Normally, the cdr of a cons cell is either the empty list or another cons cell. A list in which the cdr of a cons cell is something else is an improper list, and is printed using a dot.
For example,
'(2 . 3)denotes this list:
_______________
| | |
| o | o |
|___|___|___|___|
| |
| |
2 3
This list could be written as a literal, or could be constructed using the cons function:
(cons 2 3)
Contrast this with '(2 3)
_______________ _____________
| | | | | / |
| o | ----|----->| o | / |
|___|___|_______| |____|___|/___|
| |
| |
2 3
As another example,
'(2 3 . 4)denotes:
_______________ ________________
| | | | | |
| o | ----|----->| o | o |
|___|___|_______| |____|___|___|___|
| | |
| | |
2 3 4
A common use for improper lists is to store name/value pairs in an association list. Here's an example. (Another example can be found in the MUPL interpreter assignment, used in previous 341 offerings, which uses an association list to store environments.)
(define ages '( (alice . 23) (ben . 21) (joe . 74))) (assoc 'ben ages) => '(ben . 21), not just 21!!
Except for association lists, though, generally I suggest not using improper lists. (They were more important when memory was very scarce and saving a cons cell was a bigger deal.) But you should know what they are in case you see a list with a strange dot in it.
Instant, inline mini-exercise: what gets printed when you evaluate these expressions?
(cons 4 (cons 5 (cons 6 7))) '(3 . (4 . (5 . ())))
We've used functions with a variable number of arguments (for example +), but have only written them with a fixed number of arguments.
Example definitions with a variable number of arguments:
(define (squid a b . c) (display a) (newline) (display b) (newline) (display c) (newline))squid requires at least 2 arguments. Any remaining arguments (perhaps 0) are put into a list, which is bound to c.
This function can take 0 or more arguments:
(define (average . lst)
(if (null? lst)
(error "can't take the average of an empty list")
(/ (apply + lst) (length lst))))
Instant, inline mini-exercise: what gets printed when you evaluate these expressions?
(squid 10 20 30 40) (squid 10)
"Backquote" or "quasiquote" expressions are useful when you want to construct a list for which you know most, but not all, of the desired structure in advance. For example, suppose that you want to return a list of band members that includes a mysterious 5th Beatle. With what we know so far you could do this:
(define (sixties-bands m)
(list '(peter paul mary)
(list 'john 'paul 'george 'ringo m)
'(simon garfunkle)))
Since we know all of the structure except for the 5th Beatle, instead we
could use quasiquoting:
(define (quasibands m)
`((peter paul mary)
(john paul george ringo ,m)
(simon garfunkle)))
Here everything in the quasiquoted list is quoted, except when it is
preceded by a comma (which unquotes it).
You can also splice in a list in the middle of another using an @ sign.
(define x '(clam squid))Then
`(octopus ,@x mollusc oyster) => (octopus clam squid mollusc oyster)compare with:
`(octopus ,x mollusc oyster) => (octopus (clam squid) mollusc oyster)
The `, , and @ characters above are a shorthand for quasiquote, unquote, and unquote-splicing respectively. We could rewrite two of the above examples as:
(quasiquote (octopus (unquote x) mollusc oyster)) (quasiquote (octopus (unquote-splicing) x mollusc oyster))