I know that it can be proven PROLOG is Turing-complete by constructing a program that simulates a Turing machine like this:
turing(Tape0, Tape) :-
perform(q0, [], Ls, Tape0, Rs),
reverse(Ls, Ls1),
append(Ls1, Rs, Tape).
perform(qf, Ls, Ls, Rs, Rs) :- !.
perform(Q0, Ls0, Ls, Rs0, Rs) :-
symbol(Rs0, Sym, RsRest),
once(rule(Q0, Sym, Q1, NewSym, Action)),
action(Action, Ls0, Ls1, [NewSym|RsRest], Rs1),
perform(Q1, Ls1, Ls, Rs1, Rs).
symbol([], b, []).
symbol([Sym|Rs], Sym, Rs).
action(left, Ls0, Ls, Rs0, Rs) :- left(Ls0, Ls, Rs0, Rs).
action(stay, Ls, Ls, Rs, Rs).
action(right, Ls0, [Sym|Ls0], [Sym|Rs], Rs).
left([], [], Rs0, [b|Rs0]).
left([L|Ls], Ls, Rs, [L|Rs]).
However, I’m wondering which parts of the PROLOG language one could strip away (esp. function symbols, clause overloading, recursion, unification) without losing Turing completeness. Are function symbols themselves Turing complete?