IIUC, it's a bit different. Kleislis reify functions with type (A => F[B]), providing composition of these functions. (See http://underscore.io/blog/posts/2015/10/14/reification.html) Composition of Kleislis is like old style FRP in that it is synchronous.
However the hot/cold distinction in Rx is because execution is not deferred, as I understand it. IIUC observables / streams / whatever they are called in Rx start running as soon as they are defined. If `naturalNumbers` is the event stream of natural numbers, the result of
naturalNumbers.map(x => print(x))
might not output 0, 1, ..., because a whole bunch of natural numbers might have already been emitted before `map` is called. It is this difficulty with reasoning that motivates hold/cold streams (again, as I understand it). A simple solution is to separate defining the network and running it. e.g. by requiring calling `run` method to get a result. Then substitution is maintained in the "world" prior to calling `run`, and this distinction is unnecessary.
The hot/cold distinction is indeed because most Rx Observables use deferred creation (cold) and most Rx Operators use deferred creation (cold) until the equivalent to a run is called (subscribe) making the Observable hot.
The complications to this that make for so much documentation come from the places where those "mostly" answers are wrong: Rx has ways to build hot Observables that are not deferred and begin immediately; Rx has a few rare exception Operators that can force an Observable hot, those confusing matters; finally, Rx cold Observables by default don't share deferred execution so multiple subscriptions create multiple "heat transition" side effects (ie, an observable is "run" every time it is subscribed). There are mechanics and operators in place to deal with all of these cases in Rx, but that adds to the learning curve of knowing when deferred execution takes place. (So yes the separation you describe exists between creating a network of cold observable and making them all "hot", but it does bring its own complications only furthering the need for the hot/cold distinction in cases where you are trying to avoid repeating things like side effects, which will happen when you aren't properly sharing the same "hot" source.)
So yes, Hot/Cold is entirely about deferred versus immediate observables/streams and both the surprises of finding a hot observable when you expected a cold one (as in the case of your example) or even a cold observable when you expected a hot one (side effects and memory leaks and "no execution" problems because you forgot to make anything hot).
However the hot/cold distinction in Rx is because execution is not deferred, as I understand it. IIUC observables / streams / whatever they are called in Rx start running as soon as they are defined. If `naturalNumbers` is the event stream of natural numbers, the result of
might not output 0, 1, ..., because a whole bunch of natural numbers might have already been emitted before `map` is called. It is this difficulty with reasoning that motivates hold/cold streams (again, as I understand it). A simple solution is to separate defining the network and running it. e.g. by requiring calling `run` method to get a result. Then substitution is maintained in the "world" prior to calling `run`, and this distinction is unnecessary.