Exercises

The exercises in this section are supposed to increase you experience in writing purely functional code. In some cases it might be useful to use let expressions or where blocks, but this will not always be required.

Exercise 3 is again of utmost importance. traverseList is a specialized version of the more general traverse, one of the most powerful and versatile functions available in the Prelude (check out its type!).

1. Module Data.List in base exports functions find and elem. Inspect their types and use these in the implementation of handleRequest. This should allow you to completely get rid of the where block.

2. Refactor handleRequest to use Either, such that handleRequest : DB -> Request -> Either Failure Album, where

   data Failure : Type where
     UnknownUser : Email -> Failure
     InvalidPassword : Failure
     AccessDenied : Email -> Album -> Failure
   

   Hint: You may find nested case statements helpful.

3. Define an enumeration type listing the four nucleobases occurring in DNA strands. Define also a type alias DNA for lists of nucleobases. Declare and implement function readBase for converting a single character (type Char) to a nucleobase. You can use character literals in your implementation like so: 'A', 'a'. Note, that this function might fail, so adjust the result type accordingly.

4. Implement the following function, which tries to convert all values in a list with a function, which might fail. The result should be a Just holding the list of converted values in unmodified order, if and only if every single conversion was successful.

   traverseList : (a -> Maybe b) -> List a -> Maybe (List b)
   

   You can verify, that the function behaves correctly with the following test: traverseList Just [1,2,3] = Just [1,2,3].

5. Implement function readDNA : String -> Maybe DNA using the functions and types defined in exercises 2 and 3. You will also need function unpack from the Prelude.

6. Implement function complement : DNA -> DNA to calculate the complement of a strand of DNA.