convert function from using two `let` and `in` to use only one `let`

Question

I found this type zipper and insert functions defined like this:

type 'a zipper = 'a list * int;;

exception Empty

let empty = ([], 0)

let insert ((l, n): 'a zipper) (a: 'a) : 'a zipper =
  let rec ins ll nn =
    if nn = 0 then a::ll 
    else 
      match ll with
      | [] -> raise Empty 
      | h::q -> h::(ins q (nn-1))
  in 
  (ins l n, n)

How can I convert this function to use only one let and without that in (ins l n, n)

Answer 1

Reducing the number of local function definitions is mostly a non-sensical metric, but you can certainly do it

let cons x (l,n) = (x::l,n+1)
let rec insert (l, n) a =
  if n = 0 then a::l,n
  else
    match l with
    | [] -> raise Empty 
    | h::q -> cons h (insert (q,n-1) a)