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| ------------------------------ MODULE TwoPhase ------------------------------
(***************************************************************************)
(* This specification is discussed in "Two-Phase Commit", Lecture 6 of the *)
(* TLA+ Video Course. It describes the Two-Phase Commit protocol, in *)
(* which a transaction manager (TM) coordinates the resource managers *)
(* (RMs) to implement the Transaction Commit specification of module *)
(* TCommit. In this specification, RMs spontaneously issue Prepared *)
(* messages. We ignore the Prepare messages that the TM can send to the *)
(* RMs. *)
(* *)
(* For simplicity, we also eliminate Abort messages sent by an RM when it *)
(* decides to abort. Such a message would cause the TM to abort the *)
(* transaction, an event represented here by the TM spontaneously deciding *)
(* to abort. *)
(***************************************************************************)
CONSTANT RM \* The set of resource managers
VARIABLES
rmState, \* rmState[r] is the state of resource manager r.
tmState, \* The state of the transaction manager.
tmPrepared, \* The set of RMs from which the TM has received "Prepared"
\* messages.
msgs
(***********************************************************************)
(* In the protocol, processes communicate with one another by sending *)
(* messages. For simplicity, we represent message passing with the *)
(* variable msgs whose value is the set of all messages that have been *)
(* sent. A message is sent by adding it to the set msgs. An action *)
(* that, in an implementation, would be enabled by the receipt of a *)
(* certain message is here enabled by the presence of that message in *)
(* msgs. For simplicity, messages are never removed from msgs. This *)
(* allows a single message to be received by multiple receivers. *)
(* Receipt of the same message twice is therefore allowed; but in this *)
(* particular protocol, that's not a problem. *)
(***********************************************************************)
Messages ==
(*************************************************************************)
(* The set of all possible messages. Messages of type "Prepared" are *)
(* sent from the RM indicated by the message's rm field to the TM. *)
(* Messages of type "Commit" and "Abort" are broadcast by the TM, to be *)
(* received by all RMs. The set msgs contains just a single copy of *)
(* such a message. *)
(*************************************************************************)
[type : {"Prepared"}, rm : RM] \cup [type : {"Commit", "Abort"}]
TPTypeOK ==
(*************************************************************************)
(* The type-correctness invariant *)
(*************************************************************************)
/\ rmState \in [RM -> {"working", "prepared", "committed", "aborted"}]
/\ tmState \in {"init", "done"}
/\ tmPrepared \subseteq RM
/\ msgs \subseteq Messages
TPInit ==
(*************************************************************************)
(* The initial predicate. *)
(*************************************************************************)
/\ rmState = [r \in RM |-> "working"]
/\ tmState = "init"
/\ tmPrepared = {}
/\ msgs = {}
-----------------------------------------------------------------------------
(***************************************************************************)
(* We now define the actions that may be performed by the processes, first *)
(* the TM's actions, then the RMs' actions. *)
(***************************************************************************)
TMRcvPrepared(r) ==
(*************************************************************************)
(* The TM receives a "Prepared" message from resource manager r. We *)
(* could add the additional enabling condition r \notin tmPrepared, *)
(* which disables the action if the TM has already received this *)
(* message. But there is no need, because in that case the action has *)
(* no effect; it leaves the state unchanged. *)
(*************************************************************************)
/\ tmState = "init"
/\ [type |-> "Prepared", rm |-> r] \in msgs
/\ tmPrepared' = tmPrepared \cup {r}
/\ UNCHANGED <<rmState, tmState, msgs>>
TMCommit ==
(*************************************************************************)
(* The TM commits the transaction; enabled iff the TM is in its initial *)
(* state and every RM has sent a "Prepared" message. *)
(*************************************************************************)
/\ tmState = "init"
/\ tmPrepared = RM
/\ tmState' = "done"
/\ msgs' = msgs \cup {[type |-> "Commit"]}
/\ UNCHANGED <<rmState, tmPrepared>>
TMAbort ==
(*************************************************************************)
(* The TM spontaneously aborts the transaction. *)
(*************************************************************************)
/\ tmState = "init"
/\ tmState' = "done"
/\ msgs' = msgs \cup {[type |-> "Abort"]}
/\ UNCHANGED <<rmState, tmPrepared>>
RMPrepare(r) ==
(*************************************************************************)
(* Resource manager r prepares. *)
(*************************************************************************)
/\ rmState[r] = "working"
/\ rmState' = [rmState EXCEPT ![r] = "prepared"]
/\ msgs' = msgs \cup {[type |-> "Prepared", rm |-> r]}
/\ UNCHANGED <<tmState, tmPrepared>>
RMChooseToAbort(r) ==
(*************************************************************************)
(* Resource manager r spontaneously decides to abort. As noted above, r *)
(* does not send any message in our simplified spec. *)
(*************************************************************************)
/\ rmState[r] = "working"
/\ rmState' = [rmState EXCEPT ![r] = "aborted"]
/\ UNCHANGED <<tmState, tmPrepared, msgs>>
RMRcvCommitMsg(r) ==
(*************************************************************************)
(* Resource manager r is told by the TM to commit. *)
(*************************************************************************)
/\ [type |-> "Commit"] \in msgs
/\ rmState' = [rmState EXCEPT ![r] = "committed"]
/\ UNCHANGED <<tmState, tmPrepared, msgs>>
RMRcvAbortMsg(r) ==
(*************************************************************************)
(* Resource manager r is told by the TM to abort. *)
(*************************************************************************)
/\ [type |-> "Abort"] \in msgs
/\ rmState' = [rmState EXCEPT ![r] = "aborted"]
/\ UNCHANGED <<tmState, tmPrepared, msgs>>
TPNext ==
\/ TMCommit \/ TMAbort
\/ \E r \in RM :
TMRcvPrepared(r) \/ RMPrepare(r) \/ RMChooseToAbort(r)
\/ RMRcvCommitMsg(r) \/ RMRcvAbortMsg(r)
-----------------------------------------------------------------------------
(***************************************************************************)
(* The material below this point is not discussed in Video Lecture 6. It *)
(* will be explained in Video Lecture 8. *)
(***************************************************************************)
TPSpec == TPInit /\ [][TPNext]_<<rmState, tmState, tmPrepared, msgs>>
(*************************************************************************)
(* The complete spec of the Two-Phase Commit protocol. *)
(*************************************************************************)
THEOREM TPSpec => []TPTypeOK
(*************************************************************************)
(* This theorem asserts that the type-correctness predicate TPTypeOK is *)
(* an invariant of the specification. *)
(*************************************************************************)
-----------------------------------------------------------------------------
(***************************************************************************)
(* We now assert that the Two-Phase Commit protocol implements the *)
(* Transaction Commit protocol of module TCommit. The following statement *)
(* imports all the definitions from module TCommit into the current *)
(* module. *)
(***************************************************************************)
INSTANCE TCommit
THEOREM TPSpec => TCSpec
(*************************************************************************)
(* This theorem asserts that the specification TPSpec of the Two-Phase *)
(* Commit protocol implements the specification TCSpec of the *)
(* Transaction Commit protocol. *)
(*************************************************************************)
(***************************************************************************)
(* The two theorems in this module have been checked with TLC for six *)
(* RMs, a configuration with 50816 reachable states, in a little over a *)
(* minute on a 1 GHz PC. *)
(***************************************************************************)
=============================================================================
\* Modification History
\* Last modified Fri Dec 10 11:31:27 CST 2021 by thegloves
\* Created Fri Dec 10 11:31:00 CST 2021 by thegloves
|