Some Additional Racket Topics: Improper Lists, Functions with a Variable Number of Arguments

Improper Lists

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)

                 _______________   
                |       |       |  
                |   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)

                 _______________        ________________ 
                |       |       |      |        |       |
                |   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 . ())))

Functions with a Variable Number of Arguments

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))

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)