How to run a spec through some set of models

[Nam Nguyen]

Hello list,

In https://lamport.azurewebsites.net/pubs/pluscal.pdf, it was mentioned that "TLC will check partial correctness and termination of the usual recursive version of quicksort for all 4-element arrays A with values in a set of 4 numbers in about 100 seconds."

My question: How would I be able to perform similar run with a specification I wrote in TLA+? My spec is pretty standard:

CONSTANT A0

VARIABLES A, i, j

vars == ...

Init == ...

Next == ...

Spec == Init /\ [][Next]_vars

where A0 is a sequence provided by a model to be sorted.

What I like to achieve is to run my spec through all sequences of length <= 4 of numbers from the set 1..4 (repeats are okay).

Thanks!

[Stephan Merz]

Hello,

I presume that your initial condition includes "A = A0" so that the algorithm is run on the fixed value provided by A0. Instead, make A0 an additional variable that is never changed by the algorithm (but you will refer to it in your correctness condition) and write an initial condition that allows A0 to take any sequence in the set you are interested in. Something like

TestData == {-5, 0, 27, 42}

TestSequences == UNION { [1..n -> TestData] : n \in 0 .. 4 }

Init == A0 \in TestSequences /\ A = A0 /\ ...

Don't forget to add A0 to the UNCHANGED clauses in your actions.

Stephan

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