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Still in research (please don't share) |
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One big state machine can become difficult to understand
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How can we break a state machine into parts such that when combined they form the whole?
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The Cartesian product of states can be used when we need to keep track of two states running in parallel.
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There are different two different ways we can advance two state machines that run in parallel, either by stepping one of them and leaving the other alone or stepping both of them in lockstep.
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Angelic product, allows of stepping one of the state machines:
type SM s i o = i -> s -> (s, o)
angelic : SM s i o -> SM t j p -> SM (s, t) (i + j) (o + p)
angelic f g ij (s, t) case ij of
Left i -> let (s', o) = f i s in ((s', t), Left o)
Right j -> let (t', p) = g j t in ((s, t'), Right p)
video : SM {playing, stopped} {stop, play} ()
audio : SM {mutued, unmuted} {mute, unmute} ()
player = angelic video audio
- Tensor product, allows us to step both state machines in lockstep:
tensor : SM s i o -> SM t j p -> SM (s, t) (i, j) (o, p)
tensor f g (i, j) (s, t) =
let
(o, s') = f i s
(p, t') = g j t
in
((s', t'), (o, p))
See also:
- "Concurrent state machines" in Nystrom;
- Orthogonal regions in UML state machines;
- Programming interfaces and basic topology by Peter Hancock and Pierre Hyvernat (2009).
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http://gameprogrammingpatterns.com/state.html#hierarchical-state-machines
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Hierarchically nested states in UML state machines
- Game Programming Patterns by Robert Nystrom (2014, chapter 7);
- Development and Deployment of Multiplayer Online Games, Vol. II by Sergey Ignatchenko (2020, chapter 5);
- Statecharts: A visual formalism for complex systems by David Harel (1987);
- UML state machines.