Chapter 3 Problem Set

The essentials of the Types and Typeclasses chapter are: writing type signatures for functions, reading string inputs with the Read class, and dealing with Integral to Fractional conversions when they are needed.

1. You can explicitly say what type a number is by using two colons and the type you want - for example, (5::Int) or (5::Float). Find the types of each of the operations below, or say in English why it does not work. Do not just copy error messages.

   • (/)
   • (5::Int) / (10::Int)
   • (5::Int) / (10::Float)
   • (5::Float) / (10::Float)

2. Write a function to find the average of numbers in a list. This should bring up the difficulty that you cannot divide an integer by an integer(!).

   Examples: avg [10,20] should give 15 or 15.0, and avg [3.5, 4.5] should give 4.0.

3. Write a signature and function body for add10Word which reads an integer from a string and adds 10 to it.

   Example: add10Word "15" should produce 25.

4. Write a signature and function body for numberInSentence, which takes a number and returns the sentence “I have ___ pounds of flour.”

   Example: numberInSentence 5.5 reports “I have 5.5 pounds of flour.”

5. Write a signature and function body for doubleDebt which takes a String and puts out a Float. The String contains a floating point number that represents how much money someone owes, and the Float output is twice that much.

   Example: doubleDebt "50.10" produces 100.20.

6. Write a signature and function body for sampleStdDev that finds the [sample standard deviation] (https://en.wikipedia.org/wiki/Standard_deviation) of a list of (the right kind of) numbers. Check the type signature for square root (sqrt)!

   Please do not skip this problem with the excuse that you do not know how to find standard deviation. Look it up or ask someone who knows!

7. Possibly Challenging: Write the function median to find the median of a list of items that can be ordered. (Use the type Int, if you prefer.) Assume the list is sorted.

We will learn how to sort a list later, but it goes like this:

    import Data.List
    result = sort xs