Booleans, Numbers, and Other Basic Types

• Exercises
  • Exercise 0: Preparation
  • Exercise 1: Type Predicates
  • Exercise 2: Empty lists
  • Exercise 3: Equality
  • Exercise 4: Reflection
  • Exercise 5: What is not?
  • Exercise 6: What is not? Revisited
  • Exercise 7: Combining Boolean Values
  • Exercise 8: Ranges
  • Exercise 9: Types of Numbers
  • Exercise 10: The Type of a Square Root
  • Exercise 11: More Types of Numbers
  • Exercise 12: A Large Number
  • Exercise 13: Inexact Roots
  • Exercise 14: Inexact Fractions
• Notes

You may want to refer to the reading on Boolean values and predicates and the reading on numbers before or while you work on this lab.

Exercises

Exercise 0: Preparation

a. If you haven't done so already, you may wish to skim the readings.

b. Start DrScheme.

Exercise 1: Type Predicates

Fill in the following table (or as much as you think is appropriate)

Exercise 2: Empty lists

Which of the following does Scheme consider an empty list?

• null
• 'null
• ()
• (list a)
• (list)
• 'nothing

Exercise 3: Equality

Consider the following definitions

(define alpha (list 'a 'b 'c))
(define beta (list 'a 'b 'c))
(define gamma alpha)

Determine which of the lists are eq?, eqv?, or equal?.

Exercise 4: Reflection

Did you see anything surprising in the previous exercises?

Exercise 5: What is not?

a. What type is not?

b. What predicate would you use to verify your answer?

Exercise 6: What is not? Revisited

The symbol not is the name of something, as you determined in the preceding exercise. However, the symbol itself, considered as a datum, is not a procedure. Does Scheme agree with this classification? How could one ask Scheme whether the symbol not is a procedure?

Exercise 7: Combining Boolean Values

Fill in the following tables for each of the operations and and or.

and

or

Exercise 8: Ranges

a. Write a Boolean expression that determines if the value named by grade is between 0 and 100, inclusive.

b. Test that expression using different values of grade.

Exercise 9: Types of Numbers

Have DrScheme confirm that 3/4 is a rational number but not an integer and that the square root of -1 is a complex number but not a real number.

Exercise 10: The Type of a Square Root

Confirm that the value DrScheme computes for (sqrt 2) is an inexact real that is also rational.

Exercise 11: More Types of Numbers

As you've just seen, some kinds of numbers are subsets of other kinds of numbers. Determine the relationships between the various kinds of numbers.

Exercise 12: A Large Number

Write a Scheme numeral for 1.507 times ten to the fifteenth power, as an exact number. Have Scheme evaluate the numeral.

Exercise 13: Inexact Roots

a. Have DrScheme find the square of the square root of 2 and subtract 2 from the result.

b. Ideally, the difference should be 0; why isn't it?

c. How big is the difference?

d. Will you have the same problem if you start with 4? Why or why not?

Exercise 14: Inexact Fractions

Write a Scheme numeral for one-third, as an inexact number. Have Scheme evaluate the numeral.

Notes

Today's lab currently lacks notes.