Conditional Expressions

Summary: In this lab, you will have the opportunity to explore Scheme's two primary conditional control operations, if and cond.

Contents:

• Exercises
  • Exercise 0: Preparation
  • Exercise 1: Who Won?
  • Exercise 2: Categorizing Values
  • Exercise 3: Categorizing Lists
  • Exercise 4: The Sphinx's Riddle
  • Exercise 5: Who Won? Revisited
• For Those With Extra Time
  • Extra 1: Validating Dates
  • Exercise 2: Classifying Numbers
  • Exercise 3: Classifying Numbers, Revisited
• Notes
  • Notes on Exercise 5

Exercises

Exercise 0: Preparation

You may find it helpful to rescan the readings on Boolean values and numbers.

After making sure that you're prepared, start DrScheme.

Exercise 1: Who Won?

Define and test a Scheme procedure, (report-victory score), that takes one argument, a real number, and returns the symbol won if score is positive, the symbol lost if it is negative, and the string tied if it is zero.

a. Use if for all the tests within your procedure.

b. Use cond for all the tests within your procedure.

Exercise 2: Categorizing Values

Write a procedure, (type-of val), that returns

• the symbol boolean, if val is a boolean;
• the symbol character, if val is a character;
• the symbol number, if val is a number;
• the symbol procedure, if val is a procedure;
• the symbol string, if val is a string;
• the symbol symbol, if val is a symbol; or
• the symbol miscellaneous, if val is anything else.

Exercise 3: Categorizing Lists

Define and test a Scheme procedure list-type that takes one argument, a list, and returns the symbol empty if the argument is the empty list and the symbol non-empty otherwise.

Exercise 4: The Sphinx's Riddle

As you may know, one of the famous riddles of the Sphinx goes something like the following:

What is it that walks upon four legs, then two legs, then three legs?

The answer is, of course, humans.

Write a Scheme predicate, legs, that, given someone's age, tells how many legs they walk upon. (You get to choose reasonable ages for the three phases of life.)

Exercise 5: Who Won? Revisited

You may recall a previous question that asked for the following: Define and test a Scheme procedure (report-victory score) that takes one argument, a real number, and returns the symbol won if score is positive, the symbol lost if it is negative, and the string tied if it is zero.

In that problem, you wrote one version that used if and one version that used cond. However, it is also possible to write report-victory using only and, or, and not. Try doing so.

If you are confused, you might want to look at the notes on this problem.

For Those With Extra Time

Extra 1: Validating Dates

Write a procedure, (valid-date? month day), that returns #t if the numbers month and day describe a valid month and day and false otherwise. For example,

> (valid-date? 1 30)
#t
> (valid-date? 2 30)
#f
> (valid-date? 9 30)
#t
> (valid-date? 9 31)
#f
> (valid-date? 9 -1)
#f
> (valid-date? 9 250)
#f

a. Write this procedure using if as the primary control structure.

b. Write this procedure using cond as the primary control structure.

c. Write this procedure without if and cond (that is, using and, or, and, possibly, not).

Exercise 2: Classifying Numbers

Write a procedure, (classify-number num), that creates a string that classifies num according to its exactness and its least general type (selected from integer, rational, and complex).

> (classify-number 25)
"exact integer"
> (classify-number -3.5)
"inexact rational"
> (classify-number 3+4i)
"exact complex">

You can assume that num is a number.

Exercise 3: Classifying Numbers, Revisited

Write a procedure, (classify-number num), that returns a string that describes num subject to the following restrictions.

• Describe zero as "zero";
• Just as in the previous problem, return the return the exactness of the value (that is, results should begin with exact or inexact:
• For non-complex values, include the sign (positive or negative);
• For exact rational/real values, use the type rational; and
• For inexact rational/real values, use the type real.

For example,

> (classify-number 23)
"exact positive integer"
> (classify-number #i23)
"inexact positive integer"
> (classify-number -2.3)
"inexact negative real"
> (classify-number 24/7)
"exact positive rational"

Notes

Notes on Exercise 5

To write the procedure report-victory without if and cond, we need to take advantage of the way and and or behave. Recall that and either returns false (if it encounters a false) or the last value (if it fails to encounter a false value) and that or returns the first non-false value, if one is there.

Hence, we'll use an and for each test and group them together within an or.

The first test looks something like this: (and (> score 0) 'won). Note that this test returns #f if score is less than or equal to 0 and the symbol won otherwise.

We can then put that in an or expression. Here's a start.

(or (and (> score 0) 'won)
    'something-else)

Now, if score is greater than 0, we get won and otherwise we get something-else.

The remainder is up to the reader to figure out.

Return to the problem.