Re: [tlaplus] Trouble Verifying Sorting Property on A Simple Spec

Are you familiar with the concept of vacuous truth? It’s the idea that, if you can’t prove something false, then it’s true by default. This is the principle behind implication: P => Q is true (vacuously) even when P is false.

Remember that “correctness” generally means that your Spec implies some property. You are constructing purposefully contradictory Specs which actually evaluate to false since they cannot be satisfied by any state space, and false implies the vacuous truth of any and all other logical statements.

Maybe TLC could throw a warning here, I think that’s fair. But, it’s just a case of a formal system doing exactly what we tell to.

On Fri, Oct 29, 2021 at 6:21 PM Jeremy Wright <jeremy@xxxxxxxxxxxx> wrote:
Thank you for the response Hillel, but I still think there is something I don't understand. I

t seems that if I setup a Spec with no behaviors, I can ask TLC anything and it will tell me it's okay. This bothers me.

The spec's I'm using here are "obvious", however if I design a more complex system, and I make a mistake such that my system system has no valid behaviors, TLC won't tell me there is a problem. Not only will TLC not compain, it tells me there are no problems for ANY property I ask it to check.

For example:

I'll restate the video, for those that prefer to read.

I define a spec with 1 and only 1 state.

------------------------------ MODULE nonsense ------------------------------

EXTENDS TLC, Integers

VARIABLES A

vars == A

Init == A = 1

Next == A' = 1

EventuallyRubbish == <>(A = 999)

Spec == Init /\ [][Next]_vars /\ <>[](A = 0)

=============================================================================

The Spec includes a temporal property which is not in the state space. There is no state where A=0, but TLC never warns me that my system does nothing. Here it is obviously not in the state space, but a more complex system that might not be so obvious. I recall the phrase, "beware of success", but this feels fragile to me. Am I missing something fundamental about how I express the Spec line?

Sincerely,
Jeremy

On Thu, Oct 28, 2021 at 4:05 PM Hillel Wayne <hwayne@xxxxxxxxx> wrote:

The problem is the line

Spec == Init /\ [][Next]_vars /\ EventuallySortedAsc /\ EventuallySortedDes

Since there are no models where EventuallySortedAsc /\ EventuallySortedDes, Spec = FALSE. If you change it to

Spec == Init /\ [][Next]_vars

Then it should work as expected.

H

On 10/28/2021 1:17 PM, Jeremy Wright wrote:
Hello,

I am trying to write a simple spec for sorting. However, I've expressed a temporal property that I feel shouldn't be valid, yet TLC permits it.

Here is a video walkthrough of my question: https://www.loom.com/share/25f4eaaecd914d158551cbc061104a06

This spec is intended to be a simple abstraction of what sorting is. A sequence is (potentially) unsorted, then in one magical step it's sorted. I'm applying a refinement to it in another spec to show that, for example, bubble sort implements "sort by magic".

However, I have two temporal properties, which I feel conflict.

IsSortedAsc(seq) == \A a,b \in 1..N: a < b => seq[a] <= seq[b]
IsSortedDes(seq) == \A a,b \in 1..N: a < b => seq[a] >= seq[b]
EventuallySortedDes ==  <>[]IsSortedDes(A)
EventuallySortedAsc ==   <>[]IsSortedAsc(A)

I'm trying to express that eventually, the sequence is sorted In Ascending order or Descending Order. When I apply a model that checks if both are simultaneously true, TLC says this is successful.

Model Screenshot:

Thank you for any potential help. I fully expect I'm doing something incorrect, but I'm not quite sure where.

Sincerely,
Jeremy Wright

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