Exercises

Exercise 3.1.   [*] Take a look at this function definition:

;; Number  →  Number
;; compute the after-tax weekly wage from the hours someone worked
;; pay-per-hour: $12.55
;; tax rate: 15%
;; social security: 5.5%
;; insurance cost: $100
(define (after-tax-income hours)
  (- ; gross income:
     (* hours 12.55)
     ; taxes:
     (* (* hours 12.55) .15)
     ; social security:
     (* (* hours 12.55) .055)
     ; insurance
     100))

;; example/test:
(= (after-tax-income 40) 299.09)

Use local to simplify the function body (“go slow!”). 

Exercise 3.2.   [*] Developing the program strings-to-numbers* in exercise 1.2 required the definition of several functions. It is good practice to reorganize programs such as those with local into a single function definition. 

Exercise 3.3.   Develop the program numeric-matrix?. The function consumes a string matrix. It produces true if all strings represent a number; otherwise its return value is false.

Here are the data definitions:

;; A Matrix is one of:
;; --- empty
;; --- (cons LOS Matrix)
;; Constraint: In a matrix, the length of all LOS is the same. 

;; A LOS is one of: 
;; --- empty
;; --- (cons String LON)

Hint: The program requires several function definitions.

Constraint: Develop the program in two stages. First design all functions at the top-level. Second organize them using local so that there is only one top-level function. 

Exercise 3.4.   Design make-spread. The function consumes two natural numbers: n and m. Its result is a rectangular list: rectangle S-expression such as this:

(list
  (list (list 'td "cell00") (list 'td "cell01"))
  (list (list 'td "cell10") (list 'td "cell11"))
  (list (list 'td "cell20") (list 'td "cell21"))
  (list (list 'td "cell30") (list 'td "cell31")))

with 4 rows and 2 columns.

Hint: Use the function string-append, which performs the obvious operation on strings.

Use the function to develop the function make-table, which consumes two natural numbers and creates the following S-expression for n = 3 and m = 2:

(list 'table
  (list 'tr (list 'td "cell00") (list 'td "cell01"))
  (list 'tr (list 'td "cell10") (list 'td "cell11"))
  (list 'tr (list 'td "cell20") (list 'td "cell21")))