exception Unstable;;  (* generally thrown when there is a divide by zero *)

exception Fatal;;  (* generally indicates an uncorrected bug *)

(* represents a closed interval [lo,hi] of the real line *)

type interval = {
  lo : float;
  hi : float;
};;

(* represents a function u:real->real, its derivative du, and 2nd derivative *)

type univariate = {
  u : interval -> interval;
  du : interval -> interval;
  ddu : interval -> interval;
};;

(* represents the value f of a function and its derivative at some point y *)

type line = {
  f : interval;
  df : interval;
};;

(*
  represents approximation data for a function f on a rectangular domain [x,z].
  l gives the value and the derivative of f at some point y in the domain.
  dd gives interval bounds on the second derivative over the entire domain.
  w i is an upper bound on widths (z - y) and (y - x).
*)

type taylor_interval = {
  l : line;
  w : float;
  dd : interval;
};;