHANGED req_msgs
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/\ \E resp : SendResp(resp) \/ UNCHANGED resp_msgs
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BY DEF Next, vars, msg_vars,
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ClientPrewriteOptimisistic, ClientPrewrited, ClientCommit, ClientLockKey,
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ClientLockedKey, ClientRetryLockKey, ClientPrewritePessimistic,
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ClientPrewrited, ClientCommit, ServerLockKey, ServerPrewritePessimistic,
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ServerPrewriteOptimistic, ServerCommit, ServerCleanupStaleLock,
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ServerCleanup, ServerResolveCommitted, ServerResolveRollbacked
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LEMMA SpecNextTsMonotonicity == Spec => NextTsMonotonicity
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<1> SUFFICES ASSUME NEW ts \in Ts, TypeOK
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PROVE (ts <= next_ts) /\ [][Next]_vars => [](ts <= next_ts)
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BY SpecTypeOK DEF NextTsMonotonicity, Spec
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<1>2. (ts <= next_ts) /\ [Next]_vars => (ts <= next_ts)'
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BY NextInv DEF TypeOK, Ts, vars
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<1>3. QED
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BY <1>2, PTL
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LEMMA SpecMsgMonotonicity == Spec => MsgMonotonicity
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<1>1. ASSUME NEW req \in ReqMessages
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PROVE req \in req_msgs /\ [][Next]_vars => [](req \in req_msgs)
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<2>1. req \in req_msgs /\ (\E reqs : SendReqs(reqs)) => (req \in req_msgs)'
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BY DEF SendReqs
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<2>2. req \in req_msgs /\ [Next]_vars => (req \in req_msgs)'
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BY <2>1, NextInv DEF vars, msg_vars
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<2>3. QED
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BY <2>2, PTL
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<1>2. ASSUME NEW resp \in RespMessages
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PROVE resp \in resp_msgs /\ [][Next]_vars => [](resp \in resp_msgs)
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<3>1. resp \in resp_msgs /\ (\E resp2 : SendResp(resp2)) => (resp \in resp_msgs)'
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BY DEF SendResp
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<3>2. resp \in resp_msgs /\ [Next]_vars => (resp \in resp_msgs)'
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BY <3>1, NextInv DEF vars, msg_vars
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<3>3. QED
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BY <3>2, PTL
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<1>3. QED
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BY <1>1, <1>2, SpecTypeOK DEF MsgMonotonicity, Spec
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=============================================================================
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