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*From*: Isaac DeFrain <isaacdefrain@xxxxxxxxx>*Date*: Wed, 14 Apr 2021 12:14:29 -0600*References*: <ca126b11-a19f-4cb2-b67c-fcd9df861299n@googlegroups.com> <CAM3xQxH4BdebG+fYKYN4XokHabKazhRRYS1TzGRWv81+OS0Pnw@mail.gmail.com> <c46bd513-edfa-41cf-aca1-00b4aa3e669fn@googlegroups.com> <84c27c0d-ecc1-7b8d-13c6-32bd48f81a07@gmail.com>

Okay so I clearly misinterpreted the original question... my apologies.

I now understand the issue you are encountering, Seup, as I am also encountering the same issue with ~> in a spec. This must be a bug in TLC.

Best,

Isaac DeFrain

On Sat, Apr 10, 2021 at 3:31 PM Hillel Wayne <hwayne@xxxxxxxxx> wrote:

--For

(x > 0) ~> (y = 5), x is set to 1 in state 2, meaningy = 5must be true in a future state from 2. The error trace includes the step wherex = -1due to an implementation detail of TLC: based on how it calculates liveness, it doesn't guarantee that a liveness-violating trace will be the shortest one possible.

Re the

FALSE ~> (y = 5), no idea. Think it might be a bug?[](FALSE => <>TRUE)also fails, which doesn't seem right.H

On 4/10/2021 2:41 PM, seup yun 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 DeFrain

On 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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**Follow-Ups**:**Re: [tlaplus] meaning of the lead to (~>) operator***From:*Markus Kuppe

**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

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

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