Exercises for Week 4: IO, Test Data and Properties

Here are some exercises designed to help you practice programming with IO, test data generation, and properties.

Please prepare yourself for these exercises by printing them out, and also printing out the code samples and documentation that is referred to by links.

If you do not have time to do all these exercises, don't worry. The exercises are intended to provide enough work to keep the most experienced students busy. If you do all exercises marked with an (*) you have probably understood this week's material.

Good luck!

0 (*). Exercises from the Book

1 (*). Properties of the Look Function

look :: Eq a => a -> [(a,b)] -> Maybe b
look x []           = Nothing
look x ((x',y):xys)
  | x == x'         = Just y
  | otherwise       = look x xys

Also define a property prop_LookJust that expresses that if the look function delivers a result (Just y), then the pair (x,y) should have been in the table.

Also write one property prop_Look that combines prop_LookNothing and prop_Just into one property.

2. Monadic helper functions

sequence_ :: Monad m => [m ()] -> m ()
onlyIf    :: Monad m => Bool -> m () -> m ()

"onlyIf" takes a boolean and an instruction, and creates an instruction that only executes the argument instruction if the boolean was True. If the boolean was False, nothing happens. Example "onlyIf failed tryAgain" executes the instructions tryAgain only if the boolean failed is True.

Hint: You might find it easier to think of the above functions having type:

sequence_ :: [IO ()] -> IO ()
onlyIf    :: Bool -> IO () -> IO ()

What becomes different if we change the type of onlyIf to:

onlyIfM :: Monad m => m Bool -> m () -> m ()

Give an implementation of onlyIfM.

3 (*). The Number Guessing Game

In this exercise, you are going to implement the "number guessing game" in Haskell.

Here is an example of how this might work:

  Main> game
  Think of a number between 1 and 100!
  Is it 50? higher
  Is it 75? lower
  Is it 62? lower
  Is it 56? yes
  Great, I won!

Implement a function

  game :: IO ()

You might need the following functions:

  getLine :: IO String         -- reads a line of user input
  putStrLn :: String -> IO ()  -- outputs one line of text

4. A Backup Script

Haskell programs can generate instructions to be performed by the command shell using

    system :: String -> IO ()

This is one way to run other programs from Haskell, for example. The String passed to system often differs, depending on whether it is the Linux shell or the Windows one which should obey the command. For example, to copy file A to file B under Linux, the string "cp A B" is used, while under Windows it would be "copy A B". As a result, programs which use system normally work only under one operating system, which is sad, but can't be helped.

Use system to write a program that

• creates a new directory called "backup", using the "mkdir" command,
• copies all the files in the current directory into the backup, using cp or copy as appropriate

(You are supposed to copy the files one by one, not by constructing a command such as "cp *  backup", because filename expansion isn't applied to strings passed to system.)

You will need to read the list of filenames in the current directory, and to find out how, you will need to consult the documentation of Haskell's standard libraries. Here's the link:

http://www.haskell.org/ghc/docs/latest/html/libraries/index.html

There are a lot of them! The one you want is called System.Directory--find its documentation, and figure out how to read the filenames in a directory.

You will also perhaps need to perform all of a list of actions. You may find the function

    sequence :: Monad m => [m a] -> m [a]

useful for this. You must add

    import Monad

to your file if you want to use it.

If you want to, you can also use the standard functions createDirectory and copyFile from System.Directory (instead of the commands "mkdir" and "cp") to accomplish this.

5 (*). Generating Lists

Sometimes we want to generate lists of a certain length.

A. Write a generator

    listOfLength :: Integer -> Gen a -> Gen [a]

such that listOf n g generates a list of n elements, where each element is generated by g. What property would you write to test that your generator behaves as it should?

B. Now use listOf to write a generator that generates pairs of lists of the same, random, length.

C.Take a look at the standard Haskell functions zip and unzip:

  zip :: [a] -> [b] -> [(a,b)]
  unzip :: [(a,b)] -> ([a],[b])

Hint: make a datatype

  data TwoSameLengthLists a = SameLength [a] [a]

Another possibility is to use the QuickCheck function forAll, which we might see later on in the course.

6. Generating Ordered Lists

Hint: First generate a list of random, positive integers. Then, generate a first, random number in the list. Then, produce a list where the differences between each consecutive pair of elements is given by the list of positive integers.

Make sure to check that your generator generates ordered lists by writing a suitable property!