Description
Problems
1. exists and countInList – 15%
a) [5pts] Write a function exists which takes a “value” and a “list” as input. If the value is a member
of the list, the function should return True. Otherwise it should return False.
The function should have type exists :: Eq t => t -> [t] -> Bool.
(You are not allowed to use the elem function in your exists implementation.)
Examples:
> exists 1 []
False
> exists 1 [1,2,3]
True
> exists [1] [[1]]
True
> exists [1] [[3],[5]]
False
> exists ‘3’ “CptS355”
True
b) [2pts] Explain in a comment why the type is
exists :: Eq t => t -> [t] -> Bool
but not
exists :: t -> [t] -> Bool
c) [8pts] Write a function countInList which takes a value and a list and returns the number of
occurrences of that value in the input list.
The type of your function should be countInList :: (Num p, Eq t) => t -> [t] -> p.
Examples:
> countInList “5” [“3″,”5″,”5″,”-“,”4″,”5″,”1”]
3
> countInList “5” []
0
> countInList True [True, False, False, False, True, True, True]
4
> countInList [] [[],[1,2],[3,2],[5,6,7],[8],[]]
2
2. listDiff – 15%
Write a function listDiff that takes two lists as input and returns the difference of the first list with
respect to the second. The input lists may have duplicate elements. If an element appears in both lists
and if the number of duplicate copies of the element is bigger in the first list, then this element should
appear in the result as many times as the difference of the number of occurrences in the input lists.
Your function should have type listDiff :: Eq a => [a] -> [a] -> [a]. The duplicates
should not be eliminated in the result. The elements in the resulting list may have arbitrary order.
(Hint: You can make use of countInList function in your solution.)
Examples:
> listDiff [“a”,”b”,”c”] [“b”]
[“a”,”c”]
> listDiff [1,2,3] [1,1,2]
[3]
> listDiff [1,2,2,3,3,3] [1,1,2,3]
[2,3,3]
> listDiff [[2,3],[1,2],[2,3]] [[1],[2,3]]
[[2,3],[1,2]]
> listDiff [1,2,3] []
[1,2,3]
3. firstN – 15%
Write a function firstN that takes a list and a number n and returns the first n elements in the list.
The type of firstN can be either of the following:
firstN :: (Num t) => [a] -> t -> [a]
firstN :: (Eq t, Num t) => [a] -> t -> [a]
firstN :: (Ord t, Num t) => [a] -> t -> [a]
If the input list is empty or if the length of the list is less than n, then the function should return the
complete list. (You may assume that n is greater than 0.)
Examples:
> firstN [“a”, “b”, “c”, “x”, “y”] 3
[“a”, “b”, “c”]
> firstN [1,2,3,4,5,6,7] 4
[1,2,3,4]
> firstN [1,2,3,4,5,6,7] 10
[1,2,3,4,5,6,7]
> firstN [[1,2,3],[4,5],[6],[],[7,8],[]] 4
[[1,2,3],[4,5],[6],[]]
> firstN [] 5
[]
4. busFinder – 20%
Pullman Transit offers many bus routes in Pullman. Assume that they maintain the bus stops for their
routes as a list of tuples. The first element of each tuple is the bus route and the second element is the
list of stops for that route (see below for an example).
buses = [(“Lentil”,[“Chinook”, “Orchard”, “Valley”, “Emerald”,”Providence”, “Stadium”, “Main”,
“Arbor”, “Sunnyside”, “Fountain”, “Crestview”, “Wheatland”, “Walmart”, “Bishop”,
“Derby”, “Dilke”]),
(“Wheat”,[“Chinook”, “Orchard”, “Valley”, “Maple”,”Aspen”, “TerreView”, “Clay”,
“Dismores”, “Martin”, “Bishop”, “Walmart”, “PorchLight”, “Campus”]),
(“Silver”,[“TransferStation”, “PorchLight”, “Stadium”, “Bishop”,”Walmart”, “Shopco”,
“RockeyWay”]),
(“Blue”,[“TransferStation”, “State”, “Larry”, “TerreView”,”Grand”, “TacoBell”,
“Chinook”, “Library”]),
(“Gray”,[“TransferStation”, “Wawawai”, “Main”, “Sunnyside”,”Crestview”, “CityHall”,
“Stadium”, “Colorado”])
]
Assume that you are creating an application for Pullman Transit. You would like to write an Haskell
function busFinder that takes the list of bus routes and a stop name, and returns the list of the bus
routes which stop at the given bus stop.
The type of busFinder should be busFinder :: Eq t => t -> [(a, [t])] -> [a].
(Hint: You can make use of exists function you defined earlier.)
Examples:
> busFinder “Walmart” buses
[“Lentil”,”Wheat”,”Silver”]
> busFinder “Shopco” buses
[“Silver”]
> busFinder “Main” buses
[“Lentil”,”Gray”]
> busFinder “Beasley” buses
[]
5. cumulativeSums – 15%
Write a function cumulativeSums that takes a list of numbers and returns a list including the partial
sums of these numbers.
The type of cumulativeSums should be: cumulativeSums :: Num a => [a] -> [a]
(Hint: Define and use a helper function that takes a list and a number holding the accumulated sum. )
Examples:
> cumulativeSums [1,2,3,4,5,6,7,8,9,10]
[1,3,6,10,15,21,28,36,45,55]
> cumulativeSums [5,5,5,5,5,5,5]
[5,10,15,20,25,30,35]
> cumulativeSums [1,2,3,4,-4,-3,-2]
[1,3,6,10,6,3,1]
> cumulativeSums []
[]
6. groupNleft – 20%
groupNleft function takes two arguments where the first argument is a number (n) and the second
is a list (iL). The goal is to produce a result in which the elements of the original list have been collected
into ordered sub-lists each containing n elements (where n is the number argument). The leftover
elements (if there is any) are included as a sublist with less than n elements.
If iL is empty, then function should return [] (will also accept [[]]).
The type of groupNleft can be one of the following:
groupNleft :: Int -> [a] -> [[a]]
groupNleft :: (Num t) => t -> [a] -> [[a]]
Note: this function is not required to be tail-recursive.
Examples:
> groupNleft 3 [1, 2, 3, 4, 5, 6, 7, 8]
[[1,2,3],[4,5,6],[7,8]]
> groupNleft 5 [1, 2, 3, 4, 5, 6, 7, 8]
[[1,2,3,4,5],[6,7,8]]
> groupNleft 2 [(1,”a”),(2,”b”),(3,”c”),(4,”d”),(5,”e”),(6,”f”)]
[[(1,”a”),(2,”b”)],[(3,”c”),(4,”d”)],[(5,”e”),(6,”f”)]]
> groupNleft 2 [1, 2, 3, 4, 5, 6, 7, 8]
[[1,2],[3,4],[5,6],[7,8]]
> groupNleft 3 []
[] — will also accept [[]]
Testing your functions
We will be using the HUnit unit testing package in CptS355. See
http://hackage.haskell.org/package/HUnit for additional documentation.
You may install HUnit in 3 different ways:
Option1 (using cabal installer) :
Run the following commands on the terminal.
cabal update
cabal v2-install –lib HUnit
Option2 (from source) :
1. First install call-stack package
• Download the package from here: http://hackage.haskell.org/package/call-stack .
Download the call-stack-0.2.0.tar.gz file and extract it.
(To extract .gz and .tar files on Windows you may use 7zip (https://www.7-zip.org/))
• Then switch to the call-stack directory and install call-stack using the following
commands at the terminal/command prompt:
runhaskell Setup configure
runhaskell Setup build
runhaskell Setup install
• If you get “permission denied” errors:
− on Windows, run the terminal or command line as administrator.
− on Mac and Linux, run the command in ‘sudo’ mode (or login as root).
2. Next install HUnit package:
• Download the package from here: http://hackage.haskell.org/package/HUnit. Download
the HUnit-1.2.5.2.tar.gz file and extract it.
• Then switch to the HUnit directory and install HUnit using the following commands at
the terminal/command prompt:
runhaskell Setup configure
runhaskell Setup build
runhaskell Setup install
If you get “permission denied” errors, follow the above guideline.
Option3 (using stack – use this option if you already installed stack ) :
Run the following command on the terminal.
stack install Hunit
Running Tests
The file HW1SampleTests.hs provides 3 sample test cases comparing the actual output with the
expected (correct) output for each problem. This file imports the HW1 module (HW1.hs file) which will
include your implementations of the given problems.
You are expected to add at least 2 more test cases for each problem. Make sure that your test inputs
cover all boundary cases.
In HUnit, you can define a new test case using the TestCase function and the list TestList
includes the list of all test that will be run in the test suite. So, make sure to add your new test cases to
the TestList list. All tests in TestList will be run through the “runTestTT tests” command.
The instructor will further explain this during the lecture.
If you don’t add new test cases you will be deduced at least 5% in this homework.
Haskell resources:
• Learning Haskell, by Gabriele Keller and Manuel M T Chakravarty (http://learn.hfm.io/)
• Real World Haskell, by Bryan O’Sullivan, Don Stewart, and John Goerzen
(http://book.realworldhaskell.org/)
• Haskell Wiki: https://wiki.haskell.org/Haskell
• HUnit: http://hackage.haskell.org/package/HUnit
