Have also a look at Array.iteri :
It allows to not use a for, nor an extra ref.
It shall be possible to have in lib:

String.iter : (char -> unit) -> string -> unit
String.iteri : (int ->char -> unit) -> string -> unit

Then:
let map f s = let t = String.copy s in ( String.iteri (fun i c -> t.[i] <- f
c) s ; t )

However, without extra libs nor for, but with a tail-rec function :
let map f s =
    let rec iteri i n t = if i<n then (t.[i] <- f t.[i] ; iteri (succ i) n
t) else t in
    iteri 0 (String.length s) (String.copy s)

Don't known what about performances.
    LC.

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