SICP Exercise 2.21: Square Maps

The procedure square-list takes a list of numbers as argument and returns a list of the squares of those numbers.

> (square-list (list 1 2 3 4))
(1 4 9 16)

Here are two different definitions of square-list. Complete both of them by filling in the missing expressions:

(define (square-list items)
  (if (null? items)
      nil
      (cons <??> <??>)))
(define (square-list items)
  (map <??> <??>))

We're given two skeleton procedures here. The first procedure is similar to the recursive definition of scale-list in the Mapping over lists section of the book and is obviously the basis for a recursive procedure, while the second is analogous to the map-based definition of scale-list. The difference between scale-list and square-list is simply that the former scales each element of the list by some factor while the latter squares each element of the list. So our square-list implementations will bear an uncanny resemblance to scale-list, with just the scaling replaced with squaring.

Assuming we've got square defined as before:

(define (square x) (* x x))

...then we can produce the recursive implementation as follows:

(define (square-list items)
  (if (null? items)
      nil
      (cons (square (car items)) (square-list (cdr items)))))

...which produces the results:

> (square-list (list 1 2 3 4 5 6 7 8 9 10))
(1 4 9 16 25 36 49 64 81 100)

When it comes to the map-based version, we don't need to define a lambda-procedure as was necessary for scale-list, as we already have a procedure defined that provides the functionality we require: square. So we can define the map-based version as follows:

(define (square-list items)
  (map square items))

Of course this gives exactly the same results:

> (square-list (list 1 2 3 4 5 6 7 8 9 10))
(1 4 9 16 25 36 49 64 81 100)