what's the difference of the two list in scheme

Question

I'm a newbie to scheme. I'm just confused about the difference of the following two list.

(define a '(1 2))
(define a '(1 . 2))

I think a equal to b, but

(equal? a b)

return #f to me. Any help will be greatly appreciated.

Answer 1

The two aren't the same. The first is a normal list. In dotted notation it would look like this:

(1 . (2 . nil))

A normal list stores data in the car of a cons cell, and the cdr is only used to store a pointer to the next cons cell in the list, or Nil for the last cell in the list.

Your definition of a uses only one cons cell, with 1 in the car and 2 in the cdr.

If you drew them out graphically, they'd look like this:

Answer 2

The "dot" notation is used in Scheme and LISP to describe "improper lists", those that don't follow the standard list data definition. This question:

Functional Programming: what is an "improper list"?

... probably answers most of your questions. Let me know if there's anything this post doesn't answer.

Good luck!

Answer 3

They don't return equal because they are not the same data type. the first one with: (define a '(1 . 2)) is what is known as a pair. A list is a pair but not all pairs are lists. Lists are pairs that have a car and their cdr is a list. When you get the dot notation it means that the car of that pair is 1 and the cdr is 2. Since they aren't the same data type, they can't be equal.