The problem is the line
Spec == Init /\ [Next]_vars /\ EventuallySortedAsc /\ EventuallySortedDes
I am trying to write a simple spec for sorting. However, I've expressed a temporal property that I feel shouldn't be valid, yet TLC permits it.
Here is a video walkthrough of my question: https://www.loom.com/share/25f4eaaecd914d158551cbc061104a06
This spec is intended to be a simple abstraction of what sorting is. A sequence is (potentially) unsorted, then in one magical step it's sorted. I'm applying a refinement to it in another spec to show that, for example, bubble sort implements "sort by magic".
However, I have two temporal properties, which I feel conflict.
IsSortedAsc(seq) == \A a,b \in 1..N: a < b => seq[a] <= seq[b]
IsSortedDes(seq) == \A a,b \in 1..N: a < b => seq[a] >= seq[b]
EventuallySortedDes == <>IsSortedDes(A)
EventuallySortedAsc == <>IsSortedAsc(A)
I'm trying to express that eventually, the sequence is sorted In Ascending order or Descending Order. When I apply a model that checks if both are simultaneously true, TLC says this is successful.
Thank you for any potential help. I fully expect I'm doing something incorrect, but I'm not quite sure where.
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