Given a definite program, how do I obtain its Herbrand base?

Question

Given a definite program, how can I obtain its Herbrand base?

For instance, given the program $P$ below, what is its Herbrand base $B_P$?

$p(f(x)) \leftarrow p(x)$
$q(a) \leftarrow p(x)$

I know the definition of Herbrand base for a first-order language $L$, which relies on the concept of a Herbrand universe for $L$ (I am putting them below), but I don't know the connection with a Herbrand base of a program.

Herbrand base. Let $L$ be a first-order language. The Herbrand base $B_L$ is the set of all ground atoms which can be formed by using predicate symbols from $L$ with ground terms from the Herbrand universe as arguments.

Herbrand universe. The Herbrand universe $U_L$ for $L$ is the set of all ground terms, which can be formed out of constants and function symbols appearing in $L$. (In the case that $L$ has no constants, we add some constant, say $a$ to form ground terms.)

Answer 1

If $S$ is a set of formulas, by abuse of language, we can talk about the Herbrand base $B_S$ of $S$ instead of the Herbrand base $B_L$ of the underlying first-order language $L$ from which the formulas come. Now, recall that a program $P$ is a set of formulas, and you will know what he meant by $B_P$.

In the particular example, the Herbrand universe is $$H_P = \{a, f(a), f(f(a)), \ldots \} $$ and hence the Herbrand base is $$B_P = \{ p(a), q(a), p(f(a)), q(f(a)), p(f(f(a))), q(f(f(a))), \ldots \} $$