;    Finding closure of a set of attributes.
;
;    Representation of a FD X --> Y:
;
;       ((attributes in X) (attributes in Y))
;
(defun find-closure (x fds)
   (let ((x-new x)
         (x-old) )
      (loop
         (setf x-old x-new)
         (setq x-new (update-closure x-new fds))
         (if (equal x-old x-new) (return x-new)) ) ) )
          
(defun update-closure (x fds)
   (catch 'closure (u-c x fds)) )

(defun u-c (x fds)
   (dolist (fd fds x)
      (if (and (subsetp (first fd) x)
               (not (subsetp (second fd) x)) )
          (throw 'closure (union x (second fd))) ) ) )