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Prolog (and Datalog) can model relational databases.

The set of facts is called a database, the intensional database. The rules are the extensional database.

Here is an example. Here is the Prolog code.
prints([]):- nl. prints([X|Rest]):- print(X), prints(Rest). b(0). b(1). go:- prints(['X Y Z\n']), b(X), b(Y), b(Z), prints([X,' ',Y,' ',Z,'\n']), fail. :- solve(go).
Here is the output of the Prolog code.
X Y Z\n 0 0 0\n 0 0 1\n 0 1 0\n 0 1 1\n 1 0 0\n 1 0 1\n 1 1 0\n 1 1 1\n
How can we add a running count to the list of solutions generated using backtracking?

To support practical database representation, the assert and retract predicates are provided.

These predicates can be misused to simulate parts of an assignment-based language.

A common use of assert and retract is to count solutions in the presence of backtracking using fail.

Here is an example that uses assert and retract to display a running count of solutions. Here is the Prolog code.
prints([]):- nl. prints([X|Rest]):- print(X), prints(Rest). b(0). b(1). go:- assert(count(0)), prints(['#. X Y Z\n']), b(X), b(Y), b(Z), retract(count(N)), N1 is N + 1, assert(count(N1)), prints([N1,'. ',X,' ',Y,' ',Z,'\n']), fail. :- solve(go).
Here is the output of the Prolog code.
#. X Y Z\n 1. 0 0 0\n 2. 0 0 1\n 3. 0 1 0\n 4. 0 1 1\n 5. 1 0 0\n 6. 1 0 1\n 7. 1 1 0\n 8. 1 1 1\n
Exercise: Change the code (in a minimal way) to output from 0 to 7 rather than 1 to 8 without changing the first assert which asserts count(0).