Assignment 1: Intro to Haskell (65 points)

The objective of this assignment is for you to gain some
hands-on experience with Haskell. All the problems require
relatively little code ranging from 2 to 15 lines.
If any function requires more than that, you can be
sure that you need to rethink your solution.

**Note: Start Early** Haskell, while simple,
when you know how, may seem foreign at first,
particularly when it comes to recursion and
list manipulation.

## Structure and Constraints

The assignment is in two files:

1. [src/Hw1.hs](/src/Hw1.hs) has skeleton functions
   with missing bodies that you will fill in,

2. [tests/Test.hs](/tests/Test.hs) has some sample tests,
   and testing code that you will use to check your
   assignments before submitting.

You should only need to modify the parts of the files which say:

```haskell
error "TBD: ..."
```

with suitable Haskell implementations.

However, if you're asked to fill in a function definition, such as:

```haskell
f xs = error "TBD: ..."
```

you are also allowed to split this definition into multiple equations, like so:

```haskell
f []     = ...
f (x:xs) = ...
```

You are allowed to use any library function on integers,
but only the following three library functions on lists: `length`, `(++)` (append), `(==)` (is equal)


## Assignment Testing and Evaluation

All the points, will be awarded automatically, by
**evaluating your functions against a given test suite**.

[Tests.hs](/tests/Test.hs) contains a very small suite
of tests which gives you a flavor of of these tests.
When you run

```shell
$ make test
```

Your last lines should have

```
All N tests passed (...)
OVERALL SCORE = ... / ...
```

**or**

```
K out of N tests failed
OVERALL SCORE = ... / ...
```

**If your output does not have one of the above your code will receive a zero**

If for some problem, you cannot get the code to compile,
leave it as is with the `error ...` with your partial
solution enclosed below as a comment.

The other lines will give you a readout for each test.
You are encouraged to try understanding the testing code,
but you will not be graded on this.

## Submission Instructions

Submit your code via the HW-1 assignment on Gradescope.
You must submit a single zip file containing a single directory with your repository inside.
A simple way to create this zip file is:

- Run `git push` to push your local changes to your private fork of the assignment repository
- Navigate to your private fork on github and download source code as a zip

Please *do not* include the `.stack-work` or `__MACOSX` folders into the submission.

**Note:** Upon submission, Gradescope will only test your code on the *small public test suite*,
so it will show maximum 13/65 points.
After the deadline, we will regrade your submission on the full private test suite
and you will get your full points.

## Problem 1: [Roots and Persistence](http://mathworld.wolfram.com/AdditivePersistence.html)

### (a) 10 points

Fill in the implementation of

```haskell
sumList :: [Int] -> Int
sumList xs = error "TBD:sumList"
```

that such that `sumList xs` returns the sum of the integer elements of
`xs`. Once you have implemented the function, you should get the following
behavior at the prompt:

```haskell
ghci> sumList [1, 2, 3, 4]
10

ghci> sumList [1, -2, 3, 5]
7

ghci> sumList [1, 3, 5, 7, 9, 11]
36
```

## (b) 10 points

Fill in the implementation of the function

```haskell
digitsOfInt :: Int -> [Int]
digitsOfInt n = error "TBD:digitsOfInt"
```

such that `digitsOfInt n`

* returns `[]` if `n` is not positive, and otherwise
* returns the list of digits of `n` in the order in which they appear in `n`.

Once you have implemented the function, you should get the following:

```haskell
ghci> digitsOfInt 3124
[3, 1, 2, 4]

ghci> digitsOfInt 352663
[3, 5, 2, 6, 6, 3]
```

### (c) 10+10 points

Consider the process of taking a number, adding its digits,
then adding the digits of the number derived from it, etc.,
until the remaining number has only one digit.
The number of additions required to obtain a single digit
from a number `n` is called the *additive persistence* of `n`,
and the digit obtained is called the *digital root* of `n`.

For example, the sequence obtained from the starting number
`9876` is `9876`, `30`, `3`, so `9876` has an additive
persistence of `2` and a digital root of `3`.

Write two functions

```haskell
additivePersistence :: Int -> Int
additivePersistence n = error "TBD:additivePersistence"

digitalRoot :: Int -> Int
digitalRoot n = error "TBD:digitalRoot"
```

that take positive integer arguments `n` and return respectively
the additive persistence and the digital root of `n`. Once you
have implemented the functions, you should get the following
behavior at the prompt:

```haskell
ghci> additivePersistence 9876
2

ghci> digitalRoot 9876
3
```

## Problem 2: Palindromes

### (a) 15 points

Implement a function:

```haskell
listReverse :: [a] -> [a]
listReverse xs = error "TBD:listReverse"
```

such that `listReverse [x1,x2,...,xn]` returns the list `[xn,...,x2,x1]`
i.e. the input list but with the values in reversed order.
You should get the following behavior:

```haskell
ghci> listReverse [1, 2, 3, 4]
[4, 3, 2, 1]

ghci> listReverse ["a", "b", "c", "d"]
["d", "c", "b", "a"]
```

### (b) 10 points

A *palindrome* is a word that reads the same from left-to-right and
right-to-left. Write a function

```haskell
palindrome :: String -> Bool
palindrome w = error "TBD:palindrome"
```

such that `palindrome w` returns `True` if the string is a palindrome and
`False` otherwise. You should get the following behavior:

```haskell
ghci> palindrome "malayalam"
True
ghci> palindrome "myxomatosis"
False
```