Solution to CodeWars peano numbers kata

Peano.fsx

type Peano = 
  | Zero 
  | Succ of Peano

// Comapre
let rec cmp x y =
  match x, y with
    | Zero, Zero -> 0
    | Zero, Succ _ -> -1
    | Succ _, Zero -> 1
    | Succ a, Succ b -> cmp a b

// Addition
let rec add x y =
  match x, y with 
    | Zero, Zero -> Zero
    | Succ a, Zero
    | Zero, Succ a -> Succ a
    | Succ _, Succ b -> add (Succ x) b

// Subtraction
let rec sub x y =
  match x, y with 
    | Zero, Zero -> Zero
    | Succ _, Zero -> x
    | Zero, Succ _ -> failwith "negative number"
    | Succ a, Succ b -> sub a b

// Multiplication
let rec mul x y =
  match x, y with 
    | Zero, _
    | _, Zero -> Zero
    | Succ _, Succ b -> add x (mul x b)

// Integer division
let rec div x y =
  if y = Zero then failwith "divide by 0"
  elif cmp x y = 0 then Succ Zero
  elif cmp x y = -1 then Zero
  else add (Succ Zero) (div (sub x y) y) 

// Modulo
let rec modulo x y =
  match cmp x y with
    | 0 -> Zero
    | -1 -> x
    | _ -> modulo (sub x y) y

// Even
let rec even = function
  | Zero -> true
  | Succ Zero -> false
  | Succ (Succ a) -> even a

// Odd
let odd =
  not << even