Akka-examples | These examples are purely meant to illustrate

I'm trying to emulate a simple functional language using actors.

Actor systems nowadays are used basically for speeding up all kind of stuff by avoiding OS locks and stalled threads or to make microservices less painful, but initially it was supposed to be an alternative model of computation in general [1][2] and therefore should be capable to cover any programming language construct and certainly an if, right?

While I'm aware that this is occasionally met with irritation, I saw one timid attempt to move towards recursive algorithms represented using akka actors (I've refurbished it and added further examples including the one given below). That attempt halted at function calls, but why not go further and also model operators and if conditions with actors? In fact the smalltalk language applies this model and yields a precursor of the actor concept, as has been pointed out in the accepted answers below.

Surprisingly recursive function calls aren't much of an issue, but if¹ is, due to it's potentially stateful nature.

Given the clause C: if a then x else y, here's the problem:

My initial idea was, that C is an actor behaving like a function with 3 parameters (a,x,y) that returns either x or y depending on a. Being maximally parallel [2] a,x and y would be evaluated simultaneously and passed as messages to C. Now, this isn't really good, if C is the exit condition of a recursive function f, sending one branch of f in an infinite recursion. Also if x or y have side effects one can't just evaluate both of them. Let's take this recursive sum (which is not the usual factorial, stupid as such and could be made tail recursive, but that's not the point)