This predicate allows you to make several predicates over integers deterministic while preserving their generality and completeness. For example:

n_factorial(N, F) :-
        zcompare(C, N, 0),
        n_factorial_(C, N, F).

n_factorial_(=, _, 1).
n_factorial_(>, N, F) :-
        F #= F0*N, N1 #= N - 1,
        n_factorial(N1, F0).

This version is deterministic if the first argument is instantiated, because first argument indexing can distinguish the two different clauses:

?- n_factorial(30, F).
F = 265252859812191058636308480000000.

The predicate can still be used in all directions, including the most general query:

?- n_factorial(N, F).
N = 0,
F = 1 ;
N = F, F = 1 ;
N = F, F = 2 .