let square x = x * x ;;
let rec fact x = if x=0 then 1
                 else x * fact (x-1);;
let rec sum ys = match ys with
            []      -> 0                
          | (x::xs) -> x + sum xs;; 
let rec length ys = match ys with
            []      -> 0
          | (x::xs) -> 1 + length xs;;

let rec append zs ys = match zs with
               []      -> ys
             | (x::xs) -> x :: append xs ys;;

let rec map f ys = match ys with
              []      -> []
            | (x::xs) -> f x :: map f xs;;