State the assumptions of BlockDag and Sailfish

[lemmy]

@nano-o, you contributed this spec: Could you please review and approve the following refactorings?
The goal is to eventually prove properties of the Disruptor, which needs the assumptions stated and named so a proof can cite them, and the model bounds out of the way since they are not part of what would be proved.

[munimthahmid]

The new CorrectNodesFormQuorum assumption seems to address the concern I raised about Liveness in specula-org/tlaps-bench#131. I checked the change at 8fa4ac5 with TLC using the following model.

N == {a, c, b}
F == {b}
R == 1..3
GST == 1
Leader(r) == c
IsQuorum(Q) == {a, b} \subseteq Q
IsBlocking(B) == a \in B

IsQuorum is upward closed, and this model satisfies every other Sailfish assumption added in the PR. However, N \ F = {a, c} is not a quorum.

Without CorrectNodesFormQuorum, TLC violates Liveness at state 8. Node a reaches round 3 with an empty log, while c is the correct leader for round 1. With the assumption enabled, TLC rejects the same model immediately.

[nano-o]

Seems fine even if some of the assumptions may be redundant.

[lemmy]

THEOREM SomeNodeIsCorrectIsRedundant ==
    ASSUME NEW N, NEW F, NEW IsQuorum(_), NEW IsBlocking(_),
           \* CorrectNodesFormQuorum:
           IsQuorum(N \ F),
           \* QuorumMinusByzantineIsBlocking:
           \A Q \in SUBSET N : IsQuorum(Q) => IsBlocking(Q \ F),
           \* BlockingSetsIntersectQuorums:
           \A B,Q \in SUBSET N : IsBlocking(B) /\ IsQuorum(Q) => B \cap Q # {}
    \* SomeNodeIsCorrect:
    PROVE  N \ F # {}
    <1>1 (N \ F) \in SUBSET N
        OBVIOUS
    <1>2 IsBlocking((N \ F) \ F)
        BY <1>1
    <1>3 (N \ F) \ F = N \ F
        OBVIOUS
    <1>4 IsBlocking(N \ F)
        BY <1>2, <1>3
    <1>5 (N \ F) \cap (N \ F) # {}
        BY <1>1, <1>4
    <1> QED
        BY <1>5