let headoflist lst = match lst with
    | [] -> failwith "Empty list"
    | [h] -> h
    | h :: t -> h

let tailoflist lst = match lst with
    | [] -> failwith "Empty list"
    | [h] -> failwith "One element only"
    | h :: t -> t;;

let rotate_left lst = match lst with
    | [] -> []
    | h :: t -> t @ [h];;

let rec last = function
    | [] -> -1
    | [h] -> h
    | h :: t -> last t;;

let rec maxoflist lst = match lst with
    | [] -> failwith "Empty list"
    | [h] -> h
    | h :: t -> max h (maxoflist t);;

let u x y = x + y;;
let f x y = 2 * x + y;;

let rec apply f ac lst = match lst with
    | [] -> 0
    | [h] -> (f h ac)
    | h :: t -> (f h (apply f ac t));;

type nrcomplex = Real of float | Complex of (float * float);;

let add_complex x y = match (x, y) with
    | (Real x, Real y) -> Real(x +. y)
    | (Real x, Complex(ax, ay)) -> Complex(x +. ax, ay)
    | (Complex(ax, ay), Real y) -> Complex(ax, y +. ay)
    | (Complex(ax, ay), Complex(bx, by)) -> Complex(ax +. bx, ay +. by);;

let mul_complex x y = match (x, y) with
    | (Real x, Real y) -> Real(x *. y)
    | (Real x, Complex(ax, ay)) -> Complex(x *. ax, x *. ay)
    | (Complex(ax, ay), Real y) -> Complex(y *. ax, y *. ay)
    | (Complex(ax, ay), Complex(bx, by)) -> Complex((ax *. bx -. ay *. by), (ax *. by +. bx *. ay));;