# Module 01: Introduction to Haskell

List the names of your team members.

List any general citations here. Specific citations can be placed inline. Remember that every module turned in must give credit to at least two sources!

In this module you will focus on learning some of the basics of the Haskell programming language. If you already know some Haskell, you should focus on helping your partner(s) understand all the material in this module. However, keep in mind that people learn best by doing, not by being told. **The driver should be whoever has the least experience with Haskell.**

This file is a “literate Haskell document”: only lines preceded by > and a space (see below) are code; everything else (like this paragraph) is a comment, formatted using Markdown syntax. Literate Haskell documents have an extension of `.lhs`

, whereas non-literate Haskell source files use `.hs`

.

## GHCi

Run

`ghci`

from a command prompt. At the resulting`ghci`

prompt, type`:help`

.Find the command to exit

`ghci`

. What is it? Exit`ghci`

now.Using the

`cd`

command at the shell prompt, change to the directory containing this file,`01-Haskell.lhs`

.Now start

`ghci`

again. Find the command to load a module. What is it? Load this file,`01-Haskell.lhs`

, into`ghci`

. Note that by default,`ghci`

will look for files in the same directory in which it was started.

Hint: to kill a runaway `ghci`

evaluation, use Ctrl+C.

## Basic Haskell declarations

Now consider the following Haskell code.

```
> i :: Int
> i = -35
>
> n :: Integer
> n = 25
>
> c :: Char
> c = 'Z'
>
> b :: Bool
> b = True
>
> s :: String
> s = "Hello, world!"
>
> f :: Integer -> Integer
> f n = 2*n + 1
>
> g :: Integer -> Integer -> Integer
> g m n = (m - n)*(m + n)
>
> -- This is a comment
> {- So
> is
> this -}
>
> -- Uncomment me:
> -- i = 12
```

Enter

`:type n`

at the`ghci`

prompt. What does the`:type`

command do?What do you think

`::`

means?What do you think

`=`

means?What do you think

`->`

means?Find the

`ghci`

command to reload the current module. Uncomment the line`i = 12`

above, save this file, and reload. What happens? Does it change your answer to the previous question at all?

## Arithmetic

At the

`ghci`

prompt, type each of the following expressions, and record the result. Feel free to experiment with other expressions as well.`3 + 2 19 - 27 div 19 3 19 `div` 3 mod 19 3 19 `mod` 3 19 `divMod` 3 7 ^ 222 (-3) * (-7) 2*i + 3 i + n`

Explain what happens when you evaluate

`i + n`

.What are the smallest and largest possible

`Int`

values?What are the smallest and largest possible

`Integer`

values?

(Haskell has floating-point values too, but we won’t use them much in this course.)

## Booleans

Find out the syntax for each of the following operations in Haskell:

Boolean operations: and, or, not

Comparison: equal, not equal, less than, greater than, less or equal, greater or equal

if-expressions

Of course, be sure to cite any resources you use!

- Play around with the operators you discovered and try them on a bunch of examples. Record three of your most interesting experiments, the result, and what you learned from each.

## Pairs

Type

`(n,c)`

at the`ghci`

prompt. What is the result?What is the type of

`(n,c)`

?What is the result of

`fst (n,c)`

?What is the result of

`snd (n,c)`

?What is the type of

`fst`

? What does it do?

Values like `(n,c)`

are called *pairs*, or more generally, *tuples*. (Haskell also has 3-tuples, 4-tuples, … but we will not use them.)

- Write an expression
`E`

such that`fst (fst (snd (fst E))) == 6`

.

## Functions

Evaluate the following expressions:

```
f 6
f 8
g 5 4
g 2 3
```

A *function* takes one or more input values and produces a single output value.

What is the Haskell syntax for applying a function to a single argument?

What is the Haskell syntax for applying a function to multiple arguments?

Write a function which takes two

`Integer`

values as input and returns`True`

if and only if the first is greater than twice the second. What is the type of your function?

## Pattern matching

```
> wub :: Integer -> Integer
> wub 0 = 1
> wub n = n * wub (n-1)
>
> dub :: Integer -> Integer
> dub 0 = 0
> dub 1 = 1
> dub n = dub (n-1) + dub (n-2)
>
> flub :: (Integer, Integer) -> Integer
> flub p = fst p + 2 * snd p
>
> gub :: (Integer, Integer) -> Integer
> gub (x,y) = x + 2*y
```

Evaluate

`wub 0`

,`wub 1`

, and`wub 5`

.Explain in words what

`wub`

does.What does the line

`wub 0 = 1`

mean?What do you think would happen if the lines

`wub 0 = 1`

and`wub n = n * wub (n-1)`

were switched? Make a guess*before*trying it, and record your guess here.Now try it. What happens? Why?

What happens when you evaluate

`wub (-3)`

? Why?Evaluate

`wub (3+1)`

and`wub 3+1`

. Can you explain the difference?What does

`dub`

do?What happens if the lines

`dub 0 = 0`

and`dub 1 = 1`

are switched?Call

`flub`

and`gub`

on some example inputs. Record your results here. Do you notice a difference between the behavior of`flub`

and`gub`

?Explain the difference between

`flub`

and`gub`

.Which do you prefer? Why?

## Guards

```
> hailstone :: Integer -> Integer
> hailstone n
> | even n = n `div` 2
> | otherwise = 3*n + 1
```

Try evaluating

`hailstone`

on some example inputs; record them here.Try evaluating

`even`

on some example inputs. What does`even`

do?How is

`otherwise`

defined?Explain the behavior of

`hailstone`

.