Adventures in Prolog - Simplify Sum (2)

The last post showed how to compute simple addition expressions. To provide a more structured approach to the problem at hand, I decided to write a small Prolog program that actually recognizes such addition expressions. This program basically represents a Prolog conversion of the grammar underlying such addition expressions. Because Prolog notation and grammer are so close, I will not comment on the following Prolog clauses.

addition_expression(A) :- sum_term(A).
addition_expression(A) :-
A = X + Y,
addition_expression(X),
sum_term(Y).

sum_term(X) :- number(X).
sum_term(X) :- atom(X).
sum_term(X) :- prod_term(X).

prod_term(X) :- X = A * B, number(A), atom(B).
prod_term(X) :- X = A * B, atom(A), number(B).