Why vars is defined as tuples instead of set

[Chris Ortiz]

Hi tlaplus group,

I am just curious with the convention why vars is defined as tuples of variables for UNCHANGED, <<A>>_vars, [A]_vars, [][Next]_vars, WF_vars and SF_vars. My understanding is that tuples preserved ordering of elements. Maybe I am still confused or still having a hang over with Programming Language, but I like to understand why tuple is the selected convention for such variables for those semantics, instead of set. Sometimes it confused me to make sure I follow the ordering from how I defined them in vars up to the way I removed variables in my UNCHANGED expression.

Thanks,

Zitro

[Hillel Wayne]

Hi Chris,

Here's a quick toy model:

VARIABLES x, y

Swap ==
  /\ x' = y
  /\ y' = x

If vars == {x, y}, then after Swap we have vars' = {x', y'} = {y, x}. Since sets are unordered, we have vars' = vars, or UNCHANGED vars. But clearly the state of the system changed!

With vars == <<x, y>>, after Swap we have vars' = <<y, x>>. Since order matters in sequences, vars' # vars and we get the expected behavior.

H

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[Chris Ortiz]

Thank you very much Hillel. That toy model example makes sense why ordering matters.

Regards,

Zitro