• DUE DATE: October 12th, 2016 @ 11:59pm

Problem 1

1. Provide a data definition for a list of booleans (lob)
2. Design the function lob-or that consumes a list of booleans and returns the result of logically or-ing all the elements of the list. For example

   
   ;; (lob-or (cons #true (cons #false (cons #true empty)))) is equivalent to
   ;; (or #true #false #true)
   (lob-or (cons #true (cons #false (cons #true empty))))   ;; returns #true
   (lob-or (cons #false (cons #false (cons #false empty)))) ;; returns #false
                           

3. Design the function lob-and that consumes a list of booleans and returns the result of logically and-ing all the elements of the list. For example

   
   ;; (lob-and (cons #true (cons #false (cons #true empty)))) is equivalent to 
   ;; (and #true #false #true)
   (lob-and (cons #true (cons #false (cons #true empty)))) ;; returns #false
   (lob-and (cons #true (cons #true (cons #true empty))))  ;; returns #true
                           

Problem 2

1. Provide the data definition for a list of strings (los)
2. Design the function los-total-length that consumes a list of strings and returns the sum of the length of each element in the list. For example

   
   (los-total-length (cons "a" empty))             ;; returns 1
   (los-total-length (cons "aa" (cons "a" empty))) ;; returns 3
                           

3. Design the function string-at-index that consumes a list of strings and an index and returns the element at that index in the string. The first element of the list has index 0. You may assume that the index provided as input is always valid, i.e., it is greater or equal to 0 and less than the size of the list.
4. Design the function los-contains that consumes a list of strings string-list and a string s and returns true if s is in string-list, otherwise returns false.
5. Design the function los-replace-first that consumes a list of strings string-list and two strings old and new and returns the string-list but with the first old replaced by new. For example

    
   (los-replace-first (cons "a" (cons "b" (cons "a" empty))) "a" "x") 
   ;; returns 
   ;; (cons "x" (cons "b" (cons "a" empty)))
   
   (los-replace-first (cons "a" (cons "b" (cons "a" empty))) "c" "x") 
   ;; returns 
   ;; (cons "a" (cons "b" (cons "a" empty))) 
    

6. Design the function los-replace-all that consumes a list of strings string-list and two strings old and new and returns the string-list but with all old replaced by new. For example

    
   (los-replace-all (cons "a" (cons "b" (cons "a" empty))) "a" "x") 
   ;; returns 
   ;; (cons "x" (cons "b" (cons "x" empty)))
   
   (los-replace-all (cons "a" (cons "b" (cons "a" empty))) "c" "x") 
   ;; returns 
   ;; (cons "a" (cons "b" (cons "a" empty))) 
    

Problem 3

You are helping out a team that is building software for a new cash register. The team has the following incomplete data definitions.

;; An Id is a Symbol
;; INTERP: represents a product's id 

;; A Name is a String 
;; INTERP: represents the product's name 

;; Dollars is a NonNegInteger
;; INTERP: represents the amount of dollars for a price

;; Cents is a NonNegInteger 
;; WHERE: cents is greater or equal to 0 
;;        and less or equal to 99
;; INTERP: represents the amount of cents for a price

(define-struct price [dollars cents])
;; A Price is (make-price Dollars Cents)
;; INTERP: represents total amount in dollars and cents. 

;; A Quantity is a PosInteger
;; INTERP: represent the number of items 

(define-struct line-item [id name price quantity])
;; A LineItem is a (make-line-item Id Name Price Quantity)
;; INTERP: represents a line item with the products id, name price and 
;;         quantity 
 

1. Provide a data definition for a list of lineitems
2. Design the function bill-total that consumes a list of lineitems and returns the total amount for the list of items.

Problem 4

A friend wants you to design a program that will help them with their daily planning and they provided the following information.

A work day consists of

• A list of Tasks. These are the tasks that I would like to complete during the day.
• Available work hours. This is the number of hours (whole hours) that I have available to work for the day.

A Task consists of

• A task id. This is a unique symbol to identify the task.
• A description. This is a sentence that describes what I need to get done for this task.
• An estimate. The estimate is the number of hours that I think I will need to complete this task. Estimates can be on of
  • 1 hour
  • 2 hour
  • 3 hour
  • 5 hour

1. Create data definitions to capture the information for your friend's daily planning.
2. Design a function called free-hours that consumes a workday and returns the difference between the workday's available hours and the sum of all estimated hours for that day's tasks.
3. Design a function called overbooked? that consumes a workday and returns false if the total number of estimated hours for all tasks in the workday is less than or equal the available hours for that workday, and true otherwise.
4. Desgin a function called add-task that consumes a workday and a a new task and adds the task to that workday.
5. Design a function called completed-task that consumes a workday and a task id and returns an updated workday that does not include the taks with the provided task id.
6. Your friend would now like to plan his work week and he would like to you to design a program that will allow them to keep a list of workdays. They would also like you to design a program that given a list of workdays returns back the list of free hours, one for each workday. HINT: you might want to use your solution to part 2 of this problem.