The following code appends two lists

CODE
append([],Y,Y).
append([X|T],Y,[X|R]) :- append(X,Y,R).

RESULT
?- append([a],[b,c],R).
R = [a, b, c]
Yes
 

The following code appends two lists

 (define (append x y)
         (cond((null? x) y)
                (else (cons (car x) (append (cdr x) y) ))))

The following code checks if two lists are equal

  (define equal(lambda (x y)
      (cond((and(null? x) (null? y)) #t)
            ((and(not (null? x)) (not (null? y))) (equal (cdr x) (cdr y)))
            (else #f))))