Is Behavior a Comonad?

Question

Conal Elliott talks about Streams and Comonads here: http://conal.net/blog/posts/sequences-streams-and-segments

However, he doesn't mention Behavior directly. So.. is Behavior a Comonad, and if so - what does that mean practically?

For starters - I suppose Behavior can provide the extend and extract functions. The only way I see that working is if it samples the value at a specific moment in time.

Is that what Comonad would mean for Behavior? That it allows one to "fork and freeze" a Behavior?

In other words - if we have a Behavior that has these values over time: A,B,C,D,... we could extend it at the time where it's B, and get a new Behavior which contains B indefinitely (which is useful - since we could then lift or map it etc.)

Answer 1

Behavior a is isomorphic to (Time -> a). The definitions Conal gives in the section of that post "Adding continuity" match those in the comonad package.

It is not obvious to me how to make time a Monoid. Several Monoid instances are possible, but are any useful? Conal's post on future values suggests that the Max is a useful Monoid for working with time.

This works out that extract @Behavior gives the value at the earliest possible time, and duplicate @Behavior gives the value at the later of the two times. I can see both of those being useful. Perhaps there are other useful Monoids also?