# Why a third type Discrete?

In an ideal world, users of functional reactive programming would
only need to use the notions of `Behavior`

and `Event`

,
the first corresponding to value that vary in time
and the second corresponding to a stream of event ocurrences.

However, there is the problem of *incremental updates*.
Ideally, users would describe, say, the value of a GUI text field
as a `Behavior`

and the reactive-banana implementation would figure
out how to map this onto the screen without needless redrawing.
In other words, the screen should only be updated when the behavior changes.

While this would be easy to implement in simple cases,
it may not always suit the user;
there are many different ways of implementing
*incremental computations*.
But I don't know a unified theory for them, so
I have decided that the reactive-banana will give
*explicit control over updates to the user*
in the form of specialized data types like `Discrete`

,
and shall not attempt to bake experimental optimizations into the `Behavior`

type.

To sum it up:

- You get explicit control over updates (the
`changes`

function), - but you need to learn a third data type
`Discrete`

, which almost duplicates the`Behavior`

type. - Even though the type
`Behavior`

is more fundamental, you will probably use`Discrete`

more often.

That said, `Discrete`

is not a new primitive type,
but built from exising types and combinators;
you are encouraged to look at the source code.

If you are an FRP implementor, I encourage you to find a better solution. But if you are a user, you may want to accept the trade-off for now.

# Discrete time-varying values

changes :: Discrete f a -> Event f aSource

Event that records when the value changes. Simultaneous events may be pruned for efficiency reasons.

value :: Discrete f a -> Behavior f aSource

Behavior corresponding to the value. It is always true that

value x = stepper (initial x) (changes x)

stepperD :: FRP f => a -> Event f a -> Discrete f aSource

Construct a discrete time-varying value from an initial value and a stream of new values.