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[tlaplus] Re: Consensus spec safety in Paxos example

Hi Jones,

Your explanation matches my understanding, however I think the `Inv` does not correctly represent a consensus safety property. To demonstrate that, we can change the `Next` action in such a way that the invariant will still hold. For example, if we can allow a transition from {v} back to {}, the invariant is still true, but the safety is broken.

The safety invariant here has to have a temporal aspect: once the chosen set is non-empty, it stays so.

I.e. the comment "Safety: At most one value is chosen" seems misleading here. It does express some invariant, but this invariant does not on its own guarantee safety.

Thank you,

On Wednesday, May 8, 2024 at 10:58:17 PM UTC+1 Jones Martins wrote:
Hi Pavel,

The Voting module instantiates the Consensus module to prove that Voting's Spec implies Consensus' Spec.

The consensus specification itself is pretty abstract.
Init expresses that chosen = {} is true in the first state of every behavior.
Next expresses that if chosen = {} is true, then chosen' = { <some value> }.
This means that, when some value has been chosen, it never changes again, so the original  `Inv` invariant is strong enough.

By the way, `Inv` can't be augmented as you suggested. Invariants are state predicates, and state predicates don't contain primed variables.

On Wednesday 8 May 2024 at 16:41:29 UTC-3 Pavel Kalinnikov wrote:
Should this line

       /\ Cardinality(chosen) \leq 1

be augmented with something like:

       /\ Cardinality(chosen') \leq 1
       /\ chosen = {} \/ chosen' = chosen

On Wednesday, May 8, 2024 at 8:24:27 PM UTC+1 Pavel Kalinnikov wrote:

I am looking at the Consensus spec in tlaplus examples repo, which specifies the single-value consensus problem.

The Init/Next spec in this file correctly specifies consensus, because it precludes the chosen set from changing after it got to contain exactly one value.

What value does the the safety invariant in lines 36-37, and the theorem that follows it, bring to this spec? If I am interpreting it correctly, the invariant does not fully specify the safety property: it allows a sequence in which a value is chosen, then another value replaces it (the size of the chosen set is still 1, so the invariant remains true). Or a value is chosen, then the set is emptied, then another value is chosen; etc.

Is the value of this invariant+theorem in just demonstrating an interesting property? Is it not strictly needed to be in this spec?

Is there a way to fix this invariant, so that it fully represents the consensus safety property (rather than partially, like it seems).

Thank you,

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