val(X,N) :- expr(X,[],N).
expr(S1,S2,N):-term(S1,S3,N1), plus(S3,S4), expr(S4,S2,N2), N is N1+N2.
expr(S1,S2,N):- term(S1,S2,N).
term(S1,S2,N):- factor(S1,S3,N1), times(S3,S4), term(S4,S2,N2), 
  N is N1*N2.
term(S1,S2,N) :- factor(S1,S2,N).
factor(S1,S2,N) :- num(S1,S2,N).
factor(S1,S2,N) :- left_p(S1,S3),expr(S3,S4,N), right_p(S4,S2).
plus([P|S],S):- "+"= [P].
times([T|S],S):- "*" = [T].
left_p([L|S],S):- "(" = [L].
right_p([R|S],S):- ")" = [R].
num(S1,S2,N):- headMembers(S1,S2,"0123456789",N1), name(N,N1).
headMembers([],[],_,[]):- !.
headMembers([X|Y],Z,S,[X|W]) :- member(X,S),!,headMembers(Y,Z,S,W).
headMembers(X,X,_,[]).
member(X,[X|_]):- !.
member(X,[_|Y]):- member(X,Y).