total : ('a -> 'b) -> 'a -> 'b option
Converts a partial function to a total function.
In ML, there are two main ways for a function to signal that it has been called on an element outside of its intended domain of application: exceptions and options. The function total maps a function that may raise an exception to one that returns an element in the option type. Thus, if f x results in any exception other than Interrupt being raised, then total f x returns NONE. If f x raises Interrupt, then total f x likewise raises Interrupt. If f x returns y, then total f x returns SOME y.

The function total has an inverse partial. Generally speaking, (partial err o total) f equals f, provided that err is the only exception that f raises. Similarly, (total o partial err) f is equal to f.

When application of the first argument to the second argument raises Interrupt.
- 3 div 0;
! Uncaught exception:
! Div

- total (op div) (3,0);
> val it = NONE : int option

- (partial Div o total) (op div) (3,0);
! Uncaught exception:
! Div
HOL  Kananaskis-14