## Description

Overview

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

“`