3 exception Unstable;; (* generally thrown when there is a divide by zero *)
5 exception Fatal;; (* generally indicates an uncorrected bug *)
7 (* represents a closed interval [lo,hi] of the real line *)
14 (* represents a function u:real->real, its derivative du, and 2nd derivative *)
17 u : interval -> interval;
18 du : interval -> interval;
19 ddu : interval -> interval;
22 (* represents the value f of function of six variables at some point y.
23 and the value df of its six partial derivatives, evaluated at the same point y.
24 The length of the list df should always be 6.
33 represents approximation data for a function f on a rectangular domain [x,z].
34 l gives the value and partial derivatives of f at some point y in the domain.
35 dd gives interval bounds on the second derivatives over the entire domain.
36 w i is an upper bound on widths (z i - y i) and (y i - x i).
39 type taylor_interval = {
42 dd : interval list list;