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