Directed Graph from Specifying Systems

[Kulpreet Singh]

I tried using the directed graph operator Path from Specifying Systems book, however, I can't figure how to put in a state constraint that will let me use the operator.

Here's the Path spec straight from the book.

```

Path(G) == \* The set of paths in G, where a path is represented as a sequence of nodes
    {p \in Seq(G.node): /\ p # <<>>
                        /\ \A i \in 1..(Len(p) - 1): <<p[i], p[i+1] \in G.edge>>}

```

Here's how I am trying to use it in the "evaluate constant expression" section

```

Path([node |-> {1, 2, 3}, edge |-> {<<1, 2>>, <<2, 3>>}])

```

I get the error

"Attempted to enumerate { x \in S : p(x) } when S:
Seq({1, 2, 3})
is not enumerable"

I tried putting a constraint when trying to use in the TLC model checker, but I still have the issue that Seq(...) is non enumerable.

Has anyone successfully used this Path operator in a Spec? If so, would love any tips on how to make it work. Meanwhile, I have switched to using Giuliano Losa's DiGraph from https://github.com/nano-o/TLA-Library/blob/master/DiGraph.tla which works, but I am curious to know how the non-enumerable Seq(...) problem can be solved when it is invoked from inside an operator.

Regards

Kulpreet

[Markus Kuppe]

Hi Kulpreet,

TLC is unable to evaluate your expression involving Path since there are infinitely many paths, and a state constraint doesn't apply here due to your formula being constant-level. However, TLC can still evaluate if a certain path is an element of the set of all paths. For example, it can evaluate the expression: <<1,2,3>> \in Path([node |-> {1, 2, 3}, edge |-> {<<1, 2>>, <<2, 3>>}]) .

It's worth noting that the CommunityModules Graphs module [1] defines an additional operator called SimplePath, which TLC evaluates without any issues. Other operators such as AreConnectedIn and IsStronglyConnected are defined based on SimplePath.

Markus

[1] https://github.com/tlaplus/CommunityModules/blob/master/modules/Graphs.tla

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[Kulpreet Singh]

Thanks Markus,

The link to the Graph module in CommunityMoules was very helpful. I
switched to using the SimplePath, which made my life easier.

Thanks again
Kulpreet

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