How should I go about removing a given element from a list? As an example, say I have list ['A'; 'B'; 'C'; 'D'; 'E'] and want to remove the element at index 2 to produce the list ['A'; 'B'; 'D'; 'E']? I've already written the following code which accomplishes the task, but it seems rather inefficient to traverse the start of the list when I already know the index.

let remove lst i =
    let rec remove lst lst' =
        match lst with
        | []   -> lst'
        | h::t -> if List.length lst = i then
                      lst' @ t
                  else
                      remove t (lst' @ [h])
    remove lst []

let myList = ['A'; 'B'; 'C'; 'D'; 'E']
let newList = remove myList 2

Alternatively, how should I insert an element at a given position? My code is similar to the above approach and most likely inefficient as well.

let insert lst i x =
    let rec insert lst lst' =
        match lst with
        | []   -> lst'
        | h::t -> if List.length lst = i then
                      lst' @ [x] @ lst
                  else
                      insert t (lst' @ [h])
    insert lst []

let myList = ['A'; 'B'; 'D'; 'E']
let newList = insert myList 2 'C'