TDA 452
DIT 142
HT 2016

Functional Programming 2016
Exercises for Week 4

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.

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.

0 (*). Basic IO

(Questions based on Thompson, Chapter 18).

A. Write an IO program which will first read a positive integer, say n, and then reads n integers and writes their sum. The program should prompt appropriately for its inputs and explain its output.

B. Write a program which repeatedly reads integers (one per line) until finding a zero value and outputs a sorted version of the inputs read. Which sorting algorithm is most appropriate in such a case?

C. Define the function

repeat :: IO Bool -> IO () -> IO ()
such that repeat test op has the effect of repeating op until the condition test is True.

1 (*). Properties of the Look Function

Consider the following standard Haskell function, that looks up an element in a list of pairs (table):
look :: Eq a => a -> [(a,b)] -> Maybe b
look x []           = Nothing
look x ((x',y):xys)
  | x == x'         = Just y
  | otherwise       = look x xys
Define a property prop_LookNothing that expresses that if the look function delivers Nothing, then the thing we were looking for was not in the table.

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 a property prop_Look that combines prop_LookNothing and prop_Just into one property.

2. Monadic helper functions

Give an implementation of the following functions:
sequence :: Monad m => [m a] -> m [a]
mapM     :: Monad m => (a->m b) -> [a] -> m [a]
onlyIf   :: Monad m => Bool -> m () -> m ()
sequence takes a list of instructions resulting in a value of type a, and creates one big instruction that executes all of these, gathering all results into one result list. Example: the instructions
sequence [ readFile file | file <- files ]
mapM readFile files
both reads the contents of all files in the list files, and produces the contents of each of the files.

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. For 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 a] -> IO [a]
mapM     :: (a->IO b) -> [a] -> IO [b]
onlyIf   :: Bool -> IO () -> IO ()

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!
The text that looks like this is what the user types in. The other text is produced by your program.

Implement a function

game :: IO ()
That plays one instance of this game.

You might need the following functions:

getLine :: IO String         -- reads a line of user input
putStrLn :: String -> IO ()  -- outputs one line of text
Before you start programming, think of a good guessing strategy for the computer that minimizes the number of guesses!

4. A Backup Script

The library module System.Directory provides functions for working with files and directories. Use these functions to write a program that

Hints: One way to find out what functions a module contains is so use the :browse command in GHCi.

Prelude> :module System.Directory
Prelude System.Directory> :browse
createDirectory :: FilePath -> IO ()
doesDirectoryExist :: FilePath -> IO Bool

This gives you the names and types of the functions, but you probably still need to consult the documentation to find out how to use them. Here's the link to the documentation of the modules included with the latest version of GHC:

You will perhaps also need to perform all of a list of actions. You may find the function sequence from exercise 2 useful for this.

5 (*). Generating Lists

Sometimes we want to generate lists of a certain length.

A. Write a generator

listOf :: 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])
Write down two properties for these; one that says that zip is the inverse of unzip, and one that unzip is the inverse of zip. Note that unzip is not always the inverse of zip, so you need a condition! Could you make use of the generator you just defined?

6. Generating Ordered Lists

A.Write a function ordered that checks if a list is ordered; each element in the list should be smaller than or equal to the next element.

B. Write a generator that generates random lists of integers that are sorted (ordered). You are not allowed to make use of the function sort! (And not of the generator orderedList from the lecture either...)

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.