(* Division entière par l'algorithme d'Euclide *)

module Division

  use int.Int
  use ref.Refint

  let division (a b: int) (* renvoie une paire d'entiers (quotient,reste) *)
    requires { 0 <= a && 0 < b }
    ensures  { let (q,r) = result in q * b + r = a && 0 <= r < b }
  =
    let q = ref 0 in
    let r = ref a in
    while !r >= b do
      invariant { a = !q * b + !r && 0 <= !q && 0 <= !r }
      variant   { !r - b }
      q := (!q) + 1;
      r := (!r) - b
    done;
    (!q,!r)

end