% length of the list
len([], 0).
len([H|T], B) :-len(T, NT), B is NT + 1.
% return the ith element of the list
match([H|_],0,H) :-!.
match([_|T],N,H) :-N > 0,N1 is N-1,match(T,N1,H).

palindrome --> [].
palindrome --> [_].
palindrome --> [X], palindrome, [X].

?- listing(palindrome//0).
palindrome(A, A).
palindrome([_|A], A).
palindrome([C|A], D) :-
    palindrome(A, B),
    B=[C|D].

true.

?- phrase(palindrome,[a,X,c,b,Y]).
X = b, Y = a ;
false.

?- phrase(palindrome,[s,i,a,m,a,i,s]).
true ;
false.

?- phrase(palindrome,[s,i,a,m,m,a,i,s]).
true ;
false.

?- phrase(palindrome, Xs).
  Xs = []
; Xs = [_A]
; Xs = [_A,_A]
; Xs = [_A,_B,_A]
; Xs = [_A,_B,_B,_A]
; Xs = [_A,_B,_C,_B,_A] ...