Introduction to Functional Programming (in Java!)

1.1. Write a method that takes a list of integers and returns a new list with all elements multiplied by two.

1.2. Write a method that takes a list of doubles and returns a new list with all elements multiplied by two.

1.3. Write a method that takes a list of integers and returns a new list with all the elements’ successors (i.e. the elements incremented by 1).

1.4. Write a method that takes a list of integers and returns a new list of booleans indicating if an element is prime.

1.5. (Discussion) What is common among all previous implementations? Could a single list function (a more general function) be used to achieve all results? Starting from the signatures of previous functions, write the signature for this general function which we will call map.

1.6. (Discussion) How can we pass functions as parameter (to another function) in Java? Consider unary functions of the form: $ f : A \rightarrow B$ (where $ A$ and $ B$ are generic).

1.7. (!) Write an implementation for map.