It is very common that actions are disjoint, i.e. Post(s,A) \cap Post(s,B) = {}, but my explanation also covers the case where this is not so.
Hope this helps, Stephan On 23 Sep 2019, at 04:35, Shiyao MA < i@xxxxxxxxx> wrote:
Hi Merz,
What I understand from Hillel's reply is that, If Post(s, A) /= Post(s, B).
Then Post(s, A/\B) = φ
Best,
On Sunday, 22 September 2019 14:35:13 UTC+8, Stephan Merz wrote: Let me rephrase Hillel's intuition: suppose we have a nextstate relation
Next == A \/ B \/ ...
Given state s, TLC will process action A by computing the set
Post(s,A) == { t : (s,t) = A } [1]
Clearly, we have that
Post(s, A /\ B) \subseteq Post(s,A)
and therefore any state u such that (s,u) = A /\ B is a member of Post(s,A) and will be generated by TLC. Because it is also a member of Post(s,B), the state u will be regenerated when TLC processes action B.
Stephan [1] The restrictions that TLC imposes ensure that Post(s,A) is effectively computable and finite. In particular, it is well defined, which is all that matters here.
I'm having some trouble coming up with a valid spec where that would matter. You're saying that OP1, OP2, and OP1 /\ OP2 are all valid actions, but also that the conjunction includes transitions that aren't included in either individual action. As far as I know, the semantics of TLA+, in particular that the nextstate relation must completely specify all variables, make that impossible. But I'd be happy to be proven wrong on this!
With that in mind, I suspect that TLC doesn't check those transitions. You'd have to ask Markus to know for sure, though.
On 9/19/19 10:01 PM, Shiyao MA wrote:
Hi Hillel,
I was thinking about how the TLC checker searches for all the possible states *regardless* what exactly an OP refers to.
So for example,
Given a spec:
Next == OP1 \/ OP2 \/ OP3
Spec == Init /\ [][Next]_vars
and consider the case where the checker is at state S. The checker now proceeds to search all the *direct* child states (in a BFS style).
My question and predication is, for the above Next operation which contains a set of operations joined with *\/*, a state transition will never be conducted by applying both OP1 and OP2 (or any two of the three) on the current state S.
The checker enumerates the possible direct child states by applying OP1, OP2, and OP3 separately.
Best,
On Friday, 20 September 2019 00:29:07 UTC+8, Hillel Wayne wrote: Hi Shiyao related code: VoteFor(a, b, v) == /\ maxBal[a] =< b /\ \A vt \in votes[a] : vt[1] /= b /\ \A c \in Acceptor \ {a} : \A vt \in votes[c] : (vt[1] = b) => (vt[2] = v) /\ \E Q \in Quorum : ShowsSafeAt(Q, b, v) /\ votes' = [votes EXCEPT ![a] = votes[a] \cup {<<b, v>>}] /\ maxBal' = [maxBal EXCEPT ![a] = b]
If VoteFor specifies maxBal', and IncreaseMaxBal specifies maxBal', then they can only be true that the same time if there is some value for maxBal' that satisfies both actions. Given TLC isn't giving you an error, I'm guessing you also have UNCHANGED votes in IncreaseMaxBal? Then they definitely both can't be true at the same time, as VoteFor would specify that votes changes and IncreaseMaxBal does not.
H
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