Can someone explain the difference between Cons and Append in scheme?

Question

I read both of them and they seem to both construct a single list, what's their difference?

Answer 1

cons is the constructor for all pairs.

A proper list is () (the empty list, aka nil) or a pair where the cdr is a proper list. Any chain of pairs where the last one has () as it's cdr is a proper list (in addition to the empty list itself).

A dotted list is a pair that does not have a proper list as it's cdr. Thus a chain of pairs where the last cdr is not () matches this.

;; dotted lists
(cons 1 2)          ; ==> (1 . 2) 
(cons 1 (cons 2 3)) ; ==> (1 2 . 3) or (1 . (2 . 3))

;; proper lists
(cons 1 '())          ; ==> (1) or (1 . ())
(cons 1 (cons 2 '())) ; ==> (1 2) or (1 . (2 . ()))

append is a procedure that uses cons to make a list with all the elements of the argument lists left to right. A common implementation of append for just two lists would be:

(define (append lst tail)
  (if (null? lst)
      tail
      (cons (car lst)
            (append (cdr lst)
                    tail))))

append will fail if one of the arguments except the last is not a proper list. Tail and can be any value:

(append '(1 2 3) '(4 5))       ; ==> (1 2 3 4 5) or (1 . (2 . (3 . (4 . (5 . ())))))
(append '(1 2 3) '(4 5 . 6))   ; ==> (1 2 3 4 5 . 6) or (1 . (2 . (3 . (4 . (5 . 6)))))
(append '(1 2 3) #f)           ; ==> (1 2 3 . #f) or (1 . (2 . (3 . #f)))
(append '(1 2 . 3) '(4 5 . 6)) ; ==> error `car` of number not allowed