colored-petri-nets

This is a library to describe colored Petri nets and CPN++, an enhanced version of colored Petri nets for modeling programs.

© Felix Freiberger, 2018-2019, Saarland University

A Word of Caution

This library is quite experimental. For now, there is no proper documentation, and the API shouldn't be considered stable.

Petri Net Semantics

In this library, the colors of tokens in the nets are simple JavaScript values, consisting of booleans, integers, arrays and objects. For example, these are valid colors:

• true
• 42
• "Hello World!
• [42, []]
• { object: {}, array: [] }

Transitions work by having patterns on incoming flows and expressions on outgoing flows. A transition is enabled if

• all incoming flows can find a token that matches the pattern,
• the incoming flows produce bindings that are compatible and
• the resulting binding fulfills the guard.

If a transition is executed, the outgoing flows produce tokens corresponding to their expressions, which may reference the binding.

As an example, a transition with two inflows with the patterns [ x ] and x, the guard x > 10 and an outflow with the expression (x + 1) * 2 behaves like this:

• If the inflows try to read 5 and 5, respectively, the transition is not enabled, because the first pattern expects an array.
• If the inflows try to read [ 4 ] and 5, respectively, the transition is not enabled, because the bindings are not compatible.
• If the inflows try to read [ 5 ] and 5, respectively, the transition is not enabled, because the binding does not satisfy the guard. If the inflows try to read [ 20 ] and 20, respectively, the transition is enabled, and the outflow produces a token colored 42.

The syntax for patterns and expressions is inspired by JavaScript. Here are examples of valid patterns:

• x
• _ (a wildcard, drops the value)
• []
• [a, b, c]
• [a, b, [c, d]]
• [a, , c] (equivalent to [a, _, c])
• [a, b, _]
• {}
• { a: a, b: c }
• { a, b }
• { a }
• [a, { b : c, d: [e, f] }]
• { one, two, ...rest } (rest will be an object with all properties except one and two)
• { ...obj } (equivalent to obj except it rejects non-objects)
• [ one, two, ...rest ] (rest will be an array with the all remaining items)
• [ ...arr ] (equivalent to arr except it rejects non-arrays)

Here are examples of valid expressions:

• var
• 1337
• true
• "hello world"
• "hello \"world"
• "back\\slash"
• 1 + 28
• 1 - 28
• "hello" + " " + "world"
• 3 * 9
• a * ( b + c)
• 1 > 2
• 2 >= 2
• 2 <= 1
• 2 < 1
• 2 == 1
• 2 != 1
• a || b
• a && b
• !a
• []
• [ 42, 1337-1336 ]
• [1, 1, 0].length
• [9, 8] @ [7] @ [6, 5] (array concatenation)
• {}
• {a:7, b : x, c }
• { a, ...b, c }
• { a: 1, ...x, b: 2, ...y, a: 2 }
• { x, y }.y.z
• true ? 42 : 1337
• eval(a + b, vars) (evaluates a + b in the binding expressed by the object vars)

An Example

The following Petri net computes the first 10 numbers of the Fibonacci sequence and puts a token with an array of them in the place done:

{
    "places": [
        {
            "key": "calc",
            "displayName": "calculate Fibonacci sequence",
            "extensions": {}
        },
        {
            "key": "done",
            "displayName": "calculation finished",
            "extensions": {}
        }
    ],
    "transitions": [
        {
            "key": "add-fib",
            "displayName": "add one fibonacci number",
            "guard": "list.length < 10",
            "inFlows": [
                {
                    "source": "calc",
                    "pattern": "{ a, b, list }"
                }
            ],
            "outFlows": [
                {
                    "target": "calc",
                    "expression": "{ a: b, b: a + b, list: list @ [a] }"
                }
            ],
            "extensions": {}
        },
        {
            "key": "exit",
            "displayName": "exit the main loop",
            "guard": "list.length == 10",
            "inFlows": [
                {
                    "source": "calc",
                    "pattern": "{ list }"
                }
            ],
            "outFlows": [
                {
                    "target": "done",
                    "expression": "list"
                }
            ],
            "extensions": {}
        }
    ],
    "initialMarking": {
        "tokens": {
            "calc": [
                {
                    "color": {
                        "a": 0,
                        "b": 1,
                        "list": []
                    }
                }
            ]
        },
        "extensions": {}
    }
}

More specifially, the above is the JSON object representation of the net. The following code parses this to a JavaScript object, converts it to a real PetriNet instance, then uses the API to query the behavior of the net:

const { PetriNet } = require('@pseuco/colored-petri-nets');

const fs = require('fs');

const netString = fs.readFileSync('net.json');
const netObject = JSON.parse(netString);

// build an actual PetriNet object from the plain object representation.
const net = PetriNet.fromObject(netObject);

let marking = net.initialMarking;

while (true) {
    console.log(JSON.stringify(marking.toObject()));

    let successors = marking.enabledMoves();
    if (successors.length > 1) throw new Error("Found nondeterminism!");
    if (successors.length < 1) {
        console.log("Terminated.");
        return;
    }

    console.log(` ↓ ${successors[0].transition.displayName}`);

    marking = successors[0].marking;
}