Doing arithmetic with current state value and next state value of a variable in TLA+

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Jefferson Andrade

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May 27, 2021, 4:11:15 PMMay 27
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Hello,

I want to write a (piece of a) formula like this:

y' = x' - x

But every time I try to run the model I get the error, «In evaluation, the identifier x is either undefined or not an operator.»

What is going on? Is it really not possible to write such formulas? why? How can I work around this?

Thanks.

Andrew Helwer

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May 27, 2021, 5:35:20 PMMay 27
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Can you post a minimal functional spec which reproduces this error?

joan...@gmail.com

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May 27, 2021, 6:48:40 PMMay 27
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The minimal spec follows.

---------------------------- MODULE minimal_ex1 ----------------------------
EXTENDS Integers, Reals
VARIABLES x, y

TypeOK == /\ x \in -128..127
          /\ y \in -128..127

Init == ((x \in -128..127) /\ (y = 0))

VS_Pitch_Wheel_Rotation == 
    y' = ((x' - x + 128) % 256) - 128
                             
Next == VS_Pitch_Wheel_Rotation      

Spec == Init /\ [][Next]_<<x,y>> 
=============================================================================
\* Modification History
\* Last modified Thu May 27 19:45:21 BRT 2021 by jefferson
\* Created Thu May 27 19:45:08 BRT 2021 by jefferson

When the model is run, it produces the following error messages:

TLC threw an unexpected exception.
This was probably caused by an error in the spec or model.
See the User Output or TLC Console for clues to what happened.
The exception was a java.lang.RuntimeException
In evaluation, the identifier x is either undefined or not an operator.
line 11, col 12 to line 11, col 12 of module minimal_ex1

The error occurred when TLC was evaluating the nested
expressions at the following positions:
0. Line 11, column 5 to line 11, column 37 in minimal_ex1
1. Line 11, column 10 to line 11, column 37 in minimal_ex1
2. Line 11, column 11 to line 11, column 30 in minimal_ex1
3. Line 11, column 12 to line 11, column 23 in minimal_ex1
4. Line 11, column 12 to line 11, column 17 in minimal_ex1
5. Line 11, column 12 to line 11, column 13 in minimal_ex1
6. Line 11, column 12 to line 11, column 12 in minimal_ex1

Thanks for your help.
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Leslie Lamport

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May 27, 2021, 6:56:56 PMMay 27
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And what do you expect the possible executions of that spec starting with y = 0 to be?

Leslie Lamport

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May 27, 2021, 7:22:05 PMMay 27
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I'm sorry, I meant executions starting with x = y = 0.   Actually, you just need to list the possible second states of such an execution.

Leslie

Isaac DeFrain

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May 27, 2021, 9:46:09 PMMay 27
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Hello Jefferson,

It seems that the issue stems from the evaluation semantics of TLC. In VS_Pitch_Wheel_Rotation, you use the value x', however, TLC evaluates each conjunct in order (from first to last). Unfortunately, there is no value given for x' since we have not said how the value of x changes (this is what the cryptic "the identifier x is either undefined" bit is about). For example, admittedly this is not very interesting, but it should bring the point home, changing the action to

VS_Pitch_Wheel_Rotation ==
    /\ UNCHANGED x
    /\ y' = ((x' - x + 128) % 256) - 128

results in a successful model run. You must say how the value of x evolves before you can use the value of x in the successor state, i.e. x'.

To be clear, this is a TLC thing and not a TLA+ thing (there are no evaluation semantics for TLA+; it's math). Strictly speaking,

/\ UNCHANGED x
/\ y' = ((x' - x + 128) % 256) - 128

and

/\ y' = ((x' - x + 128) % 256) - 128
/\ UNCHANGED x

are equivalent in TLA+ (because conjunction is commutative), but they are not treated as equivalent by TLC.

I hope this helps!


Best,

Isaac DeFrain


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joan...@gmail.com

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May 28, 2021, 2:23:48 PMMay 28
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Hi Isaac,

Thank you immensely for your help. You were very kind of you to take the time to explain the problem to me. Really appreciate it.

Regards,
Jefferson Andrade.

joan...@gmail.com

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May 28, 2021, 4:23:17 PMMay 28
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Hello,

This was the smallest exert I could put together to reproduce the error I was having. The entire module is much larger and is intended to model how a set of sensors react to the inputs of a set of actuators. I am sorry if the example makes no sense.

But thanks for your reply and your input. I problem has been fixed now.

Regards,
Jefferson.

Isaac DeFrain

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May 28, 2021, 6:04:04 PMMay 28
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Hey Jefferson,

You’re very welcome! I’m glad you got things working properly.


Best,

Isaac

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Isaac DeFrain
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