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# Test 1
## Marking table
The exercises are defined so that it is hard to get a first-class mark.
| Mark | Cut-off |
| ------------ | ------------------ |
| 1st | 28 marks and above |
| upper second | 24-27 marks |
| lower second | 20-23 marks |
| third | 16-19 marks |
| fail | 0-15 marks |
All questions have equal weight, with eight marks each, with a total of 40
marks.
## Preparation
* The test must be completed on JupyterLab.
* Run `git pull` on JupyterLab to make sure you have the latest version of the
course repository.
* We have defined some helper functions for your in the `Types.hs` file. You are
encouraged to make use of them in your solutions.
* Do __not__ modify either the file `Types.hs` or the file
`Test1-Template.hs`.
* Copy the file `Test1-Template.hs` to a new file called
`Test1.hs` and write your solutions in `Test1.hs`.
__Don't change the header of this file, including the module declaration, and,
moreover, don't change the type signature of any of the given functions for
you to complete.__
__If you do make changes, then we will not be able to mark your submission and
hence it will receive zero marks!__
* Solve the exercises below in the file `Test1.hs`.
## Submission procedure
* If your submission doesn't compile or fails to pass the presubmit script on
JupyterLab, it will get zero marks.
* Run the presubmit script provided to you on your submission from Jupyter by
running `./presubmit.sh Test1` in the terminal (in the same folder as
your submission).
* This will check that your submission is in the correct format.
* If it is, submit it on Canvas.
* Otherwise fix and repeat the presubmission procedure.
## Plagiarism
Plagiarism will not be tolerated. Copying and contract cheating have led to full
loss of marks, and even module or degree failure, in the past.
You will need to sign a declaration on Canvas, before submission, that you
understand the [rules](/README.md#plagiarism) and are abiding by them, in order
for your submission to qualify.
## Background material
- Each question has some **Background Material**, an **Implementation Task** and
possibly some **Examples**.
- Read this material first, then implement the requested function.
- The corresponding type appears in the file `Test1-Template.hs` (to be
copied by you).
- Replace the default function implementation of `undefined` with your own
function.
## More Rules
* This is an open book test.
* You may consult your own notes, the course materials, any of the recommended
books or [Hoogle](https://hoogle.haskell.org/).
* Feel free to write helper functions whenever convenient.
* All the exercises may be solved without importing additional modules. Do not
import any modules, as it may interfere with the marking.
## Submission Deadline
* The official submission deadline is 1pm.
* If you are provided extra time by the Welfare office then your submission
deadline is 1:30pm or 2:00pm.
* Submissions close 10 minutes after your deadline, and late submissions have 5%
penalty
## Question 1 — Even majority (**8 marks**)
**Task** Write the following function `evenMajority`, that takes a list of
integers, and tells whether more than half of them are even.
```haskell
evenMajority :: [Int] -> Bool
evenMajority ns = undefined
```
## Question 2 — 5-smooth numbers (**8 marks**)
A 5-smooth number is an integer which has no prime factor larger than 5. For an
integer N, we define S(N) as the set of 5-smooth numbers less than or equal to
N. For example S(20) = {1,2,3,4,5,6,8,9,10,12,15,16,18,20}
**Task** Define the following function `get5SmoothNumbers`, that gives a list of
all 5-smooth numbers less than or equal to a given number.
```haskell
get5SmoothNumbers :: Int -> [Int]
get5SmoothNumbers k = undefined
```
Examples:
```hs
*Test1> get5SmoothNumbers 25
[1,2,3,4,5,6,8,9,10,12,15,16,18,20,24,25]
*Test1> get5SmoothNumbers 50
[1,2,3,4,5,6,8,9,10,12,15,16,18,20,24,25,27,30,32,36,40,45,48,50]
```
## Question 3 — Train stops (**8 marks**)
Consider the following type of train stops on the West Midlands Railway line,
from Redditch to Birmingham New Street.
```haskell
data TrainStop = BirminghamNewStreet
| FiveWays
| University
| SellyOak
| Bournville
| KingsNorton
| Northfield
| Longbridge
| BarntGreen
| Alvechurch
| Redditch
deriving (Eq, Show)
```
We define the function `theStopAfter` on this type, which encodes the
information of which stop comes immediately after which stop.
```haskell
theStopAfter :: TrainStop -> TrainStop
theStopAfter Redditch = Alvechurch
theStopAfter Alvechurch = BarntGreen
theStopAfter BarntGreen = Longbridge
theStopAfter Longbridge = Northfield
theStopAfter Northfield = KingsNorton
theStopAfter KingsNorton = Bournville
theStopAfter Bournville = SellyOak
theStopAfter SellyOak = University
theStopAfter University = FiveWays
theStopAfter FiveWays = BirminghamNewStreet
theStopAfter BirminghamNewStreet = undefined
```
Note that the function is undefined on `BirminghamNewStreet` because that is the
last possible stop on this line. You should ensure that this function is never
called on `BirminghamNewStreet`, because the program will crash if you do that.
**Task** Define the following function `comesBefore`, using the given
`theStopAfter` function, such that `comesBefore s1 s2` is `True` if and only if
`s1` is a stop preceding stop `s2`.
```haskell
comesBefore :: TrainStop -> TrainStop -> Bool
comesBefore s1 s2 = undefined
```
Some examples:
```hs
*Test1> comesBefore University BirminghamNewStreet
True
*Test1> comesBefore Bournville FiveWays
True
*Test1> comesBefore BirminghamNewStreet University
False
*Test1> comesBefore University KingsNorton
False
*Test1> comesBefore University University
False
```
## Question 4 — Repeated applications of a function (**8 marks**)
**Task** Write a function `countApplications`
```haskell
countApplications :: (a -> a) -> (a -> Bool) -> a -> Int
countApplications f p x = undefined
```
that takes
1. a function `f :: a -> a`,
1. a termination condition `p :: a -> Bool`, and
1. an input `x :: a`,
and counts the number of times that the function `f` must be repeatedly applied
to `x` until the output satisfies the condition `p`.
Here is an example of how to use this function:
```hs
*Test1> countApplications (\n -> n `div` 2) odd 8
3
*Test1> countApplications (\n -> n `div` 2) odd 10
1
```
We will only test your implementation of `countApplications` on functions that
do terminate with respect to the termination condition.
## Question 5 — Higher order functions (**8 marks**)
**Task** Write a function `f` of the following type
```haskell
f :: (a -> a -> r) -> ((a -> r) -> a) -> r
f g h = undefined
```
The function should terminate for all terminating inputs. Your solution should
not use recursion or `undefined`.

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-- setting the "warn-incomplete-patterns" flag asks GHC to warn you
-- about possible missing cases in pattern-matching definitions
{-# OPTIONS_GHC -fwarn-incomplete-patterns #-}
-- see https://wiki.haskell.org/Safe_Haskell
{-# LANGUAGE Safe #-}
module Test1 ( evenMajority
, get5SmoothNumbers
, comesBefore
, countApplications
, f
) where
import Types
{- QUESTION 1 -}
_countEvens :: [Int] -> Int
_countEvens ns = foldl (\acc x -> if even x then acc + 1 else acc) 0 ns
evenMajority :: [Int] -> Bool
evenMajority ns = let half = (length ns) `div` 2 in (_countEvens ns) > half
{- QUESTION 2 -}
_is5Smooth :: Int -> Bool
_is5Smooth n = foldl (\acc x -> acc && x <= 5) True (primeFactors n)
get5SmoothNumbers :: Int -> [Int]
get5SmoothNumbers n = filter _is5Smooth [1..n]
{- QUESTION 3 -}
_getStationsBefore :: TrainStop -> Maybe TrainStop -> [TrainStop]
_getStationsBefore finalStop Nothing = _getStationsBefore finalStop (Just Redditch)
_getStationsBefore finalStop (Just previousStop) | finalStop == previousStop = []
| otherwise = previousStop:(_getStationsBefore finalStop (Just (theStopAfter previousStop)))
comesBefore :: TrainStop -> TrainStop -> Bool
comesBefore s1 s2 = not (foldl (\acc x -> acc && x /= s1) True (_getStationsBefore s2 Nothing))
{- QUESTION 4 -}
_countApplications :: (a -> a) -> (a -> Bool) -> a -> Int -> Int
_countApplications f p acc tries | (p acc) = tries
| otherwise = _countApplications f p (f acc) (tries + 1)
countApplications :: (a -> a) -> (a -> Bool) -> a -> Int
countApplications f p x = _countApplications f p x 0
{- QUESTION 5 -}
_cloneArgument :: (a -> a -> r) -> (a -> r)
_cloneArgument f = (\x -> f x x)
f :: (a -> a -> r) -> ((a -> r) -> a) -> r
f g h = let i = (_cloneArgument g) in
g (h i) (h i)

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-- setting the "warn-incomplete-patterns" flag asks GHC to warn you
-- about possible missing cases in pattern-matching definitions
{-# OPTIONS_GHC -fwarn-incomplete-patterns #-}
-- see https://wiki.haskell.org/Safe_Haskell
{-# LANGUAGE Safe #-}
---------------------------------------------------------------------------------
-------------------------- DO **NOT** MODIFY THIS FILE --------------------------
---------------------------------------------------------------------------------
module Types where
-- Question 2
factors :: Int -> [Int]
factors n = [ k | k <- [1..n] , n `mod` k == 0 ]
isPrime :: Int -> Bool
isPrime n = factors n == [1, n]
primeFactors :: Int -> [Int]
primeFactors n = [x | x <- [1..n], n `mod` x == 0 && isPrime x]
-- Question 3
data TrainStop = BirminghamNewStreet
| FiveWays
| University
| SellyOak
| Bournville
| KingsNorton
| Northfield
| Longbridge
| BarntGreen
| Alvechurch
| Redditch
deriving (Eq, Show)
theStopAfter :: TrainStop -> TrainStop
theStopAfter Redditch = Alvechurch
theStopAfter Alvechurch = BarntGreen
theStopAfter BarntGreen = Longbridge
theStopAfter Longbridge = Northfield
theStopAfter Northfield = KingsNorton
theStopAfter KingsNorton = Bournville
theStopAfter Bournville = SellyOak
theStopAfter SellyOak = University
theStopAfter University = FiveWays
theStopAfter FiveWays = BirminghamNewStreet
theStopAfter BirminghamNewStreet = undefined
-- Question 4
divideBy2 :: Int -> Int
divideBy2 n = n `div` 2

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#!/bin/sh
if [ "$1" = "" ]
then
echo "You forgot to add the assignment name, e.g. 'Assessed1'."
echo "Please run the script again with the right argument."
exit 1
fi
if ! [ -f "$1.hs" ]
then
echo "File '$1.hs' not found."
echo "Are you in the correct directory?"
exit 1
fi
echo "Trying to compile your submission..."
# Create temporary directory
temp_dir=$(mktemp -d)
ghc $1.hs -odir $temp_dir -hidir $temp_dir
if [ $? -ne 0 ]
then
echo ""
echo "Your file '$1.hs' did not compile."
echo "Please fix it before submitting."
exit 1
fi
if ! [ -f "$temp_dir/$1.o" ]
then
echo ""
echo "The module name in '$1.hs' does match not the filename '$1'."
echo "Please make sure you that"
echo -e "\t(i) your file is called something like 'TestX.hs'"
echo -e "\t(ii) you did not change the top of the template"
echo "and try again."
exit 1
fi
ghc -XSafe $1.hs -odir $temp_dir -hidir $temp_dir
if [ $? -ne 0 ]
then
echo ""
echo "Your file did not compile with '-XSafe.'"
echo "Did you remove '{-# LANGUAGE Safe #-}' from the template?"
exit 1
fi
# Create file for ensuring type signatures have not been modified
cat >> $temp_dir/Signatures.hs << 'END'
{-# LANGUAGE Safe #-}
module Signatures where
import Types
import Test1
{- QUESTION 1 -}
evenMajorityTest :: [Int] -> Bool
evenMajorityTest = evenMajority
{- QUESTION 2 -}
get5SmoothNumbersTest :: Int -> [Int]
get5SmoothNumbersTest = get5SmoothNumbers
{- QUESTION 3 -}
comesBeforeTest :: TrainStop -> TrainStop -> Bool
comesBeforeTest = comesBefore
{- QUESTION 4 -}
countApplicationsTest :: (a -> a) -> (a -> Bool) -> a -> Int
countApplicationsTest = countApplications
{- QUESTION 5 -}
fTest :: (a -> a -> r) -> ((a -> r) -> a) -> r
fTest = f
END
ghc -XSafe $temp_dir/Signatures.hs -odir $temp_dir -hidir $temp_dir
if [ $? -ne 0 ]
then
echo ""
echo "Your file did not compile with the correct type signatures."
echo "Did you modify the type signatures from the template?"
exit 1
fi
echo ""
echo "All checks passed."
echo "You are ready to submit!"
# Cleanup temporary directory
rm -r $temp_dir