module MutRec
  use int.Int
  use int.EuclideanDivision
  use mach.java.lang.ArithmeticException
  use mach.java.lang.String
  use mach.java.lang.Integer
  use mach.java.util.Random
  use mach.java.lang.Array

  let rec even (number : integer) : bool        
    ensures { result <-> mod number 2 = 0 }
    variant { if number < 0 then -number else number  }
  = 
    if number = 0  then true
    else if number < 0 then odd (number + 1)
    else odd (number - 1)
  with odd (number : integer) : bool  
    ensures { result <-> mod number 2 = 1 }
    variant { if number < 0 then -number else number  }
  =       
    if number = 0  then false    
    else if number < 0 then even (number + 1)
    else even (number - 1)
   

  let main (array string) : unit =        
    try
      let rnd = Random.create () in
      for i = 0:integer to 100:integer do
         let b = Random.next_bounded_int rnd 72 in
         if (b % 2 = 0 && odd b) || (b % 2 = 1 && even b) then
          raise ArithmeticException.E 
      done
    with
    | IllegalArgumentException.E -> absurd
    | ArithmeticException.E -> absurd
    end
end