Fixed-point engine

ForkState (activates multiple states immediately) and JoinState (activates when prerequisites complete) are both "automatic" — no extra dispatch needed. They can also chain: a fork can feed a join's prerequisites, and a join can target another fork.

The fixed-point loop resolves all of this within a single dispatch call.

The algorithm

After applying the explicit transitions for a dispatched action, the engine enters a loop:

loop:
  for each JoinState in the workflow:
    if the join is idle AND its mode threshold is now satisfied:
      activate the join

  for each newly active ForkState:
    complete the fork
    activate all its targets

  if nothing changed in this iteration → break

This is a fixed-point iteration (Kleene iteration): it terminates when a full pass produces no new changes. Since states only move forward (idle → active → completed), termination is guaranteed.

Why it matters

Consider this graph:

Without the loop, activating join-1 would need a second dispatch to enter fork-2. With it, a single GO resolves the entire chain in one call.

Termination proof

The state space is finite. Every state has exactly four statuses: idle, active, waiting, completed. Transitions are monotonic — a state can only move to a later status, never backwards. Therefore the number of possible state-space configurations is bounded, and each iteration of the fixed-point loop strictly decreases the number of idle states or terminates unchanged. The loop must terminate in at most |states| iterations.

Fork atomicity

A ForkState is entered and completed in the same loop iteration — never left active between iterations. getCurrentStates() will never return a ForkState ID; forks are routing nodes, not positions.

JoinState activation condition

A JoinState activates when:

• Its current status is idle
• The number of completed states in requires satisfies the mode threshold:
  • 'all' → all states in requires are completed
  • 'any' → at least one state in requires is completed
  • number N → at least N states in requires are completed

The check runs after every transition application, including ones triggered by fork resolution — so joins outside the original dispatch's scope can still activate as a side effect.