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
## 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 (…)
OVERALL SCORE = … / …
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
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](http://mathworld.wolfram.com/AdditivePersistence.html)
(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”