Add test 1
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commit 82aa61982e9c65f65f221fbbcdb41fe8a21321ec
Author: AKP <abi@tdpain.net>
Date: Thu Nov 9 12:33:56 2023 +0000
Question 5
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Author: AKP <abi@tdpain.net>
Date: Thu Nov 9 11:47:10 2023 +0000
Question 4
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Author: AKP <abi@tdpain.net>
Date: Thu Nov 9 11:40:56 2023 +0000
Question 3
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Date: Thu Nov 9 11:11:26 2023 +0000
Question 2
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Date: Thu Nov 9 11:05:24 2023 +0000
Question 1
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Author: AKP <abi@tdpain.net>
Date: Thu Nov 9 11:00:25 2023 +0000
Add base files
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test1/README.md
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test1/README.md
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# Test 1
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## Marking table
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The exercises are defined so that it is hard to get a first-class mark.
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| Mark | Cut-off |
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| ------------ | ------------------ |
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| 1st | 28 marks and above |
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| upper second | 24-27 marks |
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| lower second | 20-23 marks |
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| third | 16-19 marks |
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| fail | 0-15 marks |
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All questions have equal weight, with eight marks each, with a total of 40
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marks.
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## Preparation
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* The test must be completed on JupyterLab.
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* Run `git pull` on JupyterLab to make sure you have the latest version of the
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course repository.
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* We have defined some helper functions for your in the `Types.hs` file. You are
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encouraged to make use of them in your solutions.
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* Do __not__ modify either the file `Types.hs` or the file
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`Test1-Template.hs`.
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* Copy the file `Test1-Template.hs` to a new file called
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`Test1.hs` and write your solutions in `Test1.hs`.
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__Don't change the header of this file, including the module declaration, and,
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moreover, don't change the type signature of any of the given functions for
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you to complete.__
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__If you do make changes, then we will not be able to mark your submission and
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hence it will receive zero marks!__
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* Solve the exercises below in the file `Test1.hs`.
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## Submission procedure
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* If your submission doesn't compile or fails to pass the presubmit script on
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JupyterLab, it will get zero marks.
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* Run the presubmit script provided to you on your submission from Jupyter by
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running `./presubmit.sh Test1` in the terminal (in the same folder as
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your submission).
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* This will check that your submission is in the correct format.
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* If it is, submit it on Canvas.
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* Otherwise fix and repeat the presubmission procedure.
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## Plagiarism
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Plagiarism will not be tolerated. Copying and contract cheating have led to full
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loss of marks, and even module or degree failure, in the past.
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You will need to sign a declaration on Canvas, before submission, that you
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understand the [rules](/README.md#plagiarism) and are abiding by them, in order
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for your submission to qualify.
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## Background material
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- Each question has some **Background Material**, an **Implementation Task** and
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possibly some **Examples**.
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- Read this material first, then implement the requested function.
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- The corresponding type appears in the file `Test1-Template.hs` (to be
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copied by you).
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- Replace the default function implementation of `undefined` with your own
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function.
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## More Rules
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* This is an open book test.
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* You may consult your own notes, the course materials, any of the recommended
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books or [Hoogle](https://hoogle.haskell.org/).
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* Feel free to write helper functions whenever convenient.
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* All the exercises may be solved without importing additional modules. Do not
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import any modules, as it may interfere with the marking.
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## Submission Deadline
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* The official submission deadline is 1pm.
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* If you are provided extra time by the Welfare office then your submission
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deadline is 1:30pm or 2:00pm.
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* Submissions close 10 minutes after your deadline, and late submissions have 5%
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penalty
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## Question 1 — Even majority (**8 marks**)
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**Task** Write the following function `evenMajority`, that takes a list of
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integers, and tells whether more than half of them are even.
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```haskell
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evenMajority :: [Int] -> Bool
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evenMajority ns = undefined
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```
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## Question 2 — 5-smooth numbers (**8 marks**)
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A 5-smooth number is an integer which has no prime factor larger than 5. For an
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integer N, we define S(N) as the set of 5-smooth numbers less than or equal to
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N. For example S(20) = {1,2,3,4,5,6,8,9,10,12,15,16,18,20}
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**Task** Define the following function `get5SmoothNumbers`, that gives a list of
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all 5-smooth numbers less than or equal to a given number.
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```haskell
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get5SmoothNumbers :: Int -> [Int]
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get5SmoothNumbers k = undefined
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```
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Examples:
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```hs
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*Test1> get5SmoothNumbers 25
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[1,2,3,4,5,6,8,9,10,12,15,16,18,20,24,25]
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*Test1> get5SmoothNumbers 50
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[1,2,3,4,5,6,8,9,10,12,15,16,18,20,24,25,27,30,32,36,40,45,48,50]
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```
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## Question 3 — Train stops (**8 marks**)
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Consider the following type of train stops on the West Midlands Railway line,
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from Redditch to Birmingham New Street.
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```haskell
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data TrainStop = BirminghamNewStreet
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| FiveWays
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| University
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| SellyOak
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| Bournville
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| KingsNorton
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| Northfield
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| Longbridge
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| BarntGreen
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| Alvechurch
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| Redditch
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deriving (Eq, Show)
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```
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We define the function `theStopAfter` on this type, which encodes the
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information of which stop comes immediately after which stop.
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```haskell
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theStopAfter :: TrainStop -> TrainStop
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theStopAfter Redditch = Alvechurch
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theStopAfter Alvechurch = BarntGreen
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theStopAfter BarntGreen = Longbridge
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theStopAfter Longbridge = Northfield
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theStopAfter Northfield = KingsNorton
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theStopAfter KingsNorton = Bournville
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theStopAfter Bournville = SellyOak
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theStopAfter SellyOak = University
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theStopAfter University = FiveWays
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theStopAfter FiveWays = BirminghamNewStreet
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theStopAfter BirminghamNewStreet = undefined
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```
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Note that the function is undefined on `BirminghamNewStreet` because that is the
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last possible stop on this line. You should ensure that this function is never
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called on `BirminghamNewStreet`, because the program will crash if you do that.
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**Task** Define the following function `comesBefore`, using the given
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`theStopAfter` function, such that `comesBefore s1 s2` is `True` if and only if
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`s1` is a stop preceding stop `s2`.
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```haskell
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comesBefore :: TrainStop -> TrainStop -> Bool
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comesBefore s1 s2 = undefined
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```
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Some examples:
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```hs
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*Test1> comesBefore University BirminghamNewStreet
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True
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*Test1> comesBefore Bournville FiveWays
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True
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*Test1> comesBefore BirminghamNewStreet University
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False
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*Test1> comesBefore University KingsNorton
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False
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*Test1> comesBefore University University
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False
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```
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## Question 4 — Repeated applications of a function (**8 marks**)
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**Task** Write a function `countApplications`
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```haskell
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countApplications :: (a -> a) -> (a -> Bool) -> a -> Int
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countApplications f p x = undefined
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```
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that takes
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1. a function `f :: a -> a`,
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1. a termination condition `p :: a -> Bool`, and
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1. an input `x :: a`,
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and counts the number of times that the function `f` must be repeatedly applied
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to `x` until the output satisfies the condition `p`.
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Here is an example of how to use this function:
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```hs
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*Test1> countApplications (\n -> n `div` 2) odd 8
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3
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*Test1> countApplications (\n -> n `div` 2) odd 10
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1
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```
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We will only test your implementation of `countApplications` on functions that
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do terminate with respect to the termination condition.
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## Question 5 — Higher order functions (**8 marks**)
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**Task** Write a function `f` of the following type
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```haskell
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f :: (a -> a -> r) -> ((a -> r) -> a) -> r
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f g h = undefined
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```
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The function should terminate for all terminating inputs. Your solution should
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not use recursion or `undefined`.
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59
test1/Test1.hs
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59
test1/Test1.hs
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-- setting the "warn-incomplete-patterns" flag asks GHC to warn you
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-- about possible missing cases in pattern-matching definitions
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{-# OPTIONS_GHC -fwarn-incomplete-patterns #-}
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-- see https://wiki.haskell.org/Safe_Haskell
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{-# LANGUAGE Safe #-}
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module Test1 ( evenMajority
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, get5SmoothNumbers
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, comesBefore
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, countApplications
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, f
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) where
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import Types
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{- QUESTION 1 -}
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_countEvens :: [Int] -> Int
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_countEvens ns = foldl (\acc x -> if even x then acc + 1 else acc) 0 ns
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evenMajority :: [Int] -> Bool
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evenMajority ns = let half = (length ns) `div` 2 in (_countEvens ns) > half
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{- QUESTION 2 -}
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_is5Smooth :: Int -> Bool
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_is5Smooth n = foldl (\acc x -> acc && x <= 5) True (primeFactors n)
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get5SmoothNumbers :: Int -> [Int]
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get5SmoothNumbers n = filter _is5Smooth [1..n]
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{- QUESTION 3 -}
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_getStationsBefore :: TrainStop -> Maybe TrainStop -> [TrainStop]
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_getStationsBefore finalStop Nothing = _getStationsBefore finalStop (Just Redditch)
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_getStationsBefore finalStop (Just previousStop) | finalStop == previousStop = []
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| otherwise = previousStop:(_getStationsBefore finalStop (Just (theStopAfter previousStop)))
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comesBefore :: TrainStop -> TrainStop -> Bool
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comesBefore s1 s2 = not (foldl (\acc x -> acc && x /= s1) True (_getStationsBefore s2 Nothing))
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{- QUESTION 4 -}
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_countApplications :: (a -> a) -> (a -> Bool) -> a -> Int -> Int
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_countApplications f p acc tries | (p acc) = tries
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| otherwise = _countApplications f p (f acc) (tries + 1)
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countApplications :: (a -> a) -> (a -> Bool) -> a -> Int
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countApplications f p x = _countApplications f p x 0
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{- QUESTION 5 -}
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_cloneArgument :: (a -> a -> r) -> (a -> r)
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_cloneArgument f = (\x -> f x x)
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f :: (a -> a -> r) -> ((a -> r) -> a) -> r
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f g h = let i = (_cloneArgument g) in
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g (h i) (h i)
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56
test1/Types.hs
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test1/Types.hs
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-- setting the "warn-incomplete-patterns" flag asks GHC to warn you
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-- about possible missing cases in pattern-matching definitions
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{-# OPTIONS_GHC -fwarn-incomplete-patterns #-}
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-- see https://wiki.haskell.org/Safe_Haskell
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{-# LANGUAGE Safe #-}
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---------------------------------------------------------------------------------
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-------------------------- DO **NOT** MODIFY THIS FILE --------------------------
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---------------------------------------------------------------------------------
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module Types where
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-- Question 2
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factors :: Int -> [Int]
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factors n = [ k | k <- [1..n] , n `mod` k == 0 ]
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isPrime :: Int -> Bool
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isPrime n = factors n == [1, n]
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primeFactors :: Int -> [Int]
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primeFactors n = [x | x <- [1..n], n `mod` x == 0 && isPrime x]
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-- Question 3
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data TrainStop = BirminghamNewStreet
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| FiveWays
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| University
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| SellyOak
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| Bournville
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| KingsNorton
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| Northfield
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| Longbridge
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| BarntGreen
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| Alvechurch
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| Redditch
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deriving (Eq, Show)
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theStopAfter :: TrainStop -> TrainStop
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theStopAfter Redditch = Alvechurch
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theStopAfter Alvechurch = BarntGreen
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theStopAfter BarntGreen = Longbridge
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theStopAfter Longbridge = Northfield
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theStopAfter Northfield = KingsNorton
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theStopAfter KingsNorton = Bournville
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theStopAfter Bournville = SellyOak
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theStopAfter SellyOak = University
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theStopAfter University = FiveWays
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theStopAfter FiveWays = BirminghamNewStreet
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theStopAfter BirminghamNewStreet = undefined
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-- Question 4
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divideBy2 :: Int -> Int
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divideBy2 n = n `div` 2
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103
test1/presubmit.sh
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103
test1/presubmit.sh
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#!/bin/sh
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if [ "$1" = "" ]
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then
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echo "You forgot to add the assignment name, e.g. 'Assessed1'."
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echo "Please run the script again with the right argument."
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exit 1
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fi
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if ! [ -f "$1.hs" ]
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then
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echo "File '$1.hs' not found."
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echo "Are you in the correct directory?"
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exit 1
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fi
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echo "Trying to compile your submission..."
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# Create temporary directory
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temp_dir=$(mktemp -d)
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ghc $1.hs -odir $temp_dir -hidir $temp_dir
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if [ $? -ne 0 ]
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then
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echo ""
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echo "Your file '$1.hs' did not compile."
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echo "Please fix it before submitting."
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exit 1
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fi
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if ! [ -f "$temp_dir/$1.o" ]
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then
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echo ""
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echo "The module name in '$1.hs' does match not the filename '$1'."
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echo "Please make sure you that"
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echo -e "\t(i) your file is called something like 'TestX.hs'"
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echo -e "\t(ii) you did not change the top of the template"
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echo "and try again."
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exit 1
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fi
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ghc -XSafe $1.hs -odir $temp_dir -hidir $temp_dir
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if [ $? -ne 0 ]
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then
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echo ""
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echo "Your file did not compile with '-XSafe.'"
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echo "Did you remove '{-# LANGUAGE Safe #-}' from the template?"
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exit 1
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fi
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# Create file for ensuring type signatures have not been modified
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cat >> $temp_dir/Signatures.hs << 'END'
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{-# LANGUAGE Safe #-}
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module Signatures where
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import Types
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import Test1
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{- QUESTION 1 -}
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evenMajorityTest :: [Int] -> Bool
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evenMajorityTest = evenMajority
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{- QUESTION 2 -}
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get5SmoothNumbersTest :: Int -> [Int]
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get5SmoothNumbersTest = get5SmoothNumbers
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{- QUESTION 3 -}
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comesBeforeTest :: TrainStop -> TrainStop -> Bool
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comesBeforeTest = comesBefore
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{- QUESTION 4 -}
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countApplicationsTest :: (a -> a) -> (a -> Bool) -> a -> Int
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countApplicationsTest = countApplications
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{- QUESTION 5 -}
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fTest :: (a -> a -> r) -> ((a -> r) -> a) -> r
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fTest = f
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END
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ghc -XSafe $temp_dir/Signatures.hs -odir $temp_dir -hidir $temp_dir
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if [ $? -ne 0 ]
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then
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echo ""
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echo "Your file did not compile with the correct type signatures."
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echo "Did you modify the type signatures from the template?"
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exit 1
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fi
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echo ""
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echo "All checks passed."
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echo "You are ready to submit!"
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# Cleanup temporary directory
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rm -r $temp_dir
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Reference in a new issue