b_assertz(Term) :-
    assertz(Term, Ref),
    undo(erase(Ref)).

Without undo/1 we can achieve something similar by leaving a choicepoint using the almost portable^{79assertz/2 is not part of the ISO standard but supported by multiple systems.} alternative below.

b_assertz(Term) :-
    assertz(Term, Ref),
    (   true
    ;   erase(Ref),
        fail
    ).

The undo/1 based solution avoids leaving a choice point open and, more importantly, keeps undoing the assert also if the choice point from the second alternative is pruned.

Currently the following remarks apply

• Goal is copied when it is registered.

• “First opportunity” means after backtracking or at the first call port reached.

• Multiple undo goals may be scheduled that are executed as a batch. If multiple goals raise an exception, the most urgent is preserved after all goals have been executed.

• It is not allowed for Goal to call undo/1. An attempt to do so results in a permission_error exception.

• Note that an exception that is caught higher in the call stack backtracks and therefore ensures Goal is called.

See also snapshot/1 and transaction/1.