Assignment 1: Getting Started

Reading

• Getting Started with DrScheme
• From Scheme and the Art of Programming:
  • The Foreword and Preface (optional, but recommended)
  • Sections 1.1 - 2.3 (from data and definitions up through conditionals)

Instructions

Put your name, e-mail address, and the assignment number in a comment at the top of your file. In Scheme, a comment starts with the character `;' (a semicolon) and continues to the end of the line. For example, my a1.ss file would begin:

     ;;; Oscar Waddell (owaddell@cs.indiana.edu)
     ;;; Lab Section 1234
     ;;; H211 Assignment 1

Handing in your solutions

When you are ready to turn in your solutions, go to the submissions page. You can hand in your assignment as many times as you want before the due date. Your last submission is the one that will be kept and graded. (Note: The handin link should now be operational!)

DrScheme users: Always save your work by selecting ``Save Definitions as Text'' from the ``File'' menu. Do not click the ``Save'' button.

Exercises

1. Use define to establish the following variable bindings.

   Variable	Value
   zero	0
   pi	3.14159
   wheel	27

   Test your code by evaluating the definitions (e.g., in DrScheme, click ``Execute'') and then try typing the name of each variable in the interaction window. The result should look like this:

      > zero
      0
      > pi
      3.14159
      > wheel
      27
   

2. Translate the following arithmetic expressions into the fully parenthesized ``prefix notation'' of Scheme expressions. Establish a binding (using define) for each of the variables in the following table to the corresponding prefix expression. The first one is translated for you as an example (you will need to establish the variable binding yourself in a1.ss).

   Remember from algebra that you perform multiplication and division before addition and subtraction, and that you should perform multiplications and divisions from left to right, and likewise perform additions and subtractions from left to right.

   Do not simplify the expressions.

   Variable	Infix Expression	Prefix Expression
   a	2 * (3 + 5)	(* 2 (+ 3 5))
   b	(5 + 4) * 3
   c	(-7 / (8 + (9 * 5)))
   d	(7 * 0.5) + (6 * 0.4) + (5 * 0.3)
   e	(100 + 94 + 96) / 3
   f	(11 - (((27 / 18) / 131) + 927))

   Check to see that your expressions evaluate to the expected values. For example, if we execute the definitions, the value bound to the variable a should be 16:

      > (define a (* 2 (+ 3 5)))
      > a
      16
   

3. In mathematics, formulas are used to describe values. For example, the area of a circle is equal to pi times the square of the radius r. We can define a Scheme procedure that computes the area of a circle as follows.

       (define circle-area
         (lambda (r)
           (* pi (square r))))
   
       (define square
         (lambda (x)
           (* x x)))

   Note that we already established a binding for the variable pi in exercise 1. We also defined and used a helper procedure square to square the radius.

   Here's an example showing the result we obtain when we apply the procedure we've just defined:

      > (circle-area 12)
      452.38896
   

   To help us determine which is the best deal at Mama Mia's Pizza, define a procedure price-per-square-inch that takes two arguments: the diameter of the pizza and the price. Your procedure should return the price per square inch of pizza.

   Here are some examples:

      > (price-per-square-inch 10 5.99)
      0.07626711314971082
      > (price-per-square-inch 12 7.99)
      0.07064717052334787
      > (price-per-square-inch 14 10.99)
      0.07139242048953374
      > (price-per-square-inch 16 12.99)
      0.06460701428257666
   

4. Define a procedure celsius->fahrenheit that converts from degrees celsius to degrees fahrenheit using the formula

      F = (9/5 * C) + 32

   For example, we should get the following:

      > (celsius->fahrenheit 100)
      212
      > (celsius->fahrenheit 0)
      32
   

5. Define a procedure fahrenheit->celsius that converts degrees fahrenheit to degrees celsius. For example, we should get the following:

      > (fahrenheit->celsius 212)
      100
      > (fahrenheit->celsius 98.6)
      37.0
   

6. Define a procedure compute-score that computes the weighted score for the course. The procedure takes four arguments: the combined score for the homeworks, the score for midterm 1, the score for midterm 2, and the score for the final exam. The weights for the various components are given below.

   Component	Weight
   homework	10%
   midterm1	25%
   midterm2	25%
   final	40%

   For example, we should get the following:

      > (compute-score 70 80 90 100)
      89.5
      > (compute-score 100 92 95 87)
      91.55000000000001
   

Checklist

Your file should contain definitions for: zero, pi, wheel, a, b, c, d, e, f, price-per-square-inch, celsius->fahrenheit, fahrenheit->celsius, and compute-score.

When you're all done, review the submission instructions.