Background

• Section 2.3 of the Racket Guide

Recursion

• Fill in the missing expression for the recursive case of the factorial function

    #lang racket
    (define (fact n)
      (cond
        [(zero? n) 1]
        [else                     ]))

    (module+ test
      (require rackunit)
      (check-equal? (fact 10) 3628800))

• Use the debugger to find the bug in the following program

    #lang racket
    (define (list-length list)
      (if (empty? list)
          0
          (+ 1 (list-length list))))

    (module+ test
      (require rackunit)
      (define test-list '(1 2 3))

      (check-equal? (length test-list) (list-length test-list)))

The first / rest pattern

Section 2.3.2 of the Racket Guide gives several examples of recursively traversing a list, in particular

(define (my-map f lst)
  (cond
   [(empty? lst) empty]
   [else (cons (f (first lst))
               (my-map f (rest lst)))]))

This function uses a very important pattern, processing the first element of the list with first and recursively processing the remaining elements with rest. In this part of the lab you use this example as a starting point to rewrite the rainbow example from quick to use explicit recursion (i.e. calling first and rest), rather calling than map.

• Make an auxilary function color-mapper that takes two parameters p and color-list and calls (colorize p color) for each element color of color-list.
• Your function can steal the structure of my-map but you shouldn't call map or my-map
• If you have extra time, repeat the exercise with for/list instead of first and rest.