Strategies to avoid exploring symmetric combinations in non-model values?

[J.D. Meadows]

Let's say that I have a set of integers, and I totally need them to be numbers and not model values so that they are comparable and I can perform arithmetic. Eg.: 

Vals == 1..5

Tuples = Vals \X Vals \X Vals

with (t \in Tuples){

...

}

But then in my particular problem I know that <<1,2,3>> is equivalent to <<3,1,2>> and <<2,3,1>>. Is there some way of filtering Tuples so that I can avoid exploring the two latter equivalent cases? Ideally the solution should scale to long sequences, not just 3 elements.

It would be nice if I could define a set of symmetric values in the model overview form.

Or if I could define an external generator coded in Java that I could plug in into the spec. That way I could keep track of already generated states in the Java code and only return non-equivalent combinations.

Or maybe have TLA+ accept some external file that I could generate with a programming language of my choice.

[Hillel Wayne]

If the order doesn't matter, could you instead use a bag? Then all three of your sequences would map to the same value (1 :> 1 @@ 2 :> 1 @@ 3 :> 1). If you needed to convert it back to a sequence, you could use FoldFunction with Append to pick an arbitrary sequence representation of the bag.

H

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[Chris]

There is very hacky approach to try and explicitly normalise the state after each step.

I have a partial example of this where I was trying to normalise all the ballot numbers in a Paxos implementation, as well as removing un-receivable messages to make the state space finite for small models.

The paxos variant: https://github.com/Cjen1/consensus-tlaplus/blob/vector-paxos/VectorPaxos/VectorPaxos.tla

The normalisation step: https://github.com/Cjen1/consensus-tlaplus/blob/vector-paxos/VectorPaxos/Finite.tla

I can't quite remember if this approach ended up working in TLA, but there is also stateright implementation where I could directly change the symmetry function.

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