module Recursive
  use int.Int
  use seq.Seq
  use mach.java.lang.IndexOutOfBoundsException
  use mach.java.lang.Integer
  use mach.java.util.List 

  type t
  
  let rec count_true_rec (l : list bool) (i : integer) : integer
    requires { length l < Integer.max_integer }
    ensures { i <= length l -> result <= length l - i }
    requires { 0 <= i }
    variant { length l  - i }
  =
    let e_x = i+1 in 
    try
      if i >= size l then 0
      else if get l i then 1 + count_true_rec l e_x
      else count_true_rec l e_x
    with
     IndexOutOfBoundsException.E -> absurd
    end
    
  let count_true (l : list bool) : integer
    requires { length l < Integer.max_integer }
  =
    count_true_rec l 0

end