How can the actor model be applied to allow pure functional languages to have side-effects?
Erlang is an example. I actually don't know Erlang, so I'm going to use some pseudocode:

Suppose you have two threads, Alice and Bob. They talk by calling each other's Send member route, which blocks until the other end replies. Alice can keep some "mutable state" for a single integer as follows:

Alice:
  function main_loop(state):
     message = Receive()
     if message == "get":
        Reply(state)
     else
        Reply("Okay")
        main_loop(message)
  main_loop(0)

Bob:
  Alice.Send(100) // Store 100 into the mutable state
  Alice.Send("get") // obtain the 100
  Alice.Send(200) // Store 200
  Alice.Send("get") // get the 200