Exercises

Question 1

Without using GHCI, evaluate the results of the following expressions:

1. 3 * 4 + 5
2. 3 + 4 * 5
3. 5 ^ 3 `mod` 4
4. 97 / 4
5. 97 `div` 4
6. if (let x = 3 in x + 3) /= 5 && 3 < 4 then 1 else 2
7. not otherwise
8. fst (0, 1, 2)
9. succ (1 / 2)
10. sqrt 2
11. 1 `elem` [1, 2, 3]
12. let f x = x + 1; g x = x * 2 in (g . f) 1
13. [1, 2, 3] ++ [4, 5, 6]
14. head [1, 2, 3]
15. tail [1, 2, 3]
16. init [1, 2, 3]
17. [1, 2, 3] !! 0
18. null []
19. length [1, 2, 3]
20. drop 2 [1, 2, 3]
21. take 5 [-1..]
22. dropWhile even [2, 6, 4, 5, 1, 2, 3]
23. sum [fst x | x <- [(i, j) | i <- [1..4], j <- [-1..1]]]

Question 2

Write a function eqLast that receives two nonempty lists and checks whether the last element of both are the same. Example runs follow:

ghci> eqLast [1,2,3] [4,5]
False
ghci> eqLast "ac" "dc"
True

Question 3

A palindrome is a word that reads the same forward or backward. Write a function isPalindrome that checks if a string is a palindrome. Example runs follow:

ghci> isPalindrome "a"
True
ghci> isPalindrome "bcde"
False
ghci> isPalindrome "racecar"
True

Question 4

You are writing a function to determine the cost of a ride. The cost of a ride is determined by \(f + rd\) where \(f\) is the flag down fare, \(r\) is the per km rate of the ride and \(d\) is the distance of the ride in km. Write a function taxiFare that receives \(f\), \(r\) and \(d\) and computes the total cost. Example runs follow:

ghci> grab = taxiFare 3 0.5
ghci> gojek = taxiFare 2.5 0.6
ghci> grab 3
4.5
ghci> gojek 3
4.3
ghci> grab 10
8.0
ghci> gojek 10
8.5

Question 5

Nowadays, we can customize the food that we order. For example, you can order your burger with extra or no cheese. In this exercise, we will write a function that takes a string as the customization and compute the price for burgers with the code names for the customization. You are given the price list for ingredients:

Write a function burgerPrice that takes in a burger as a string of characters (each character represents an ingredient in the burger) and returns the price of the burger. While doing so, define an auxilliary function ingredientPrice that receives a single ingredient (as a character) and returns its price. Define ingredientPrice as part of burgerPrice using a where binding. Example runs follow:

ghci> burgerPrice "BVPB"
3.2
ghci> burgerPrice "BVPCOMB"
5.3

Question 6

Write a function sumDigits that receives a nonnegative integer and gives the sum of its digits. Example runs follow:

ghci> sumDigits 123
6
ghci> sumDigits 12356
17

Question 7

Write a function @: that receives a list and a tuple of two values (start, stop), and performs list slicing with indices starting from start and ending at (and excluding) stop. The step size is 1. Assume that both the start and stop values are nonnegative integers. Example runs follow:

ghci> [1, 2, 3] @: (1, 4)
[2,3]
ghci> [1, 2, 3] @: (4, 1)
[]
ghci> [1, 2, 3] @: (0,1)
[1]
ghci> [1, 2, 3] @: (1,67)
[2,3]

Syntactically, the way to define this function might be the following:

ls @: (start, stop) = your implementation here