No you don't, you merely need each index into an array to be a monad over all possible values it can contain. An array is itself and modifications are (take as arguments and return) its indices.

> you merely need each index into an array to be a monad over all possible values it can contain

Now keep a straight face and say "L1 cache" once again.

And how is that implemented under the hood?

Same as in a higher-level statically typed imperative language: mutable arrays contained within larger dynamic buffers for amoritized constant-time append and prepend.

So it isn't really functional at all. It just hides the side effects behind a lot of complexity.

This is precisely what functional programming does. Purely functional abstractions are just that, abstractions.