Cons element to list vs cons list to element in Scheme

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The primitive cons simply sticks together two things, the fact that some of those things are considered lists is incidental. For instance, this works and creates a pair (also known as a cons cell):

(cons 1 2)
=> '(1 . 2)     ; a pair

Now, if the second argument to cons happens to be a list, then the result will be a new list, and the first argument to cons will be added at the head of the old list. In other words: to create a list you need a list, even if it’s empty:

(cons 1 '(2 3))
=> '(1 2 3)     ; a list

(cons 1 (cons 2 '()))
=> '(1 2)       ; a list

(cons 1 '())
=> '(1)         ; a list

But if the second argument to cons is not a list, then the result will be just a pair, or an improper list, meaning that it doesn’t end in '() as it should to be considered a list:

(cons '(1 2) 3)
=> '((1 2) . 3) ; a pair, not a list

(cons 1 (cons 2 3))
=> '(1 2 . 3)   ; an improper list

Just to clarify, you can’t use cons to add elements at the end of a list. The usual way to build a list is going from right-to-left, adding elements in reverse at the head position – say you want to build the list '(1 2 3), then you have to cons the elements in the order 3 2 1:

(cons 3 '())                   ; list is '(3)
(cons 2 (cons 3 '()))          ; list is '(2 3)
(cons 1 (cons 2 (cons 3 '()))) ; list is '(1 2 3)

For those rare occasions where you need to add one element at the end (and believe me, doing so generally means that you’re thinking the algorithm wrong) you can use append, which receives two lists as arguments:

(append '(1 2 3) '(4))
=> '(1 2 3 4)

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