When I was learning about functional programming in college, I got about as far as learning about the avoidance of side effects, at which point I started asking myself, "how would one write a video game in an FP language if you're not supposed to e.g. update the player's on-screen position in response to a keystroke"? The answer I got was to either generate an entire new game-state for each update (which seemed unwieldy), or work around the problem using monads, which admittedly I never really understood. I went back to procedural programming since that looked like the more straightforward way to implement the kinds of programs I wanted to write.
My question now is, do people ever actually write video games using functional programming? And if so, how would an FP-based arcade-style video game realistically handle things like updating the state of the player and the monsters at 60fps, as the game progresses?