use Nat drop
use Optional None Some

search : (Nat -> Int) -> Nat -> Nat -> Optional Nat
search hit bot top =
  -- go : Nat -> Nat -> Optional Nat
  go bot top =
    if bot >= top then None
    else
      mid = (bot + top) / 2
      match hit mid with
        +0 -> Some mid
        -1 -> go bot (drop mid 1)
        +1 -> go (mid + 1) top
        _ -> bug "unexpected"
  go bot top