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*From*: Calvin Loncaric <c.a.loncaric@xxxxxxxxx>*Date*: Sat, 10 Apr 2021 14:28:03 -0700*References*: <ca126b11-a19f-4cb2-b67c-fcd9df861299n@googlegroups.com> <CAM3xQxH4BdebG+fYKYN4XokHabKazhRRYS1TzGRWv81+OS0Pnw@mail.gmail.com> <c46bd513-edfa-41cf-aca1-00b4aa3e669fn@googlegroups.com>

The (FALSE) ~> (y = 5) case looks like a bug to me! I was able to reproduce it in a very simplified example on my own computer. It is either a bug or we have *both* deeply misunderstood the ~> operator.

The trace you showed for the (x > 0) ~> (y = 5) case does not look like a bug. It looks like a true counterexample to me. In the trace, there is a state where x>0 (e.g. state 2) and that state is *not* followed by a later state where y=5. Therefore, x>0 does not always lead to y=5. The property is indeed violated.

On Sat, Apr 10, 2021 at 1:32 PM seup yun <syun4541@xxxxxxxxx> wrote:

here is the error trace i'm getting when using the formula (x > 0) ~> (y = 5)and when using the fomrula (FALSE) ~> (y = 5)I don't understand why these formulas even causes the error, what am i missing? why mplication operator evaluated as false when left operand of the implication is FALSE?--2021년 4월 11일 일요일 오전 3시 22분 22초 UTC+9에 isaacd...@xxxxxxxxx님이 작성:Hello Seup,What is the error trace you're getting?From the actions you have defined, as long as x remains <= 0, we never need to increment y. A possible behavior is Init, SetX, IncX, SetX, IncX, ...It may be enough to simply change the enabling condition for IncY to x >= 0 (but that may not be "allowed" by what you are trying to specify).Best,Isaac DeFrainOn Sat, Apr 10, 2021 at 10:56 AM seup yun <syun...@xxxxxxxxx> wrote:Hi,I'm trying to specify "If some operation does not happens, then some condition eventually becomes true"full specification is following:-------------------------------- MODULE test --------------------------------

EXTENDS Integers

VARIABLE x,y

Init ==

/\ x = 0

/\ y = 0

IncX ==

/\ x' = IF x < 5 THEN (x + 1) ELSE 5

/\ UNCHANGED <<y>>

IncY ==

/\ x > 0

/\ y' = IF y < 5 THEN (y + 1) ELSE 5

/\ UNCHANGED <<x>>

SetX ==

/\ x' = -1

/\ UNCHANGED <<y>>

Next ==

\/ IncX

\/ IncY

\/ SetX

Invariant1 ==

/\ x < 6

/\ y < 6

temporalFormula1 == (x > 0) ~> (y = 5)

=============================================================================and behavior spec is:Init /\ [][Next]_<<x,y>> /\ WF_x(IncX) /\ WF_x(SetX) /\ WF_<<x,y>>(IncY)my question is, why temporalFormula1 is violated?I know that (x > 0) ~> (y = 5) means:□((x > 0) => <>(y = 5)) which is\A n \in Nat. \sigma^{+n} ⊨ (x > 0) =>¬□(y = 5) which is¬\A n \in Nat. \sigma^{+n} ⊨ (x > 0) => \sigma^{+n} ⊨ \E m \in Nat. \sigma{+m} ⊨ (y = 5) which is\A n \in Nat. \sigma^{+n} ⊨ (x > 0) => \E m \in Nat. \sigma^{+n+m} ⊨ (y = 5)so, i believed that error-trace should not contains the state that x is -1 but it does.I even tried the formula (FALSE) ~> (y = 5) but it still fails with similar error trace. what's my mistake here?--

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**References**:**[tlaplus] meaning of the lead to (~>) operator***From:*seup yun

**Re: [tlaplus] meaning of the lead to (~>) operator***From:*Isaac DeFrain

**Re: [tlaplus] meaning of the lead to (~>) operator***From:*seup yun

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