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Re: [tlaplus] Re: Parsing issues with prime operator in user-defined operators



In your lemma, IdxSet

On Thursday, July 11, 2024 at 7:55:00 AM UTC+2 Ugur Y. Yavuz wrote:
@Damien: That is also correct, but IdxSet = IdxSet' as IdxSet is a constant (under the quantifier). On my end, the following claim goes through trivially:

WellFormedTest(IdxSet) == \A p \in ProcSet :
                             CASE pc[p] = "L0" -> TRUE 
                               [] pc[p] = "L1" /\ l[p] \in IdxSet -> TRUE 
                               [] pc[p] = "L1" /\ l[p] \notin IdxSet -> FALSE

LEMMA WellFormedTestPrime == 
   \A IdxSet \in 0..L'-1 : 
      WellFormedTest(IdxSet)' = (\A p \in ProcSet :
                                    CASE pc'[p] = "L0" -> TRUE 
                                      [] pc'[p] = "L1" /\ l'[p] \in IdxSet -> TRUE 
                                      [] pc'[p] = "L1" /\ l'[p] \notin IdxSet -> FALSE)
  BY DEF WellFormedTest


On Wednesday 10 July 2024 at 10:46:27 UTC-4 Ugur Y. Yavuz wrote:

> Is this an issue with SANY or the TLAPM parser?


This is regarding SANY. It came up while I was working on a TLAPS proof, but it would also happen if I tried to define the action elsewhere.


> It's not a bug. The _expression_ WellFormed(full_indices)' has a double prime.

It doesn't have a double prime, in the sense that once you substitute the provided argument's definition in the predicate, there is no variable which is double primed (see the _expression_ it is semantically equivalent to). That's why I wasn't sure if the parser rejecting this _expression_ was intended behavior.

On Wednesday 10 July 2024 at 00:13:07 UTC-4 Leslie Lamport wrote:

It’s not a bug.  The _expression_ WellFormed(full_indices)' has a double prime.

 

From: tla...@xxxxxxxxxxxxxxxx <tla...@xxxxxxxxxxxxxxxx> On Behalf Of Andrew Helwer
Sent: Tuesday, July 9, 2024 18:51
To: tlaplus <tla...@xxxxxxxxxxxxxxxx>
Subject: [tlaplus] Re: Parsing issues with prime operator in user-defined operators

 

Is this an issue with SANY or the TLAPM parser?

On Monday, July 8, 2024 at 10:48:54AM UTC-4 Ugur Y. Yavuz wrote:

Hello, I have a question about the prime operator, particularly how it gets parsed in conjunction with user-defined operators.

 

Consider the following operator definition, where pc and l are among the variables of the specification, and ProcSet is a constant:

 

WellFormed(IdxSet) ==
    \A p \in ProcSet :
        CASE pc[p] = "L0"                       -> TRUE
          [] pc[p] = "L1" /\ l[p] \in IdxSet    -> TRUE
          [] pc[p] = "L1" /\ l[p] \notin IdxSet -> FALSE

 

Note that we have:

 

WellFormed(IdxSet)' =
    \A p \in ProcSet :
        CASE pc'[p] = "L0"                        -> TRUE
          [] pc'[p] = "L1" /\ l'[p] in IdxSet     -> TRUE
          [] pc'[p] = "L1" /\ l'[p] \notin IdxSet -> FALSE


Suppose L and A are also variables of the specification, and that we aim to prove the invariant \E IdxSet \in SUBSET 0..L-1 : WellFormed(IdxSet) in TLAPS. After proving it for the initial configuration, we need to prove it for a subsequent configuration, reached from one where the inductive invariant holds; i.e., \E IdxSet \in SUBSET 0..L'-1 : WellFormed(IdxSet)'. Suppose the witness for this claim needs to be a function of the specification variables' values in the next configuration. Say we want to proceed as follows:

 

...
<3> DEFINE full_indices == {idx \in 0..(L'-1) : A'[idx] > 0}
<3>1. WellFormed(full_indices)'

 

However, this results in a parser error: "Level error in applying operator ': The level of argument 1 exceeds the maximum level allowed by the operator."

Is this intended behavior? The _expression_ seems equivalent to:

 

\A p \in ProcSet :
    CASE pc'[p] = "L0" -> TRUE
      [] pc'[p] = "L1" /\ l'[p] in {idx \in 0..(L'-1) : A'[idx] > 0} -> TRUE
      [] pc'[p] = "L1" /\ l'[p] \notin {idx \in 0..(L'-1) : A'[idx] > 0} -> FALSE

 

which I can express in TLA+. This issue arose in a larger proof, and I simplified it as much as possible. I circumvented it with several rewrites, which I believe shouldn't be necessary at a first glance. I can provide more context if needed.

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