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

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 written using a dot.

For example,

'(2 . 3)

denotes this list:

                 _______________   
                |       |       |  
                |   o   |   o   |   
                |___|___|___|___|   
                    |       |       
                    |       |       
                    2       3

And

'(2 3 . 4)

denotes:

                 _______________        ________________ 
                |       |       |      |        |       |
                |   o   |   ----|----->|    o   |   o   |
                |___|___|_______|      |____|___|___|___|
                    |                       | 	    | 	 
                    |                       |	    | 
                    2                       3       4

A common use for improper lists is to store name/value pairs in a so-called association list. The MULP interpreter uses an association list of exactly this sort to store environments.

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))

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))))

Quasiquotes

"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))