[Haskell-cafe] FRP: Why is Behavior not a Monad?

[martin]

Hello all,

it appears to be difficult to define a Monad instance for Behavior and in many (if not all) reactive libraries Behavior
is not a Monad. Why is that so?

If a Beahvior is conceptionally a function from Time to something,

	newtype Behavior a = Behavior (Time -> a)

then its Monad instance should work like a Reader Monad.

Alternatively one can look at the join function

	join :: Behavior (Behavior a) -> Behavior a.

This corresponds to the situation where you switch between Channels on a TV remote controle and each Channel is a
behavior of Image. Then

	join Behavior (Behavior image)

should give you the video stream you see on the screen. How can one possibly live without this operation?

I assume this has something to do with the actual implementation and not so much with the semantics, because
semantically I don't see any problems.

So,
- why is Behavior not a Monad and
- how would you express the TV-remote example without a Monad?