Lisp Array Maximal Adjacement Difference
(defun array-maximal-adjacent-difference (a)
  (let* ((vec (coerce a 'vector))
         (c (length vec))
         (dif 0))
    (loop for i from 1 below (1- c)
          do (setf dif (max dif
                             (abs (- (aref vec i) (aref vec (1- i))))
                             (abs (- (aref vec i) (aref vec (1+ i)))))))
    dif))

This checks the gap between each pair of neighbors and returns the largest difference.