I think this is a TLC bug, but since it involves fairness and somewhat-unusual temporal properties I want to confirm it's actually a bug and not me misunderstanding temporal logic.
---- MODULE main ----
EXTENDS Naturals
VARIABLE x
A == x' = (x + 1) % 3
B == x' \in 0..2
Init == x = 0
Next == (A \/ B)
Spec == Init /\ [][Next]_x /\ WF_x(A)
====
VARIABLE x
A == x' = (x + 1) % 3
B == x' \in 0..2
Init == x = 0
Next == (A \/ B)
Spec == Init /\ [][Next]_x /\ WF_x(A)
====
There are three temporal properties I checked: Spec, WF_x(A), and []<><<A>>_x. The first two should be tautologically true, the last should be true for this spec. Each of the three fails with the same error trace:
In the first step, both A and B are true. In the second step, A is false and B is true. If we go back to state one, we have an infinite number of steps where A is true, so all three properties should be satisfied. Replacing B with x' \in {0, 1} does not cause a spec failure, even though in the existing spec failure x is never 2.
It seems like it could be one of three things:
- TLC is finding a false positive.
- TLC is finding a true positive, but not outputting the correct error trace.
- I'm misunderstanding how fairness works.
This should be machine-closed (A is a subaction of Next) but there could be another subtle issue I don't know about.
Hillel