Functional Programming Exercise Session 1

1. Implement a function myReverse: List ty -> List ty that reverses lists.

   myReverse [1,2,3] == [3,2,1]
   

2. Write a function revString: String -> String that reverses strings. You may find the Prelude functions unpack: String -> List Char and its inverse pack useful.

   revString "hello" == "olleh"
   

3. Implement a function palindrome: String -> Bool that tests whether a string is a palindrome.

   palindrome "idris" == False
   palindrome "idrisirdi" == True
   

4. Implement a function myCycle: List ty -> Nat -> List ty that takes a list and repeats it the required number of times.

   myCycle ['a', 'b'] 3 == ['a', 'b', 'a', 'b', 'a', 'b']
   

5. Write a function deal: List ty -> (List ty, List ty) that splits a list into two lists, containing its even and odd elements. You may find it useful to start by writing functions odds: List ty -> List ty and evens: List ty -> List ty.

   deal ['a','b','c','d'] == (['a', 'c'], ['b', 'd'])
   

6. Write a function top_three : Ord a => List a -> List a that outputs the three largest elements of a list. You may find the following predefined functions useful: take : Nat -> List a -> List a and sort : Ord a => List a -> List a. Check out the documentation (:doc) for the details.

   top_three [2,1,4,3,0] == [4,3,2]
   

7. Write a function myUnzip: List (ty, ty') -> (List ty, List ty') that unzips a zipped list.

   myUnzip [(2,'a'),(5,'b')] == ([2, 5], ['a', 'b'])
   

8. Idris has some nice syntax for updating elements of a record. Recall the Address record definition from the lectures. Type it out (and mind the typo, country should be type String not string.) Check the type of record {city = "Tallinn"} or record {city = "Tallinn", postcode=10138}. Define a new record type called Street that has fields number: Int and street : String. Write functions getStreet: Address -> Street and setStreet: Street -> Address -> Address.