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.