In this case, the play/pause button becomes part of the "video." So now the video includes a piece of state which has perhaps been toggled to "paused." And at that point F(i) = F(i+1)... = F(i+n), since nothing will have changed for n moments (until the user interacts again). Kinda hard though to fully get this in the abstract. I struggled with the same questions. All I can say is SICP, all of Rich Hickey's videos, redux, elm, resources listed on haskel.com all helped.

Also putting it all together in writing here https://softwarefordays.com/post/functional-programming-and-....

In this^ blog I've included an interactive user interface that can be seen as purely functional, even though it's a stateful ATM program. I'm actually hoping that this blog could help teach someone what took me 2 years to finally realize. I think it could be worthwhile given your questions - if you take a look, please let me know what you think!