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