Submission instructions

Email the folowing files to pawel@cs.ioc.ee:

• a single file called Solutions.idr, with all of your solutions
• a file called statement.txt that says “I your_name certify that the solutions submitted are my own”

Deadline 12:00 19/02/2020

Functional Programming Assignment 1

1. Given a list of integers, construct the list of their successive differences

   differences [] == []
   differences [5] == []
   differences [5, 7, 12, 20] == [2, 5, 8]
   

2. Uppercase the first character of each word in a string

   titlecase "hello" == "Hello"
   titlecase "it was the best of times" == "It Was The Best Of Times"
   

   Hints: recall pack and unpack from last week, and read the documentation for words and unwords. The function toUpper will also be useful.

3. Interactively titlecase the user’s input using the repl function.

   *idris> :exec interactive_titlecase
   string> it was the best of times
   It Was The Best Of Times
   ^D
   

4. Return the average number of vowels in the words of a string, where a vowel is an element of [‘a’, ‘e’, ‘i’, ‘o’, ‘u’], in either upper- or lowercase.

   avg_vowels "a e i o u"
   1.0
   avg_vowels "it was the best of times"
   1.1666666666666667
   avg_vowels "aAa EeE iIi xXx"
   2.25
   

   Hints:

   • write a local function is_vowel : Char -> Bool, using elem,
   • write a local function average : List Nat -> Double, using cast and arithmetic.
   • use map unpack . words to get a list of lists of characters to analyze.
5. Find all elements in both of two lists that satisfy a given predicate with a function satInBoth : (Eq t) => (t -> Bool) -> List t -> List t -> List t.

   sat_in_both (< 5) [2,4,6,5] [3,4,6] == [4]
   sat_in_both (==0) [1..10]   [0..1]  == []
   satInBoth ((==5) . length) ["hello","world"] ["hello","bye"] == ["hello"]
   

   Hint: use Data.List.intersect by importing Data.List.

6. Write the Ackermann function ack : Nat -> Nat -> Nat.

   ack 1 1 == 3
   ack 1 2 == 4
   ack 3 2 == 29
   ack 4 0 == 13
   

7. Write a function that takes a list of integers and a default integer and returns a pair of the least and greatest elements of the list, or two copies of the default if the list is empty.

   least_greatest 5 [2,3,8,4,7] == (2,8)
   least_greatest 0 [6..1]      == (0,6)
   

   Hints: Write a local function with the following signature: min_max' : List Integer -> (Integer , Integer) -> (Integer , Integer) where the second argument is an accumulator consisting of the least and greatest numbers seen so far in the list. Note that you can pattern match on both the list and the pair. Use the min and max functions from the standard library

8. Write a function producing the sum of first n even natural numbers.

   sumevens 0 == 0
   sumevens 1 == 0
   sumevens 2 == 2
   sumevens 3 == 6
   sumevens 4 == 12
   

9. Write a function that sums all the prime numbers that are less than or equal to a given number.

   sum_primes 5 == 10
   sum_primes 10 == 17
   sum_primes 100 == 1060
   sum_primes 1000 == 76127