# Re: [tlaplus] Re: Doing arithmetic with current state value and next state value of a variable in TLA+

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

On Thu, May 27, 2021 at 5:22 PM Leslie Lamport <tlaplus.ll@xxxxxxxxx> wrote:
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

On Thursday, May 27, 2021 at 3:56:56 PM UTC-7 Leslie Lamport wrote:
And what do you expect the possible executions of that spec starting with y = 0 to be?

On Thursday, May 27, 2021 at 3:48:40 PM UTC-7 joan...@xxxxxxxxx wrote:
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.

On Thu, 2021-05-27 at 14:35 -0700, Andrew Helwer wrote:
Can you post a minimal functional spec which reproduces this error?

On Thursday, May 27, 2021 at 4:11:15 PM UTC-4 joan...@xxxxxxxxx wrote:
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.

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