The goal of this problem set is to practice designing data representations using structures and functions for processing such forms of data. Furthermore, you must follow the design recipe and the guidelines when you develop functions.

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Problems A1

Consider the following structure definitions:

(define-struct lecture-hall (number capacity))
(define-struct automobile (year make model))
(define-struct football-player (name position number))
(define-struct highway (lanes speed))
(define-struct shirt (material size color))

1. What are the names of the constructors and the selectors that each of the structures adds to Racket? Draw box representations for each of these structures.
2. Provide data definitions for the structure definitions above. Make appropriate assumptions about what data goes with which field.
3. Develop templates for functions that consume the structures above.

Problem A2

Here is a data definition for keeping track of time on a clock (which, of course, is just a computer with a display attached to it):

(define-struct time (hours minutes))
;; Time = (make-time Number Number)
;; Constraints: 
;; The first number is always between 0 and 11; 
;; the second number is always between 0 and 59. 

Use these definitions for the following exercises:

1. Design the function tock from Time to Time. It adds one minute to the given time.
2. Design the function time->text, which converts a time to a text. The text should look like the display of a common alarm clock, i.e., it should separate the minutes from the hours with a colon. Hint: a text is an image, not a string, but you will need a string version of the time, too. See HelpDesk (image.ss) for more on the text function.
3. Optional: After you have developed these functions, you may wish to add the following lines to your program:

   
   (big-bang (make-time 0 0)
     (on-tick tock 0.1)
     (to-draw time->text))
   
   

   If you do, be sure to delete them before you turn in your solution. We will subtract points if you leave them in.

Problem A3

You've found a summer job with the pyschology department. They'd like you to develop a program that helps people control the movement of a ball across the screen. (They wish to study brain models and reaction times and this is just a small part of it.)

The ball can move on straight lines only, that is, up, down, left, or right. Pressing the arrow keys on the keyboard changes the ball's location.

1. Develop a data representation for the current position of the ball. The position is best described with a pair of positive integers.
2. Develop a data representation for velocity of the ball. You may assume that the ball always moves exactly 10 pixels at a time but remember that velocity also includes the direction of the movement.
3. Develop a data representation for the ball.
4. Design the function ball-next, which consumes (the representation of) a ball and create a ball that represents where it will be after one "tick."
5. Design the function ball-image, which consumes (the representation of) a ball and produces a rectangle of 300 x 300 pixels with a red dot (diameter 10 pixels) placed at the ball's position.

6. Design a function ball-change, which consumes a ball and a "key event," which represents the user hitting a key on the keyboard. If the key event represents the user hitting the up-arrow key, then ball-change produces a new ball which is just like the input ball, except that the new ball is moving upward; similarly for key events representing the left-, right- and down-arrow keys: they cause the resulting ball to be one that is moving left, right, or down, respectively. Passing any other keystroke to ball-change causes the ball to be unchanged.

   You can read about key events in the help desk—the on-key clause of big-bang is a good place to start.

7. Optional: After you have developed these functions, you may wish to add the following lines to your program:

   
   (big-bang some-initial-ball
     (on-tick ball-next 1/28)
     (to-draw ball-image)
     (on-key ball-change))
   
   

   If you do, be sure to delete them before you turn in your solution. We will subtract points if you leave them in.