OCaml common functions to manipulate Lists

List.ml

(* Cons Operator (::) - Prepend an element to an list *)
(* * Operator (@) - Concatenate tow lists *)

(* List Length #1 *)
let rec length l =
    match l with
    | [] -> 0
    | h::t -> 1 + length t;; (* h = head; t = tail*)

(* List length Optimized #2 *)
(* Exchange 'h' value for an wildcar *)
let rec length2 l =
    match l with
    | [] -> 0
    | _::t -> 1 + length2 t;; (* _ = wildcard *)

(* List length Optimized #3 *)
(* Uses 'tail recursion' *)
let rec length_inner l n =
    match l with
      [] -> n
    | _::t -> length_inner t (n + 1);;

(* This is just an alias to 'length_inner'
 * It encapsulates the 'n' parameter
 *)
let rec length3 l = length_inner l 0;;

(* Returns the elements with odd indexes *)
let rec odd l =
    match l with
      [] - > []
    | [a] -> [a]
    | a::_::t -> a :: odd t;;

(* Returns the elements with even indexes *)
let rec even l =
    match l with
    | [] | [_] -> []
    | _ :: a :: t -> a :: even t;;

(* Counts the number of true elements in a list *)
let rec count_true l =
    match l with
    | [] -> 0
    | h :: t -> if h = true then 1 + count_true t else count_true t;;

let rec count_true_inner l n =
    match l with
    | [] -> n
    | h :: t -> if h = true then count_true_inner t (n+1) else count_true_inner t n;;

let rec count_true2 l = count_true_inner l 0;;