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##### 2.3.6.2 Dotted Pair Notation

Dotted pair notation is a general syntax for cons cells that represents the car and cdr explicitly. In this syntax, (a . b) stands for a cons cell whose car is the object a and whose cdr is the object b. Dotted pair notation is more general than list syntax because the cdr does not have to be a list. However, it is more cumbersome in cases where list syntax would work. In dotted pair notation, the list ‘(1 2 3)’ is written as ‘(1 . (2 . (3 . nil)))’. For nil-terminated lists, you can use either notation, but list notation is usually clearer and more convenient. When printing a list, the dotted pair notation is only used if the cdr of a cons cell is not a list.

Here's an example using boxes to illustrate dotted pair notation. This example shows the pair (rose . violet):

--- ---
|   |   |--> violet
--- ---
|
|
--> rose

You can combine dotted pair notation with list notation to represent conveniently a chain of cons cells with a non-nil final cdr. You write a dot after the last element of the list, followed by the cdr of the final cons cell. For example, (rose violet . buttercup) is equivalent to (rose . (violet . buttercup)). The object looks like this:

--- ---      --- ---
|   |   |--> |   |   |--> buttercup
--- ---      --- ---
|            |
|            |
--> rose     --> violet

The syntax (rose . violet . buttercup) is invalid because there is nothing that it could mean. If anything, it would say to put buttercup in the cdr of a cons cell whose cdr is already used for violet.

The list (rose violet) is equivalent to (rose . (violet)), and looks like this:

--- ---      --- ---
|   |   |--> |   |   |--> nil
--- ---      --- ---
|            |
|            |
--> rose     --> violet

Similarly, the three-element list (rose violet buttercup) is equivalent to (rose . (violet . (buttercup))). It looks like this:

--- ---      --- ---      --- ---
|   |   |--> |   |   |--> |   |   |--> nil
--- ---      --- ---      --- ---
|            |            |
|            |            |
--> rose     --> violet   --> buttercup