Assignment 1: Intro to Haskell Solution

$30.00 $26.40



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:


error “TBD: …”


with suitable Haskell implementations.

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


f xs = error “TBD: …”


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


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

Most of 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


$ stack test


Your last lines should have


All N tests passed (…)





K out of N tests failed



**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

To submit your code, do:


$ make prepare


This will create a file named `hw1-haskell.tgz` for submission. Submit this file to the Canvas assignment.

Make sure you also commit and push the changes to your gitlab repository as well.

## Problem 1: [Roots and Persistence](

(a) 10 points

Fill in the implementation of


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:


ghci> sumList [1, 2, 3, 4]


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


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



## (b) 10 points

Fill in the implementation of the function


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:


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


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:


ghci> additivePersistence 9876


ghci> digitalRoot 9876



## Problem 2: Palindromes

(a) 15 points

Implement a function:


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:


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


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:


ghci> palindrome “malayalam”


ghci> palindrome “myxomatosis”