Weak fairness until a majority

[Jack Vanlightly]

Hi all,

Let's say that I have an ensemble of nodes and each node has a counter. I have the action Increment which increments the counter of a node, if the value is 0.

Increment == 

    \E n \in Nodes : 

        /\ counter[n] = 0

        /\ counter' = [counter EXCEPT ![n] = @ + 1]

I would like to express weak fairness of Increment, but only while a minority of nodes have incremented their counter. So once a majority have incremented their counter, the weak fairness no longer applies.

Is there a way of defining weak fairness in this way?

Thanks

Jack Vanlightly

[Stephan Merz]

How about

Nodes0 == {n \in Nodes : counter[n] = 0}

Nodes1 == {n \in Nodes : counter[n] = 1}
WF_vars(Card(Nodes0) > Card(Nodes1) /\ Increment)

Stephan

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[Hillel Wayne]

One tweak, if `counter` is unbound then it should be

Nodes0 == {n \in Nodes : counter[n] = 0}

NodesInc == {n \in Nodes : counter[n] >= 1}
WF_vars(Card(Nodes0) >= Card(NodesInc) /\ Increment)

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[Jack Vanlightly]

So if I want to express weak fairness of an action with some conditions, I simply write WF_vars(conditions /\ MyAction)?

[Markus Kuppe]

Yes, just recall WF_v(A) <=> <>[](ENABLED <<A>>_v) => []<>(<<A>>_v) . Your condition or A in general rather may be any action-level formula. For a concrete example, see https://github.com/lemmy/BlockingQueue/blob/14a1baed2dd80ce83f32687c67749b39320ea121/BlockingQueue.tla#L136-L143.

Markus

[Jack Vanlightly]

Great, I get it, thanks to you all!