Questions from last time

• The programming languages we will study this term are all dynamically typed. This means that not only the value but also the type of variables can change at runtime. Why does this make testing even more important?

• What kind of software problems is testing not well suited to find?

• Why might mutable state (e.g. instance variables in Java) make writing unit tests harder?

Setup

• make a directory labs/L04 inside your ~/cs2613 git repository
• All of your work from today should be committed in that directory (and pushed before you leave).

Structural recursion, on numbers

Use structural (note that structural here is only indirectly related to Racket structs) recursion on natural numbers (not the simulated ones from above, but regular Racket numbers like 1, 42, and 1337) to define a function (sum-factors n max-factor) that sums all factors of n (including 1) no larger than max-factor

Recall the template for structural recursion on natural numbers:

(define (my-nat-fn n)
  (cond
    [(zero? n) ...]
    [(positive? n) ... (my-nat-fn (sub1 n)) ...]))

Try to use only one recursive call to sum-factors like in the template. Keep in mind that the n in the template might be a different parameter of your function. You can use the builtin function remainder to test for divisibility.

The following tests should pass

;; 1+2+3 = 6
(check-expect (sum-factors 6 5) 6)
;; 1+2+4+7+14 = 28
(check-expect (sum-factors 28 27) 28)

Substitute in a list

Complete FICS Exercise 13.

Note the template for structural recursion.

(define (my-list-fn lst)
  (cond
    [(empty? lst) ...]
    [(cons? lst) ... (first lst) ...
                 ... (my-list-fn (rest lst)) ...]))

Here is a test case based on the linked test

(check-expect
 (substitute 3 "three" (list "four" 3 4 "three" 3))
 (list "four" "three" 4 "three" "three"))

Uniquifying lists

Complete FICS Exercise 15. Although probably not intended by the original question, use the built-in BSL function member? to simplify your solution. Otherwise use only the constructs specified in Exercise 14, and structural recursion. Here is one test case derived from the linked text.

(check-expect
 (unique-right
  (list 1 4 2 1 5 4))
 (list 2 1 5 4))

Add an element to all lists

Recall the template for structural recursion on lists

(define (my-list-fn lst)
  (cond
    [(empty? lst) ...]
    [(cons? lst) ... (first lst) ...
                 ... (my-list-fn (rest lst)) ...])

Use this template to write a function cons-all that adds a given element to the front of each given sublist. This is related to FICS Exercises 23-25 (but you only need to write cons-all, not do those exercises).

The following test case illustrates the use of cons-all. You will need to use the language #lang htdp/bsl+ or "Beginning Student with List Abbreviations" or replace the use of ' in the following.

(check-expect (cons-all 3 '((2 4) () (5)))
              '((3 2 4) (3) (3 5)))

Before Next Lab