Declarative Programming Homework 1

CS 357 Declarative Programming
Homework 1
General instructions
Prepare a single file homework1.hs containing all the requested function definitions.
1.1 Simple functions on numbers (10pts)
1. (10pts) Write a Haskell function test :: Int - Int - Bool that takes two integers
and returns True if and only if the two integers are both odd.
1.2 List manipulation (30pts)
1. (10pts) Write a Haskell function stutter :: [Char] - [Char] that takes a list of elements and returns a list where every element has been duplicated. For example,
stutter "Hello World" evaluates to "HHeelllloo WWoorrlldd".
2. (10pts) Write a Haskell function compress :: [Char] - [Char] that eliminates consecutive duplicate elements of a list. For example, compress "HHeelllloo WWoorrlldd"
evaluates to "Hello World".
3. (10pts) Write a Haskell function zipSum :: [Int] - [Int] - [Int] that takes two
equally sized lists of ints and returns a single list of ints in which each element at a given
index is the sum of the corresponding values at that index from the input lists. For example, zipSum [1,2,3] [4,5,6] evaluates to [5,7,9].
1.3 Using lists for sets: writing recursive functions over lists (40pts)
Let us use the Haskell type [Integer] to represent sets of integers. The representation invariants
are that there are no duplicates in the list, and that the order of the list elements is increasing.
Do not use any of the built-in Haskell functions that manipulate lists as sets.
1. (10pts) Write a Haskell function setUnion :: [Integer] - [Integer] - [Integer]
that takes two sets and returns their union.
2. (10pts) Write a Haskell function setIntersection :: [Integer] - [Integer] - [Integer]
that takes two sets and returns their intersection.
3. (10pts) Write a Haskell function setDifference :: [Integer] - [Integer] - [Integer]
that takes two sets and returns their set difference.
4. (10pts) Write a Haskell function setEqual :: [Integer] - [Integer] - Bool that
takes two sets and returns True if and only if the two sets are equal.
CS 357 Declarative Programming, Spring 2018 2
1.4 More involved functions on numbers (20pts)
1. (20 pts) Quoting from Wikipedia, https://en.wikipedia.org/wiki/Digital_root:
The digital root of a non-negative integer is the (single digit) value obtained by
an iterative process of summing digits, on each iteration using the result from
the previous iteration to compute a digit sum. The process continues until a
single-digit number is reached.
Write a Haskell function dr :: Integer - Int that takes an integer and computes its
digital root. For example, dr 65536 evaluates to 7.
How to turn in
Use the UNM Learn facility as follows: Navigate to https://learn.unm.edu/ and log in. Then
click on CS-357L-000 (Spring 2018) . Now click on Assignments in the left side navigation
menu. After that, click on the appropriate homework assignment link. Now attach your .hs
file(s) and click submit. You are allowed to submit as many times as you like but only the latest
submission will be graded.