Exercise 1

This exercise will be an introduction to working with the Haskell tools. For this course, we will be using the Glasgow Haskell Compiler (but other Haskell implementations should be usable as well).

Some links to the GHC software have been provided. You will also find GHC on the CSIL Linux computers. The Haskell tutorials and references on the same page may be helpful as well.

1. Start by getting GHC installed (or going to CSIL). We will start by using the GHC interactive environment. (Type ghci at the Linux prompt to start it.) Once GHCi is started, you'll see a prompt like this:

   Prelude>

2. You can start experimenting with Haskell at this prompt.

   Try typing some expressions at this prompt and look at the results. Some example things to try:

   9 * 4
   1 + 2 * 3
   1+1 == 2
   2^300
   sum [1,2,3,4,5]
   [1,2,3] ++ [4,5]
   take 3 [5,6,7,8,9,10]
   div 15 3
   15 `div` 3
   5 + 6
   (+) 5 6

3. In your favourite text editor, create a file exer1.hs containing the following three function definitions (that calculate the discriminant and two solutions to a quadratic formula):

   det a b c = b^2 - 4*a*c
   quadsol1 a b c = (-b - sqrt (det a b c))/2*a
   quadsol2 a b c = (-b + sqrt (det a b c))/2*a

4. Save your exer1.hs. You can test it in GHCi like this:

   Prelude> :l exer1.hs
   *Main> det 1 4 2
   8
   *Main> quadsol1 1 4 2
   -3.414213562373095
   *Main> quadsol2 1 4 2
   -0.5857864376269049

5. Add to your exer1.hs a function square that takes one number as an argument and returns the square that value. (So, square 4 should return 16.)

   In GHCi, you can reload your exer1.hs and test it like this:

   *Main> :r
   Ok, modules loaded: Main.
   *Main> square 8
   64

6. Add another function to your exer1.hs called third that returns the third element of a list. It should behave like this: (including no need to check for the error if there is no third element)

   *Main> third [7,8,9,10,11,12]
   9
   *Main> third [1,2]
   *** Exception…

7. Finally, in your exer1.hs, write a function hailstone n that find the next element in a hailstone sequence. That is, for even n, it should return n/2; for odd n, it should return 3n + 1. (Hint: the Haskell div function does integer division; the / always returns a Float, which is not what you want.)

   > hailstone 14
   7
   > hailstone 31
   94

Submit your work for this exercise in CourSys. [You aren't submitting anything for parts 2 and 4: we'll trust that you have done them.]