Balanced parentheses with prolog

output.txt

?- balanced_parens(Q).
Q = "" ;
Q = "()" ;
Q = "(())" ;
Q = "((()))" ;
Q = "(()())" ;
Q = "(((())))" ;
Q = "((()()))" ;
Q = "(()(()))" ;
Q = "(()()())" ;
Q = "((())())" ;
Q = "(()()())" ;
Q = "((((()))))" ;
Q = "(((()())))" ;
Q = "((()(())))" ;
Q = "((()()()))" ;
Q = "(((())()))" ;
Q = "((()()()))" .

parens.prolog

append3(A, B, C, D) :-
  append(A, B, AB),
  append(AB, C, D).

balanced([]).

balanced(List) :-
  append3([open], Inner, [close], List),
  balanced(Inner).

balanced(List) :-
  append(Left, Right, List),
  Left  \= [],
  Right \= [],
  balanced(Left),
  balanced(Right).

% gross
parens_notation([], "").
parens_notation([open | T], S) :-
  parens_notation(T, Tp),
  string_concat("(", Tp, S).
parens_notation([close | T], S) :-
  parens_notation(T, Tp),
  string_concat(")", Tp, S).

balanced_parens(X) :-
  balanced(L),
  parens_notation(L, X).