forked from tlaplus/Examples
-
Notifications
You must be signed in to change notification settings - Fork 0
Commit
This commit does not belong to any branch on this repository, and may belong to a fork outside of the repository.
- Loading branch information
Showing
5 changed files
with
311 additions
and
5 deletions.
There are no files selected for viewing
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,132 @@ | ||
| ----------------------------- MODULE DiskSynod ----------------------------- | ||
|
|
||
| EXTENDS Synod, FiniteSets | ||
|
|
||
| CONSTANTS Ballot(_), Disk, IsMajority(_) | ||
| ASSUME /\ \A p \in Proc : /\ Ballot(p) \subseteq {n \in Nat : n > 0} | ||
| /\ \A q \in Proc \ {p} : Ballot(p) \cap Ballot(q) = {} | ||
| /\ IsMajority(Disk) | ||
| /\ \A S, T \in SUBSET Disk : | ||
| IsMajority(S) /\ IsMajority(T) => (S \cup T # {}) | ||
|
|
||
| DiskBlock == [mbal : (UNION {Ballot(p) : p \in Proc}) \cup {0}, | ||
| bal : (UNION {Ballot(p) : p \in Proc}) \cup {0}, | ||
| inp : Inputs \cup {NotAnInput}] | ||
|
|
||
| InitDB == [mbal |-> 0, bal |-> 0, inp |-> NotAnInput] | ||
|
|
||
| VARIABLES disk , dblock , phase, disksWritten, blocksRead | ||
|
|
||
| vars == <<input, output, disk , phase, dblock , disksWritten, blocksRead>> | ||
|
|
||
| Init == /\ input \in [Proc -> Inputs] | ||
| /\ output = [p \in Proc |-> NotAnInput] | ||
| /\ disk = [d \in Disk |-> [p \in Proc |-> InitDB ]] | ||
| /\ phase = [p \in Proc |-> 0] | ||
| /\ dblock = [p \in Proc |-> InitDB ] | ||
| /\ disksWritten = [p \in Proc |-> {}] | ||
| /\ blocksRead = [p \in Proc |-> [d \in Disk |-> {}]] | ||
|
|
||
| hasRead (p, d , q) == \E br \in blocksRead [p][d ] : br .proc = q | ||
|
|
||
| allBlocksRead(p) == | ||
| LET allRdBlks == UNION {blocksRead [p][d ] : d \in Disk } | ||
| IN {br.block : br \in allRdBlks} | ||
|
|
||
| InitializePhase(p) == | ||
| /\ disksWritten' = [disksWritten EXCEPT ![p] = {}] | ||
| /\ blocksRead' = [blocksRead EXCEPT ![p] = [d \in Disk |-> {}]] | ||
|
|
||
| StartBallot(p) == | ||
| /\ phase[p] \in {1, 2} | ||
| /\ phase' = [phase EXCEPT ![p] = 1] | ||
| /\ \E b \in Ballot(p) : /\ b > dblock [p].mbal | ||
| /\ dblock' = [dblock EXCEPT ![p].mbal = b] | ||
| /\ InitializePhase(p) | ||
| /\ UNCHANGED <<input, output, disk>> | ||
|
|
||
| Phase1or2Write(p, d) == | ||
| /\ phase[p] \in {1, 2} | ||
| /\ disk' = [disk EXCEPT ![d][p] = dblock[p]] | ||
| /\ disksWritten' = [disksWritten EXCEPT ![p] = @ \cup {d}] | ||
| /\ UNCHANGED <<input, output, phase, dblock , blocksRead>> | ||
|
|
||
| Phase1or2Read (p, d, q) == | ||
| /\ d \in disksWritten[p] | ||
| /\ IF disk [d ][q].mbal < dblock [p].mbal | ||
| THEN /\ blocksRead' = | ||
| [blocksRead EXCEPT | ||
| ![p][d ] = @ \cup {[block |-> disk [d ][q], proc |-> q]}] | ||
| /\ UNCHANGED <<input, output, disk , phase, dblock , disksWritten>> | ||
| ELSE StartBallot(p) | ||
|
|
||
| EndPhase1or2(p) == | ||
| /\ IsMajority({d \in disksWritten[p] : | ||
| \A q \in Proc \ {p} : hasRead (p, d , q)}) | ||
| /\ \/ /\ phase[p] = 1 | ||
| /\ dblock' = | ||
| [dblock EXCEPT | ||
| ![p].bal = dblock [p].mbal, | ||
| ![p].inp = | ||
| LET blocksSeen == allBlocksRead(p) \cup {dblock [p]} | ||
| nonInitBlks == | ||
| {bs \in blocksSeen : bs.inp # NotAnInput} | ||
| maxBlk == | ||
| CHOOSE b \in nonInitBlks : | ||
| \A c \in nonInitBlks : b.bal >= c.bal | ||
| IN IF nonInitBlks = {} THEN input[p] | ||
| ELSE maxBlk .inp ] | ||
| /\ UNCHANGED output | ||
| \/ /\ phase[p] = 2 | ||
| /\ output' = [output EXCEPT ![p] = dblock [p].inp] | ||
| /\ UNCHANGED dblock | ||
| /\ phase' = [phase EXCEPT ![p] = @ + 1] | ||
| /\ InitializePhase(p) | ||
| /\ UNCHANGED <<input, disk>> | ||
|
|
||
| Fail(p) == | ||
| /\ \E ip \in Inputs : input' = [input EXCEPT ![p] = ip] | ||
| /\ phase' = [phase EXCEPT ![p] = 0] | ||
| /\ dblock' = [dblock EXCEPT ![p] = InitDB] | ||
| /\ output' = [output EXCEPT ![p] = NotAnInput] | ||
| /\ InitializePhase(p) | ||
| /\ UNCHANGED disk | ||
|
|
||
| Phase0Read(p, d) == | ||
| /\ phase[p] = 0 | ||
| /\ blocksRead' = [blocksRead EXCEPT | ||
| ![p][d ] = @ \cup {[block |-> disk [d][p], proc |-> p]}] | ||
| /\ UNCHANGED <<input, output, disk , phase, dblock , disksWritten>> | ||
|
|
||
|
|
||
| EndPhase0(p) == | ||
| /\ phase[p] = 0 | ||
| /\ IsMajority({d \in Disk : hasRead (p, d, p)}) | ||
| /\ \E b \in Ballot(p) : | ||
| /\ \A r \in allBlocksRead (p) : b > r.mbal | ||
| /\ dblock' = [dblock EXCEPT | ||
| ![p] = [(CHOOSE r \in allBlocksRead (p) : | ||
| \A s \in allBlocksRead (p) : r .bal >= s.bal) | ||
| EXCEPT !.mbal = b]] | ||
| /\ InitializePhase(p) | ||
| /\ phase' = [phase EXCEPT ![p] = 1] | ||
| /\ UNCHANGED <<input, output, disk>> | ||
|
|
||
| Next == \E p \in Proc : | ||
| \/ StartBallot(p) | ||
| \/ \E d \in Disk : \/ Phase0Read (p, d) | ||
| \/ Phase1or2Write(p, d) | ||
| \/ \E q \in Proc \ {p} : Phase1or2Read (p, d, q) | ||
| \/ EndPhase1or2(p) | ||
| \/ Fail(p) | ||
| \/ EndPhase0(p) | ||
|
|
||
| DiskSynodSpec == Init /\ [][Next]_vars | ||
|
|
||
| THEOREM DiskSynodSpec => SynodSpec | ||
|
|
||
|
|
||
| ============================================================================= | ||
| \* ModIFication History | ||
| \* Last modIFied Sat Jan 26 14:03:35 CET 2019 by tthai | ||
| \* Created Sat Jan 26 12:19:05 CET 2019 by tthai |
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,119 @@ | ||
| ----------------------------- MODULE HDiskSynod ----------------------------- | ||
|
|
||
| EXTENDS DiskSynod | ||
| VARIABLES allInput, chosen | ||
|
|
||
| HInit == /\ Init | ||
| /\ chosen = NotAnInput | ||
| /\ allInput = {input[p] : p \in Proc} | ||
|
|
||
| HNext == /\ Next | ||
| /\ chosen' = LET hasOutput(p) == output'[p] # NotAnInput | ||
| IN IF \/ chosen # NotAnInput | ||
| \/ \A p \in Proc : ~hasOutput(p) | ||
| THEN chosen | ||
| ELSE output'[CHOOSE p \in Proc : hasOutput(p)] | ||
| /\ allInput' = allInput \cup {input'[p] : p \in Proc} | ||
|
|
||
|
|
||
| HInv1 == | ||
| /\ input \in [Proc -> Inputs] | ||
| /\ output \in [Proc -> Inputs \cup {NotAnInput}] | ||
| /\ disk \in [Disk -> [Proc -> DiskBlock ]] | ||
| /\ phase \in [Proc -> 0..3] | ||
| /\ dblock \in [Proc -> DiskBlock ] | ||
| /\ output \in [Proc -> Inputs \cup {NotAnInput}] | ||
| /\ disksWritten \in [Proc -> SUBSET Disk ] | ||
| /\ blocksRead \in [Proc -> [Disk -> SUBSET [block : DiskBlock , proc : Proc]]] | ||
| /\ allInput \in SUBSET Inputs | ||
| /\ chosen \in Inputs \cup {NotAnInput} | ||
|
|
||
| MajoritySet == {D \in SUBSET Disk : IsMajority(D)} | ||
|
|
||
| blocksOf(p) == | ||
| LET rdBy(q, d) == {br \in blocksRead[q][d] : br.proc = p} | ||
| IN {dblock[p]} \cup {disk[d][p] : d \in Disk } | ||
| \cup {br.block : br \in UNION{rdBy(q, d) : q \in Proc, d \in Disk}} | ||
|
|
||
| allBlocks == UNION {blocksOf(p) : p \in Proc} | ||
|
|
||
| HInv2 == | ||
| /\ \A p \in Proc : | ||
| \A bk \in blocksOf (p) : /\ bk.mbal \in Ballot(p) \cup {0} | ||
| /\ bk.bal \in Ballot(p) \cup {0} | ||
| (*/\ (bk.bal = 0) ≡ (bk.inp = NotAnInput)*) | ||
| /\ (bk.bal = 0) <=> (bk.inp = NotAnInput) | ||
| /\ bk.mbal >= bk.bal | ||
| /\ bk.inp \in allInput \cup {NotAnInput} | ||
| /\ \A p \in Proc, d \in Disk : | ||
| /\ (d \in disksWritten[p]) => /\ phase[p] \in {1, 2} | ||
| /\ disk[d][p] = dblock[p] | ||
| /\ (phase[p] \in {1, 2}) => /\ (blocksRead [p][d ] # {}) => | ||
| (d \in disksWritten[p]) | ||
| /\ ~hasRead (p, d, p) | ||
| /\ \A p \in Proc : | ||
| /\ (phase[p] = 0) => /\ dblock[p] = InitDB | ||
| /\ disksWritten[p] = {} | ||
| /\ \A d \in Disk : \A br \in blocksRead[p][d] : | ||
| /\ br.proc = p | ||
| /\ br.block = disk [d ][p] | ||
| /\ (phase[p] # 0) => /\ dblock[p].mbal \in Ballot(p) | ||
| /\ dblock[p].bal \in Ballot(p) \cup {0} | ||
| /\ \A d \in Disk : \A br \in blocksRead [p][d ] : | ||
| br.block.mbal < dblock[p].mbal | ||
| /\ (phase[p] \in {2, 3}) => (dblock[p].bal = dblock[p].mbal) | ||
| /\ output[p] = IF phase[p] = 3 THEN dblock[p].inp ELSE NotAnInput | ||
| /\ chosen \in allInput \cup {NotAnInput} | ||
| /\ \A p \in Proc : /\ input[p] \in allInput | ||
| /\ (chosen = NotAnInput) => (output[p] = NotAnInput) | ||
|
|
||
| HInv3 == \A p, q \in Proc, d \in Disk : | ||
| /\ phase[p] \in {1, 2} | ||
| /\ phase[q] \in {1, 2} | ||
| /\ hasRead (p, d, q) | ||
| /\ hasRead (q, d, p) | ||
| => \/ [block |-> dblock [q], proc |-> q] \in blocksRead[p][d] | ||
| \/ [block |-> dblock [p], proc |-> p] \in blocksRead[q][d] | ||
|
|
||
| HInv4 == | ||
| \A p \in Proc : | ||
| /\ (phase[p] # 0) => | ||
| /\ \A bk \in blocksOf(p) : dblock[p].mbal >= bk.bal | ||
| /\ \A D \in MajoritySet : | ||
| \E d \in D : /\ dblock[p].mbal >= disk[d][p].mbal | ||
| /\ dblock[p].bal >= disk[d][p].bal | ||
| /\ (phase[p] = 1) => (\A bk \in blocksOf(p) : dblock[p].mbal > bk.bal) | ||
| /\ (phase[p] \in {2, 3}) => | ||
| (\E D \in MajoritySet : \A d \in D : disk[d][p].mbal = dblock[p].bal) | ||
| /\ \A bk \in blocksOf(p) : | ||
| \E D \in MajoritySet : \A d \in D : disk[d][p].mbal >= bk.bal | ||
|
|
||
| maxBalInp(b, v ) == \A bk \in allBlocks : (bk.bal >= b) => (bk.inp = v) | ||
|
|
||
| HInv5 == | ||
| \A p \in Proc : | ||
| (phase[p] = 2) => \/ maxBalInp(dblock[p].bal , dblock[p].inp) | ||
| \/ \E D \in MajoritySet, q \in Proc : | ||
| \A d \in D : /\ disk[d][q].mbal > dblock [p].bal | ||
| /\ ~hasRead (p, d , q) | ||
|
|
||
| valueChosen(v) == | ||
| \E b \in UNION {Ballot(p) : p \in Proc} : | ||
| /\ maxBalInp(b, v) | ||
| /\ \E p \in Proc, D \in MajoritySet : | ||
| \A d \in D : /\ disk[d][p].bal >= b | ||
| /\ \A q \in Proc : | ||
| /\ phase[q] = 1 | ||
| /\ dblock[q].mbal >= b | ||
| /\ hasRead(q, d, p) | ||
| => (\E br \in blocksRead[q][d] : br.block.bal >= b) | ||
|
|
||
| HInv6 == /\ (chosen # NotAnInput) => valueChosen(chosen) | ||
| /\ \A p \in Proc : output[p] \in {chosen, NotAnInput} | ||
|
|
||
|
|
||
|
|
||
| ============================================================================= | ||
| \* Modification History | ||
| \* Last modified Sat Jan 26 15:52:41 CET 2019 by tthai | ||
| \* Created Sat Jan 26 15:23:57 CET 2019 by tthai |
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -1,7 +1,9 @@ | ||
| #### <a href="https://github.com/nano-o/MultiPaxos/blob/master/DiskPaxos.tla">diskpaxos</a> | ||
| - Specification's authors: Giuliano Losa | ||
| - TLA<sup>+</sup> specification's authors: Leslie Lamport | ||
| - Pluscal specification's authors: Giuliano Losa | ||
| - <a href="https://github.com/nano-o/MultiPaxos/blob/master/DiskPaxos.tla">Pluscal files</a> | ||
| - First, Lamport wrote the TLA<sup>+</sup> specifications in his paper. Because we could not find Lamport's TLA files, we translated his writing in PDF format to TLA<sup>+</sup> and pushed them in this repository. Later, Losa wrote another specification for this algortihm in Pluscal. | ||
| - Original paper: <a href="https://lamport.azurewebsites.net/pubs/disk-paxos.pdf">Gafni, Eli, and Leslie Lamport. Disk paxos. Distributed Computing 16.1 (2003): 1-20.</a> | ||
| - Extended modules: Int | ||
| - Computation models: crashes, inaccessibility | ||
| - Some properties checked with TLC: SynodSpec | ||
| - <a href="https://github.com/nano-o/MultiPaxos/blob/master/DiskPaxos.tla">TLA<sup>+</sup> files</a> |
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,53 @@ | ||
| ------------------------------- MODULE Synod ------------------------------- | ||
|
|
||
| EXTENDS Naturals | ||
|
|
||
| CONSTANTS N , Inputs | ||
| ASSUME (N \in Nat) /\ (N > 0) | ||
|
|
||
| Proc == 1..N | ||
|
|
||
| NotAnInput == CHOOSE c : c \notin Inputs | ||
|
|
||
| VARIABLES input, output | ||
|
|
||
| ------------------------------- MODULE Inner ------------------------------- | ||
|
|
||
| VARIABLES allInput, chosen | ||
|
|
||
| IInit == /\ input \in [Proc -> Inputs] | ||
| /\ output = [p \in Proc |-> NotAnInput] | ||
| /\ chosen = NotAnInput | ||
| /\ allInput = {input[p] : p \in Proc} | ||
|
|
||
| IChoose(p) == | ||
| /\ output[p] = NotAnInput | ||
| /\ IF chosen = NotAnInput | ||
| THEN \E ip \in allInput : /\ chosen' = ip | ||
| /\ output' = [output EXCEPT ![p] = ip] | ||
| ELSE /\ output' = [output EXCEPT ![p] = chosen] | ||
| /\ UNCHANGED chosen | ||
| /\ UNCHANGED <<input, allInput>> | ||
|
|
||
| IFail(p) == | ||
| /\ output' = [output EXCEPT ![p] = NotAnInput] | ||
| /\ \E ip \in Inputs : /\ input' = [input EXCEPT ![p] = ip] | ||
| /\ allInput = allInput \cup {ip} | ||
| /\ UNCHANGED chosen | ||
|
|
||
| INext == \E p \in Proc : IChoose(p) \/ IFail (p) | ||
|
|
||
| ISpec == IInit /\ [][INext]_<<input, output, chosen, allInput>> | ||
|
|
||
| ============================================================================= | ||
|
|
||
| IS(chosen, allInput) == INSTANCE Inner | ||
|
|
||
| SynodSpec == \EE chosen, allInput : IS(chosen, allInput)!ISpec | ||
|
|
||
|
|
||
|
|
||
| ============================================================================= | ||
| \* ModIFication History | ||
| \* Last modIFied Sat Jan 26 14:27:38 CET 2019 by tthai | ||
| \* Created Sat Jan 26 14:17:53 CET 2019 by tthai |