Petri nets (a la Statebox) in Idris

As a follow-up on my talk on FPAMS, here is some basic dependently typed petri nets in Idris.

It doesn't do much yet, just basic Petri nets, no colour, no types.

No proofs... in particular initiality of the first transition in an instance (Init _ t0).

Nor Enabled <=> \Exist m. m --[t]--> m' /\ m' = m - (pre t) + (post t).

What is "dependent" here is only the size of the two partitions.

That is, a Net s t is a petrinet where the set of places is Fin s and the set of transitions Fin t.

For example:

net : Net 4 4
net = [
  ([], [0, 1]),
  ([0], [2]),
  ([1], [3]),
  ([2,3], [])
]

To create an instance, use the Inst data structure.

It has two constructors,

• Init takes a net and a transition
• Fire takes an instance and a transition

Fire the first transition

i0 : Inst 4 4
i0 = Init net 0

Fire another transition

i1 : Inst 4 4
i1 = Fire i0 1

We can now get the marking corresponding to the instances

marking i0
=> Just [0, 1]

marking i1
=> Just [1, 2]

Or obtain an instance directly from a net and a nonempty transition firing sequence.

*fnet> :t fire
fire : Net s t -> Transitions -> Inst s t