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This is my first bit of significant code in Common Lisp, an implementation of the insertion sort. Being new to Lisp in general, I'm wondering if this code follows best lisp practices in regards to program design.

;;; Return a portion of a list
(defun slice (elements from-index to-index)
  (cond
    ((= from-index to-index) nil)
    (t (cons (nth from-index elements) (slice elements (+ from-index 1) to-index)))))

;;; Return a list omitting a portion
(defun splice (elements from-index to-index)
  (append (slice elements 0 from-index) (slice elements to-index (length elements))))

;;; Move element in list to new index, return new list
(defun move (elements from-index to-index)
  (let ((spliced (splice elements from-index (+ from-index 1))))
    (append (slice spliced 0 to-index) (list (nth from-index elements)) (slice spliced to-index (length spliced)))))

;;; Find the determined (via predicate) correct index for an element in a list
(defun find-ordered-index (elements predicate index &optional (key index))
  (cond
    ((or (= index 0) (= key 0)) 0)
    ((funcall predicate (nth (- key 1) elements) (nth index elements)) (find-ordered-index elements predicate index (- key 1)))
    (t key)))

;;; Return sorted list
(defun insertion-sort (elements predicate &optional (index 0))
  (cond
    ((= index (length elements)) elements)
    (t (insertion-sort (move elements index (find-ordered-index elements predicate index)) predicate (+ index 1)))))

This is my first bit of significant code in Common Lisp, an implementation of insertion sort. Being new to Lisp in general, I'm wondering if this code follows best Lisp practices in regards to program design.

;;; Return a portion of a list
(defun slice (elements from-index to-index)
  (cond
    ((= from-index to-index) nil)
    (t (cons (nth from-index elements) (slice elements (+ from-index 1) to-index)))))

;;; Return a list omitting a portion
(defun splice (elements from-index to-index)
  (append (slice elements 0 from-index) (slice elements to-index (length elements))))

;;; Move element in list to new index, return new list
(defun move (elements from-index to-index)
  (let ((spliced (splice elements from-index (+ from-index 1))))
    (append (slice spliced 0 to-index) (list (nth from-index elements)) (slice spliced to-index (length spliced)))))

;;; Find the determined (via predicate) correct index for an element in a list
(defun find-ordered-index (elements predicate index &optional (key index))
  (cond
    ((or (= index 0) (= key 0)) 0)
    ((funcall predicate (nth (- key 1) elements) (nth index elements)) (find-ordered-index elements predicate index (- key 1)))
    (t key)))

;;; Return sorted list
(defun insertion-sort (elements predicate &optional (index 0))
  (cond
    ((= index (length elements)) elements)
    (t (insertion-sort (move elements index (find-ordered-index elements predicate index)) predicate (+ index 1)))))