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Gossa V1
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| CONSTANTS NodeCount | |
| VARIABLES running, | |
| peer_status | |
| Nodes == 1..NodeCount |
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| Converged == | |
| ~\E local, remote \in Nodes : | |
| /\ running[local] = TRUE | |
| /\ \/ /\ peer_status[local][remote] = Dead | |
| /\ running[remote] = TRUE | |
| \/ /\ peer_status[local][remote] = Alive | |
| /\ running[remote] = FALSE |
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| CorrectlyDetectDeadNode == | |
| \E local, remote \in Nodes : | |
| /\ local /= remote | |
| /\ running[local] = TRUE | |
| /\ running[remote] = FALSE | |
| /\ peer_status[local][remote] = Alive | |
| /\ peer_status' = [peer_status EXCEPT ![local][remote] = Dead] | |
| /\ UNCHANGED running |
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| Die == | |
| \E node \in Nodes : | |
| /\ running[node] = TRUE | |
| /\ running' = [running EXCEPT ![node] = FALSE] | |
| /\ UNCHANGED peer_status |
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| --------------------------- MODULE gossa_v1 --------------------------- | |
| EXTENDS Naturals | |
| CONSTANTS NodeCount | |
| VARIABLES running, | |
| peer_status | |
| vars == <<running, peer_status>> | |
| Nodes == 1..NodeCount | |
| \* Node peer states | |
| Alive == 1 | |
| Dead == 2 | |
| Init == | |
| /\ running = [node \in Nodes |-> TRUE] | |
| /\ peer_status = [node1 \in Nodes |-> | |
| [node2 \in Nodes |-> Alive]] | |
| \***************************************************************** | |
| \* ACTIONS | |
| \***************************************************************** | |
| MergePeerStateBlindly(local_node, local_ps, remote_ps) == | |
| [node \in Nodes |-> | |
| IF node = local_node | |
| THEN local_ps[node] | |
| ELSE remote_ps[node]] | |
| Gossip == | |
| \E source, dest \in Nodes : | |
| LET gossip_sent == peer_status[source] | |
| merged_on_dest == MergePeerStateBlindly( | |
| dest, | |
| peer_status[dest], | |
| gossip_sent) | |
| gossip_replied == merged_on_dest | |
| merged_on_source == MergePeerStateBlindly( | |
| source, | |
| peer_status[source], | |
| gossip_replied) | |
| IN | |
| /\ running[source] = TRUE | |
| /\ running[dest] = TRUE | |
| /\ gossip_sent # peer_status[dest] | |
| /\ peer_status' = [peer_status EXCEPT | |
| ![dest] = merged_on_dest, | |
| ![source] = merged_on_source] | |
| /\ UNCHANGED running | |
| Die == | |
| \E node \in Nodes : | |
| /\ running[node] = TRUE | |
| /\ running' = [running EXCEPT ![node] = FALSE] | |
| /\ UNCHANGED peer_status | |
| Start == | |
| \E node \in Nodes : | |
| /\ running[node] = FALSE | |
| /\ running' = [running EXCEPT ![node] = TRUE] | |
| /\ UNCHANGED peer_status | |
| CorrectlyDetectDeadNode == | |
| \E local, remote \in Nodes : | |
| /\ local /= remote | |
| /\ running[local] = TRUE | |
| /\ running[remote] = FALSE | |
| /\ peer_status[local][remote] = Alive | |
| /\ peer_status' = [peer_status EXCEPT ![local][remote] = Dead] | |
| /\ UNCHANGED running | |
| FalselyDetectDeadNode == | |
| \E local, remote \in Nodes : | |
| /\ local /= remote | |
| /\ running[local] = TRUE | |
| /\ running[remote] = TRUE | |
| /\ peer_status[local][remote] = Alive | |
| /\ peer_status' = [peer_status EXCEPT ![local][remote] = Dead] | |
| /\ UNCHANGED running | |
| Next == | |
| \/ Gossip | |
| \/ Die | |
| \/ CorrectlyDetectDeadNode | |
| \/ FalselyDetectDeadNode | |
| \/ Start | |
| \* SAFETY PROPERTIES ------------ | |
| TypeOK == | |
| /\ running \in [Nodes -> BOOLEAN] | |
| /\ peer_status \in [Nodes -> | |
| [Nodes -> {Alive, Dead}]] | |
| \* LIVENESS PROPERTIES ------------ | |
| Converged == | |
| ~\E local, remote \in Nodes : | |
| /\ running[local] = TRUE | |
| /\ \/ /\ peer_status[local][remote] = Dead | |
| /\ running[remote] = TRUE | |
| \/ /\ peer_status[local][remote] = Alive | |
| /\ running[remote] = FALSE | |
| EventuallyConverges == | |
| ~Converged ~> Converged | |
| Liveness == | |
| WF_vars(\/ Gossip | |
| \/ CorrectlyDetectDeadNode) | |
| \* Temporal formula | |
| Spec == Init /\ [][Next]_vars | |
| LivenessSpec == Init /\ [][Next]_vars /\ Liveness | |
| ============================================================================= |
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| Gossip == | |
| \E source, dest \in Nodes : | |
| LET gossip_sent == peer_status[source] | |
| merged_on_dest == MergePeerStateBlindly( | |
| dest, | |
| peer_status[dest], | |
| gossip_sent) | |
| gossip_replied == merged_on_dest | |
| merged_on_source == MergePeerStateBlindly( | |
| source, | |
| peer_status[source], | |
| gossip_replied) | |
| IN | |
| /\ running[source] = TRUE | |
| /\ running[dest] = TRUE | |
| /\ gossip_sent /= peer_status[dest] | |
| /\ peer_status' = [peer_status EXCEPT | |
| ![dest] = merged_on_dest, | |
| ![source] = merged_on_source] | |
| /\ UNCHANGED running |
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| \* Node peer states | |
| Alive == 1 | |
| Dead == 2 | |
| Init == | |
| /\ running = [node \in Nodes |-> TRUE] | |
| /\ peer_status = [node1 \in Nodes |-> | |
| [node2 \in Nodes |-> Alive]] |
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| Liveness == | |
| WF_vars(\/ Gossip | |
| \/ CorrectlyDetectDeadNode) | |
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| MergePeerStateBlindly(local_node, local_ps, remote_ps) == | |
| [node \in Nodes |-> | |
| IF node = local_node | |
| THEN local_ps[node] | |
| ELSE remote_ps[node]] |
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| Next == | |
| \/ Gossip | |
| \/ Die | |
| \/ Start | |
| \/ CorrectlyDetectDeadNode | |
| \/ FalselyDetectDeadNode |
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| Start == | |
| \E node \in Nodes : | |
| /\ running[node] = FALSE | |
| /\ running' = [running EXCEPT ![node] = TRUE] | |
| /\ UNCHANGED peer_status |
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| TypeOK == | |
| /\ running \in [Nodes -> BOOLEAN] | |
| /\ peer_status \in [Nodes -> | |
| [Nodes -> {Alive, Dead}]] |
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