(*
** This implementation is verified!
*)

dataprop FIB (int, int) =
  | FIB0 (0, 0) | FIB1 (1, 1)
  | {n:nat} {r0,r1:int} FIB2 (n+2, r0+r1) of (FIB (n, r0), FIB (n+1, r1))
// end of [FIB] // end of [dataprop]

fun
fibats{n:nat}
  (n: int (n))
: [r:int] (FIB (n, r) | int r) = let
  fun loop
    {i:nat | i <= n}{r0,r1:int}
  (
    pf0: FIB (i, r0), pf1: FIB (i+1, r1)
  | ni: int (n-i), r0: int r0, r1: int r1
  ) : [r:int] (FIB (n, r) | int r) =
    if (ni > 0)
      then loop{i+1}(pf1, FIB2 (pf0, pf1) | ni - 1, r1, r0 + r1)
      else (pf0 | r0)
    // end of [if]
  // end of [loop]
in
  loop {0} (FIB0 (), FIB1 () | n, 0, 1)
end // end of [fibats]