{ "meta": "", "mcConfig": { "CONSTANTS": [ "rm1", "rm2", "rm3" ] }, "source": "------------------------------- MODULE TwoPhase ----------------------------- \r\n(***************************************************************************)\r\n(* This specification describes the Two-Phase Commit protocol, in which a *)\r\n(* transaction manager (TM) coordinates the resource managers (RMs) to *)\r\n(* implement the Transaction Commit specification of module $TCommit$. In *)\r\n(* this specification, RMs spontaneously issue $Prepared$ messages. We *)\r\n(* ignore the $Prepare$ messages that the TM can send to the *)\r\n(* RMs.\\vspace{.4em} *)\r\n(* *)\r\n(* For simplicity, we also eliminate $Abort$ messages sent by an RM when *)\r\n(* it decides to abort. Such a message would cause the TM to abort the *)\r\n(* transaction, an event represented here by the TM spontaneously deciding *)\r\n(* to abort.\\vspace{.4em} *)\r\n(* *)\r\n(* This specification describes only the safety properties of the *)\r\n(* protocol--that is, what is allowed to happen. What must happen would *)\r\n(* be described by liveness properties, which we do not specify. *)\r\n(***************************************************************************)\r\nCONSTANT RM \\* The set of resource managers\r\n\r\nVARIABLES\r\n rmState, \\* $rmState[rm]$ is the state of resource manager RM.\r\n tmState, \\* The state of the transaction manager.\r\n tmPrepared, \\* The set of RMs from which the TM has received $\"Prepared\"$\r\n \\* messages.\r\n msgs \r\n (***********************************************************************)\r\n (* In the protocol, processes communicate with one another by sending *)\r\n (* messages. Since we are specifying only safety, a process is not *)\r\n (* required to receive a message, so there is no need to model message *)\r\n (* loss. (There's no difference between a process not being able to *)\r\n (* receive a message because the message was lost and a process simply *)\r\n (* ignoring the message.) We therefore represent message passing with *)\r\n (* a variable $msgs$ whose value is the set of all messages that have *)\r\n (* been sent. Messages are never removed from $msgs$. An action *)\r\n (* that, in an implementation, would be enabled by the receipt of a *)\r\n (* certain message is here enabled by the existence of that message in *)\r\n (* $msgs$. (Receipt of the same message twice is therefore allowed; *)\r\n (* but in this particular protocol, receiving a message for the second *)\r\n (* time has no effect.) *)\r\n (***********************************************************************)\r\n\r\nMessage ==\r\n (*************************************************************************)\r\n (* The set of all possible messages. Messages of type $\"Prepared\"$ are *)\r\n (* sent from the RM indicated by the message's $rm$ field to the TM\\@. *)\r\n (* Messages of type $\"Commit\"$ and $\"Abort\"$ are broadcast by the TM, to *)\r\n (* be received by all RMs. The set $msgs$ contains just a single copy *)\r\n (* of such a message. *)\r\n (*************************************************************************)\r\n [type : {\"Prepared\"}, rm : RM] \\cup [type : {\"Commit\", \"Abort\"}]\r\n \r\nTPTypeOK == \r\n (*************************************************************************)\r\n (* The type-correctness invariant *)\r\n (*************************************************************************)\r\n \/\\ rmState \\in [RM -> {\"working\", \"prepared\", \"committed\", \"aborted\"}]\r\n \/\\ tmState \\in {\"init\", \"committed\", \"aborted\", \"ready\"}\r\n \/\\ tmPrepared \\subseteq RM\r\n \/\\ msgs \\subseteq Message\r\n\r\nInit == \r\n (*************************************************************************)\r\n (* The initial predicate. *)\r\n (*************************************************************************)\r\n \/\\ rmState = [rm \\in RM |-> \"working\"]\r\n \/\\ tmState = \"init\"\r\n \/\\ tmPrepared = {}\r\n \/\\ msgs = {}\r\n-----------------------------------------------------------------------------\r\n(***************************************************************************)\r\n(* We now define the actions that may be performed by the processes, first *)\r\n(* the TM's actions, then the RMs' actions. *)\r\n(***************************************************************************)\r\nTMRcvPrepared(rm) ==\r\n (*************************************************************************)\r\n (* The TM receives a $\"Prepared\"$ message from resource manager $rm$. *)\r\n (*************************************************************************)\r\n \/\\ tmState = \"init\"\r\n \/\\ [type |-> \"Prepared\", rm |-> rm] \\in msgs\r\n \/\\ tmPrepared' = tmPrepared \\cup {rm}\r\n \/\\ UNCHANGED <>\r\n\r\nTMReady ==\r\n (*************************************************************************)\r\n (* The TM gets ready. *)\r\n (*************************************************************************)\r\n \/\\ tmState = \"init\"\r\n \/\\ tmState' = \"ready\"\r\n \/\\ UNCHANGED <>\r\n\r\nTMCommit ==\r\n (*************************************************************************)\r\n (* The TM commits the transaction; enabled iff the TM is in its initial *)\r\n (* state and every RM has sent a $\"Prepared\"$ message. *)\r\n (*************************************************************************)\r\n \/\\ tmState = \"init\"\r\n \/\\ tmPrepared = RM\r\n \/\\ tmState' = \"committed\"\r\n \/\\ msgs' = msgs \\cup {[type |-> \"Commit\"]}\r\n \/\\ UNCHANGED <>\r\n\r\nTMInit ==\r\n (*************************************************************************)\r\n (* The TM sets its state to \"init\" *)\r\n (*************************************************************************)\r\n \/\\ tmState = \"ready\"\r\n \/\\ tmState' = \"init\"\r\n \/\\ UNCHANGED <>\r\n\r\nTMAbort ==\r\n (*************************************************************************)\r\n (* The TM spontaneously aborts the transaction. *)\r\n (*************************************************************************)\r\n \/\\ tmState = \"init\"\r\n \/\\ tmState' = \"aborted\"\r\n \/\\ msgs' = msgs \\cup {[type |-> \"Abort\"]}\r\n \/\\ UNCHANGED <>\r\n\r\nRMPrepare(rm) == \r\n (*************************************************************************)\r\n (* Resource manager $rm$ prepares. *)\r\n (*************************************************************************)\r\n \/\\ rmState[rm] = \"working\"\r\n \/\\ rmState' = [rmState EXCEPT ![rm] = \"prepared\"]\r\n \/\\ msgs' = msgs \\cup {[type |-> \"Prepared\", rm |-> rm]}\r\n \/\\ UNCHANGED <>\r\n \r\nRMChooseToAbort(rm) ==\r\n (*************************************************************************)\r\n (* Resource manager $rm$ spontaneously decides to abort. As noted *)\r\n (* above, $rm$ does not send any message in our simplified spec. *)\r\n (*************************************************************************)\r\n \/\\ rmState[rm] = \"working\"\r\n \/\\ rmState' = [rmState EXCEPT ![rm] = \"aborted\"]\r\n \/\\ UNCHANGED <>\r\n\r\nRMRcvCommitMsg(rm) ==\r\n (*************************************************************************)\r\n (* Resource manager $rm$ is told by the TM to commit. *)\r\n (*************************************************************************)\r\n \/\\ [type |-> \"Commit\"] \\in msgs\r\n \/\\ rmState' = [rmState EXCEPT ![rm] = \"committed\"]\r\n \/\\ UNCHANGED <>\r\n\r\nRMRcvAbortMsg(rm) ==\r\n (*************************************************************************)\r\n (* Resource manager $rm$ is told by the TM to abort. *)\r\n (*************************************************************************)\r\n \/\\ [type |-> \"Abort\"] \\in msgs\r\n \/\\ rmState' = [rmState EXCEPT ![rm] = \"aborted\"]\r\n \/\\ UNCHANGED <>\r\n\r\nNext ==\r\n \\\/ TMCommit \\\/ TMAbort \\\/ TMReady \\\/ TMInit\r\n \\\/ \\E rm \\in RM : \r\n TMRcvPrepared(rm) \\\/ RMPrepare(rm) \\\/ RMChooseToAbort(rm)\r\n \\\/ RMRcvCommitMsg(rm) \\\/ RMRcvAbortMsg(rm)\r\n-----------------------------------------------------------------------------\r\nTPSpec == Init \/\\ [][Next]_<>\r\n (*************************************************************************)\r\n (* The complete spec of the Two-Phase Commit protocol. *)\r\n (*************************************************************************)\r\n\r\nTHEOREM TPSpec => []TPTypeOK\r\n (*************************************************************************)\r\n (* This theorem asserts that the type-correctness predicate TPTypeOK is *)\r\n (* an invariant of the specification. *)\r\n (*************************************************************************)\r\n-----------------------------------------------------------------------------\r\n(***************************************************************************)\r\n(* We now assert that the Two-Phase Commit protocol implements the *)\r\n(* Transaction Commit protocol of module $TCommit$. The following *)\r\n(* statement defines $TC!TCSpec$ to be formula $TCSpec$ of module *)\r\n(* $TCommit$. (The TLA$^+$ \\textsc{instance} statement is used to rename *)\r\n(* the operators defined in module $TCommit$ avoids any name conflicts *)\r\n(* that might exist with operators in the current module.) *)\r\n(***************************************************************************)\r\nTC == INSTANCE TCommit \r\n\r\nTHEOREM TPSpec => TC!TCSpec\r\n (*************************************************************************)\r\n (* This theorem asserts that the specification TPSpec of the Two-Phase *)\r\n (* Commit protocol implements the specification TCSpec of the *)\r\n (* Transaction Commit protocol. *)\r\n (*************************************************************************)\r\n(***************************************************************************)\r\n(* The two theorems in this module have been checked with TLC for six *)\r\n(* RMs, a configuration with 50816 reachable states, in a little over a *)\r\n(* minute on a 1 GHz PC. *)\r\n(***************************************************************************)\r\n=============================================================================\r\n", "transformation": { "actors": [ "TM", "$messages", "RM 1", "RM 2", "RM 3" ], "actorSelectors": { "TM": [ "*.tmState", "*.tmPrepared" ], "RM 1": [ "*.rmState.rm1" ], "RM 2": [ "*.rmState.rm2" ], "RM 3": [ "*.rmState.rm3" ] }, "messagesSelector": "*.msgs[]", "stateSpaceSelectors": { "TM": [ [ "*.tmState", "tmState=@" ], [ "*.tmPrepared", "tmPrepared=@" ] ], "RM 1": [ [ "*.rmState.rm1", "rmState['rm1']=@" ] ], "RM 2": [ [ "*.rmState.rm2", "rmState['rm2']=@" ] ], "RM 3": [ [ "*.rmState.rm3", "rmState['rm3']=@" ] ] } }, "graph": [ { "id": "7812499366851226634", "vars": { "msgs": [], "tmState": "init", "tmPrepared": [], "rmState": { "rm1": "working", "rm2": "working", "rm3": "working" } }, "$type": "init-node" }, { "from": "7812499366851226634", "to": "3434650554768588846", "label": "TMAbort", "parameters": "", "$type": 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