TDA 555
DIT 440
HT 2019

# Introduction to Functional Programming Exercises for Week 4

## Exercises for Week 4: IO and Testing

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 lookup Function

Consider the following standard Haskell function, that looks up an element in a list of pairs (table):
```lookup :: Eq a => a -> [(a,b)] -> Maybe b
lookup x []           = Nothing
lookup x ((x',y):xys)
| x == x'         = Just y
| otherwise       = lookup 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. Properties of the prefixOf function

Consider the following Haskell function (known as `isPrefixOf` in the Data.List module), that checks if a list is a prefix of another list:
```prefixOf :: Eq a => [a] -> [a] -> Bool
prefixOf [] _          = True
prefixOf _  []         = False
prefixOf (x:xs) (y:ys) = x == y && prefixOf xs ys```

Define a property `prop_prefixOfSelf` that expresses that taking any number of elements (using `take`) from a string `s` gives a list which is a prefix of `s`.

Can you come up with a similar property for `isSuffixOf` (which checks if a list is a suffix of another list)?

An alternative implementation of `prefixOf` could be

```prefixOf_alt :: Eq a => [a] -> [a] -> Bool
prefixOf_alt xs ys = take (length ys) xs == ys```

Rather than actually using this definition, try to use this definition as a property. I.e. write a property of `prefixOf` that uses `take`, `length` and `==` as above.

Do you think this is a good property for testing `prefixOf`? Think about whether the property is mostly true or mostly false.

### 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

• creates a new directory called "backup",
• copies all the files in the current directory into the backup directory.

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

`sequence ::[IO a] -> IO [a]`
useful for this. (The actual type of sequence is more general, but for now it is easier to think of it as having this more specific type).