Behavior

Behavior is a time-varying value: a trajectory through state space:

$\text{Time}\to\text{Value}$

This follows the classic Functional Reactive Programming notion of behavior introduced by Conal Elliott and Paul Hudak: a first-class value that varies over time.

For an entity, behavior can be viewed as both an event schedule and a state history. The event schedule emphasizes occurrences and ordering. The state history emphasizes samples of state at versions, times, or cuts through the behavior.

Events do not accumulate into behavior by themselves. An observer interprets an event schedule through an accumulator, integrator, scanner, or transition function, then supplies a hold or interpolation function that maps the resulting history to values over time:

event schedule
+ initial value
+ interpretation function
+ interpolation function
-> behavior

For endogenous events in a sequential entity, the interpretation function can be viewed as a state action. Once an event has been interpreted and committed within a boundary, it may be identified with a function on state:

event : State -> State

Folding a schedule of endogenous events applies or composes those state actions from an initial state:

s1 = e1(s0)
s2 = e2(s1)
s3 = e3(s2)

The fold produces state samples or a state history. A behavior is produced when an interpolation rule, often "hold latest" for discrete entity state, maps that history into a time-varying value:

behavior(t) = interpolate(t, state history)

Behavior connects state and events:

Events can be folded, integrated, scanned, switched, or transformed by an observer to produce behavior.
Behavior can be sampled, compared, or observed for changes that emit events.
Folding committed events produces state samples.
Comparing or observing state samples can produce events.

In FRP, switching changes which behavior is currently followed. In event-sourced models, this appears when an endogenous event changes the active lifecycle mode, process behavior, projection rule, routing policy, or interpreter for future events. The event does not only update a value; it can change the rule that will produce or interpret later values.

Event-State Duality does not imply that event schedules and state histories are isomorphic. They are dual views of behavior whose transformations are model-dependent and often lossy.

External References

Conal Elliott and Paul Hudak, Functional Reactive Animation, Proceedings of the Second ACM SIGPLAN International Conference on Functional Programming, ICFP '97, pages 263-273, 1997. Author copy: conal.net/papers/icfp97.