delta_apply : ('a -> 'a delta) -> 'a -> 'a
Apply a function to an argument, re-using the argument if possible.
An application delta_apply f x applies f to x and, if the result is SAME, returns x. If the result is DIFF y, then y is returned.
If f x raises exception e, then delta_apply f x raises e.
Suppose we want to write a function that replaces every even integer in a list of pairs of integers with an odd one. The most basic replacement function is therefore
   - fun ireplace i = if i mod 2 = 0 then DIFF (i+1) else SAME
Applying ireplace to an arbitrary integer would yield an element of the int delta type. It’s not seemingly useful, but it becomes useful when used with similar functions for type operators. Then a delta function for pairs of integers is built by delta_pair ireplace ireplace, and a delta function for a list of pairs of integers is built by applying delta_map.
   - delta_map (delta_pair ireplace ireplace)
               [(1,2), (3,5), (5,7), (4,8)];
   > val it = DIFF [(1,3), (3,5), (5,7), (5,9)] : (int * int) list delta

   - delta_map (delta_pair ireplace ireplace)
               [(1,3), (3,5), (5,7), (7,9)];
   > val it = SAME : (int * int) list delta
Finally, we can move the result from the delta type to the actual type we are interested in.
   - delta_apply (delta_map (delta_pair ireplace ireplace))
               [(1,2), (3,5), (5,7), (4,8)];
   > val it = [(1,3), (3,5), (5,7), (5,9)] : (int * int) list

Used to change a function from one that returns an 'a delta element to one that returns an 'a element.
HOL  Kananaskis-14