## Exercises for Week 1: Getting Started With Haskell

This excersise set is designed as very very gentle introduction to Haskell and the interactive Haskell interpreter GHCi. You will need to have access a working Haskell system either on your computer or the school's computers.

From week 2 onwards there are scheduled exercises classes where you can ask questions and get help.

You are supposed to work through this document in an afternoon. The main tasks are to answer questions that look like this:

The questions come with a suggested answer that you can see by clicking at the question mark symbol the left. Try to answer the questions yourself before looking!

## GHCi as a simple calculator

GHCi is an Haskell interpreter, i.e. it is a program that evaluates Haskell expressions.You can start GHCi by typing `ghci`

in a terminal.

`ghci`

We will use `this style`

for the text that you as user of GHCi have to enter.
When you start GHCi you will see something like this welcome message:

```
GHCi, version 8.0.1: http://www.haskell.org/ghc/ :? for help
```

Right now, we don't care about the precise meaning of the text in the
welcome
message, but focus on the last line with the > symbol. The >
symbol indicates that GHCi is ready to receive a command. We will
explain later on what the word `Prelude`

means. The simplest
command one can give to GHCi is an Haskell expression, given an Haskell
expression GHCi will evaluate it, and write the result on the screen.
Try:
After that, as indicated by the > symbol, GHCi is ready to take a new command. We can repeat this interaction as many times as we want. Try:`4+5*6`

34

`4*(8-5)+3`

15`3.5/(3+4)*4.5`

2.25`sin 1.57`

1.0

The first expression contains asyntax error; there is no right operand of the multiplication operator (*). In the second expression we try to divide by zero. Recognizing different kinds of errors and knowing their causes will take some time to learn!`3+5*`

<interactive>:1:4: parse error (possibly incorrect indentation)

## More GHCi commands

We use the :q command to finish a GHCi session.`:q`

Leaving GHCi.
candela04>

All GHCi commands *except*evaluating an expressions start with a colon

`:`

Restart GHCi and try to answer the following questions by inspecting the welcome message.

## Two simple examples

## A programmable pocket calculator

We have seen how we can use GHCi to do simple calculations. But this is just the beginning. To go further we need to define our own functions. As a first example we look at the currency conversion problem described above. If we need to repeatedly convert pounds to SEK we can define a function that does this for us. Defining a function consists of a number of steps.

- Decide upon a name for the function. A name should be chosen that
is suggestive of it's purpose, and
does not shadow a function currently in scope. For this example we chose
the name
`pound.`

- Decide which arguments (input) the function has, and what the
result (output) of the function is. In this case this is simple:
- Input: a floating point number representing an amount of crowns.
- Output: a floating point number representing an an amount of pounds.

- Decide upon a name for the parameters of the function that
indicates the usage of the argument. In this case we use the name
`kr`

as parameter. - Express the result in terms of the parameters. In this case
the result is:
`kr/12.7775`

pound. - Decide upon the type of the function. In this case:
`pounds`**::****Double****->****Double** - Write the complete Haskell function definition. In this case:
`pounds`**::****Double****->****Double**`pounds``kr`**=**`kr``/`12.7775

- Use a text editor (Vim and Sublime text are two popular cross-platorm editors, gedit on linux, notepad++ on Windows, Atom for Mac are all examples) to write the function
definition in a file. Do this, start your editor and create a new file containing the definition above. Save this to a file with name
`ex1.hs`

. - Give GHCi a command to load the file
`:l ex1.hs`

Compiling Main ( ex1.hs, interpreted ) Ok, modules loaded: Main. *Main>

`pounds 1000`

78.2626`pounds 12345`

966.151`pounds 127775`

10000.0

`ex1.hs`

. Load the file and test your
function.
__(note the spelling error). What happens if one writes:__

`pount 10`

`pounds kr`

## Comparison and more complex functions

Up till now we have defined functions by equations of the form:nameparameter= an expressions containing the parameter, numbers and arithmetic operations.

It is not always this easy, consider the following example:

A shop sells potatoes for 3.50 SEK/kg. To stimulates large sales, the shop offers a discount of 3 SEK/kg for the quantity exceeding 10kg.

We want to define the function that calculates the price.

Let's call this function `price`

and the parameter `v`

.

When `v`

is at most 10, then the price is `3.50*v`

. If `v`

is more than 10, the price is `35+3*(v-10)`

(check this!) which is equal to `5+3*v`

. So, we have:

How does one write this in Haskell? First, notice that GHCi can compare numbers.Try:`price(v) = 3.5*v`

, if`v<=10`

`price(v) = 5+3*v`

, if`v>10`

The result of such a comparison is either`3 < 6`

True`3.5 <= 3`

False`pounds 4000 > 3*100`

True

`True`

or `False`

. Notice, that smaller than or equal to is written as `<=`

.
Now, we can write the definition of price as follows:
The Boolean expressions betweenprice::Double->Doublepricev|v<=10=3.5*v|v>10=5+3*v

`|`

and ` = `

are called *guards.*When this function is applied to a particular argument, GHCi checks the guards from top to bottom until it finds one that evaluates to

`True`

,
after that the right-hand side of the expression is used to calculate
the result. If all guards evaluate to `False`

GHCi gives an error message.
Load this function into GHCi, and test the function price on different arguments.

What is the result of applying the function to 9.5, 10.5 and 11.5, respectively?|v>11=5+3*v

What is the now result of applying the function to 9.5, 10.5 and 11.5, respectively?pricev|v<=11=3.5*v|v>10=5+3*v

`otherwise`

as a guard that is always
true. So, if `otherwise`

is used as the last guard, the
expression at the right-hand side will be used if none of the other
guards evaluates to true.
So, we can write:

price::Double->Doublepricev|v<=10=3.5*v|otherwise=5+3*v

Is `otherwise`

a Haskell keyword? What does hoogle say?

When a function is applied to a simple argument (like 5) we don't need parentheses. But if the argument is composed (like 4 + 8) parentheses are needed.

`price 7.5`

26.25`price 11`

38.5`price (4+8)`

41.0

## Functions with more than one argument

Functions can have more than one argument. As an example we define a function that defines the average of two numbers:- The name of the function:
`average`

. - Input:
*Two*floating point numbers.

Output: A floating point number giving the average of the two arguments. - Names of the parameters:
`x`

and`y`

. - The result in terms of the parameters:
`(`

`x``+``y`)`/`2 - The type:
`average`**::****Double****->****Double****->****Double** - The complete definition:
`average`**::****Double****->****Double****->****Double**`average``x``y`**=**(`x``+``y`)`/`2

`average 5 8`

6.5

## The Prelude

Some functions are very frequently used and therefore pre-defined in a module (file) called the Prelude, which is loaded automatically every time GHCi is started. An overview of the functions defined can be found in e.g., A Tour of the Haskell Prelude.To be able to program efficiently in Haskell it is necessary to know which functions are available in the prelude. In the coming weeks you will become more familiar with them.

## Operators and functions with two arguments

Operators like *,-,+ are written*infix*, which means that the operator should be

*between*its arguments. Functions are usually written prefix, meaning that they are written

*in front of*their arguments.

However, one can use a function infix by writing it between ` `. An operator can be used prefix by writing it in between parentheses. Try:

`5 `average` 4`

4.5`4 `max` (5 `max` 2)`

5`(+) 3 4`

7

## Integers

The prelude provide the function`div `

for integer division.
Try:
The function`div 17 5`

3`div 34 8`

4`div 5 9`

0`4 `div` 2`

2

`mod`

gives the remainder for integer division:
`17 `mod` 5`

2`34 `mod` 8`

2`5 `mod` 9`

5`mod 4 2`

0

`==`

which evaluates to ```
True
```

if its arguments are equal.
## A bigger example

Consider the following game:

Think of an whole number greater than one. If its even, divide it by two, otherwise multiply it by three and add one. Stop if the resulting number is one, otherwise repeat the procedure.As example, we start width 10.

- 10 is even, so the next number is: 10/2 = 5
- 5 is odd so the next number is: 3*5+1=16
- 16 is even, so the next number is: 16/2 = 8
- 8 is even, so the next number is: 8/2 = 4
- 4 is even, so the next number is: 4/2 = 2
- 2 is even, so the next number is: 1.

If we start with 7 we get: (Check this!)

7, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1.

We are interested in the question: Given a number `n`, how many
numbers are there in the sequence? For `n`=10, we get 7 numbers (10, 5,
16, 8, 4, 2, 1). For `n`=7 we get 17 numbers (See above).
Note that we include both the number `n` we start with and the final
number 1.

How can GHCi help us to answer the question? We start with defining
a function `next`

that given a number computes the next number
in the sequence.

`steps`

that takes a number `n`

as argument
and calculates the length of the generated sequence. What is ```
steps
20
```

? And `steps 3`

?
`steps`

complies with:
We call this a recursive definition. (You should have met this concept before - otherwise ask for a refund on your undergraduate education!) Write the definition in your file. Load it in to GHCi, and calculatesteps::Int->Intstepsn|n==1=1|otherwise=steps(nextn)+1

`steps`

n for several different values of n.
It all seems to work without any problem. But at the same time one can wonder:

Finally, we define the function```
numbers
```

that calculates the
actual list of numbers generated in the game:
Load the function into GHCi and try:numbers::Int->[Int]numbersn|n==1=[1]|otherwise=n:numbers(nextn)

Study the function definition: When n=1 the result is the list [1]. Otherwise we use the operator`numbers 10`

[10, 5, 16, 8, 4, 2, 1]`numbers 17`

[17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1]`numbers 1`

[1]

`:`

, named cons, which
constructs a list from an element and a list by placing the element at
the top of the list. The result of `numbers n`

is `n`

followed by the list `numbers(next n)`

.
Now we have defined the function `numbers`

we don't need to
define `steps`

anymore because there is a function `length`

in the prelude that calculates the length of a list.

`length [1,6,33,8,7,14]`

6`length (numbers 10)`

7