0-Exercises.md

Exercises

The following exercises are by no means comprehensive, but meant to give you some practice putting together the concepts from this section.

For more exercises, Part One of How to Design Programs, Second Edition is excellent.

Exercise 0

Consider the following functions, even? and and:

; even? : number -> boolean
; returns a boolean indicating whether a number is even
> (even? 4)
#true
> (even? 5)
#false

; and : boolean, boolean -> boolean
; returns true if and only if both arguments are true
> (and true true)
#true
> (and true false)
#false
> (and false false)
#false

Use these two functions to write an expression that returns whether 50 and 10 are both even.

Exercise 1

As you know, the + function works with any number of numbers, not just two of them:

> (+ 1 2 3 4 5 6)
21

For this exercise, let's pretend we can't do that.

Write an expression to sum the integers 1 through 6, subject to the following constraint:

• Whenever you use +, you can only add two numbers at a time.

Of course, you can use + itself as many times as you want.

Exercise 2

Write an expression to convert a number to a string, then convert the string to an image of text.

You may need to search the 2htdp/image documentation for the text function.

Exercise 3

Consider the following expression:

(and (odd? 19)
     (> 4
        (* (string-length "foo")
           2)))

1. What is the return type of this expression? How do you know?
2. There are five function calls in this expression. In what order are they called?
3. What does this expression simplify to?

Check your answers using the DrRacket stepper. Then try writing your own complicated expression.