Now we're talking!
Today we go through the elementary functional programming weapons you need to write functional Scala.

You can find today's contents here.

As before, you can create a simple project, starting with a single Scala file.
You'll probably need to define new classes/objects, which we recommend you add in other files.

1. Use Lists for this exercise. We want you to work with functional primitives - applications on Sets and other collections have the same principles.
   • extract only prime numbers from a List
   • given a List of integers, return a new list with the number of digits of each element
   • given a List of integers, return a new list which contains the integers and their String representation; example:
     

      List(1,2) -> List(1, "one", 2, "two")

2. implement a Cons-based List of integers
   • create two case classes: Nil for an empty list, and Cons which has a head (integer) and a tail (the rest of the list)
     • there are some important questions you should ask first before you start coding…
   • implement map, flatMap and filter
     • watch for the signatures first
     • implement recursively (bonus for who does tail recursion ;) )
     • you might want to implement some auxiliary functions
   • create an instance of a Cons-based List you've just implemented
   • extract only the prime numbers from your list, then count the number of digits for each
     • use a for-comprehension!