ELisp: Proper List

What is Proper List

A cons structure whose last tail is nil, is called Proper List, or nil-terminated list.

• ELisp: Cons Pair

;; proper lists
(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. right-most tail is nil
(cons (cons 3 4) nil)
(cons (cons 3 4) (cons 3 nil))
(cons (cons (cons 3 4) 4) nil)

(equal (list "a")
       (cons "a" nil))

(equal (list "a" "b")
       (cons "a" (cons "b" nil)))

(equal (list "a" "b" "c")
       (cons "a" (cons "b" (cons "c" nil))))

Test If a List is a Proper List

proper-list-p

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

;; all 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)))))

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

Improper List

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

;; improper list
(cons nil 3)
(cons (cons 3 nil) 3)

;; 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 last tail in the cons structure. Practically all functions that return a list, return a proper list. This is critical to know.

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