let l = [ 0; 1; 3; -1; -2; -4; 10 ];;

let rec remove_negative = function
    | [ ] -> [ ]
    | head :: tail ->
        if head < 0 then
            remove_negative tail
        else
            head :: remove_negative tail
;;

(* And here is the function I would like to be able to write: *)
let rec remove_negative l = match l with
    | [ ] -> [ ]
    | head :: tail ->
        if head < 0 then
            (* remove all the items at the beginning that are negative *)
            remove_negative tail
        else
            (* when you get one non-negative item *)
            let loop prev curr = match curr with
                | [ ] -> l
                | head :: tail ->
                    (* make the list "skip" all items that are negative *)
                    if head < 0 then
                        prev.tail <- tail
                    else ( );
                    loop prev tail
            in
            loop l tail
(* *)

let rec print_list = function
    | [ ] -> ( )
    | head :: tail ->
        print_int head;
        print_newline ( );
        print_list tail
;;

print_list( remove_negative l );;