LAWS — why this is algebra, not just a protocol

Each of the 5 opcodes has a law. The laws are what make the substrate composable, replayable, and provable. If your code obeys the laws, the substrate can optimize it, parallelize it, and roll it back safely.

01The shape

02Try it

// Lesson 6: The 5 laws
// Try to break them. The substrate will catch you.

// 1. BIND idempotence: same name + value = same event
sub.bind('x', 1);
sub.bind('x', 1);  // no event (idempotent)
sub.bind('x', 2);  // event (different value)

// 2. LINK transitivity: a→b, b→c implies a→c
sub.link('alice', 'bob', 'friend');
sub.link('bob', 'carol', 'friend');
// alice→carol is implied by transitivity

// 3. EFFECT associativity: order of composition doesn't matter
sub.bind('counter', 0);
sub.effect('counter', (n) => (n || 0) + 1);
sub.effect('counter', (n) => (n || 0) * 2);
sub.effect('counter', (n) => (n || 0) - 1);
// = ((0 + 1) * 2) - 1 = 1
// = ((0 - 1) + 1) * 2 = 0
// The substrate records both, replays both

// 4. VIEW purity: no journal pollution
sub.bind('name', 'Casey');
const x1 = sub.view('name');
const x2 = sub.view('name');
// x1 === x2; the journal is unchanged

// 5. TICK monotonicity: time only moves forward
sub.tick(0.1);
sub.tick(0.2);
sub.tick(0.1);
// All t values are increasing

03What the laws buy you

When your code obeys the 5 laws, the substrate can:

• Replay: the journal IS the state. Replay produces the same state every time.
• Roll back: the journal is a list. Remove the tail, you have the past.
• Parallelize: the laws tell you which operations commute. The substrate can reorder for speed.
• Prove: the substrate can verify that a sequence of events obeys the laws. The prover in quilt-substrate-meta does this.

This is what makes the substrate an algebra, not just a protocol. The laws are the algebra's axioms.

04What you can build

A substrate that can run anywhere. The same journal replays to the same state on a $2 ESP32 or a 64-core server. The laws are the contract.

05Next

Now let's build something real. Lesson 7: Build your first app →