Elisp: Proper List

What is Proper List

A Proper List is nil, or a Elisp: Cons Cell such that its last element is nil, or its last element is cons and its last element is nil, etc.

;; proper lists
;; because the tail is nil

(cons nil nil)
(cons 3 nil)
(cons 3 (cons 3 nil))
(cons 3 (cons 3 (cons 3 nil)))
(cons 3 (cons 3 (cons 3 (cons 3 nil))))

;; also proper lists. tail is nil
(cons (cons 3 4) nil)
(cons (cons 3 4) (cons 3 nil))
(cons (cons (cons 3 4) 4) nil)

;; also proper list
nil

Improper List

A cons that's not proper list is called Improper List .

;; improper list

(cons nil 3)
;; last element is not nil

(cons (cons 3 nil) 3)
;; last element is not nil

Test If a List is a Proper List

proper-list-p

Return length if it is a proper list, else nil.

(proper-list-p nil)
;; true

(proper-list-p (cons nil nil))
(proper-list-p (cons 3 nil))
(proper-list-p (cons 3 (cons 3 nil)))
(proper-list-p (cons 3 (cons 3 (cons 3 nil))))
(proper-list-p (cons 3 (cons 3 (cons 3 (cons 3 nil)))))
;; all true

(proper-list-p (cons (cons 3 4) nil))
;; true

;; improper list
;; all false

;; tail is not nil
(proper-list-p (cons nil 3))

;; tail is not nil
(proper-list-p (cons (cons 3 nil) 3))

Proper List vs Improper List

• Any cons structure, is a list.
• Proper list and improper list are both lists.

Most list functions, assume you have a proper list. That is, they assume you have a nil as the tail in the cons structure. Practically all functions that return a list, return a proper list. This is critical to know.

Improper list is almost never used except a single non-nested cons pair holding 2 values.