====== Introduction to Functional Programming (in Java!) ======

===== 1. A single function to implement all of them =====

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: $math[f : A \rightarrow B] (where $math[A] and $math[B] are generic).

1.7. (!) Write an implementation for ''map'' and use ''map'' to solve 1.4.


===== 2. Throwing out elements ... =====

2.1. Write a method that takes a list of integers and returns a new list containing only even elements.

2.2. Write a method that takes a list of integers and returns a new list containing the elements larger than 100.

2.3. Write a method that takes a list of integers and returns a new list containing **even** elements **larger** than 100.

2.4. Write a method that takes a list of strings and returns a new list of strings which start with letter ''B'' only.

2.5. (!) Write the signature of a generic ''filter'' function over lists.

2.6. (!!) Implement ''filter''.

===== 3. Reducing lists =====

3.1. Write a method that takes a list of integers and returns the sum of all the elements.

3.2. Write a method that takes a list of integers and returns the product of all the elements.

3.3. Write a method that takes a list of integers and returns a string representation of all elements separated by commas, e.g. “1,2,3,4”

3.4. Write a method that takes a list of integers and returns their greatest common denominator.

3.5. (Discussion) What is (could be!) common among all implementations? How should a ''fold'' function **signature** (which generalises over all previous ones) look like?

3.6. (!) Implement ''fold'' with all its prerequisites and use it to solve 3.4.

===== 4. Zipping lists =====

4.1. Write a method that takes two lists and returns a new list of all pairwise products. E.g. ''[2, 4, 2''] and ''[6, 7, 8]'' should yield ''[12, 28, 16]''

4.2. Write a method that takes two lists and returns a new list of all pairwise sums. E.g. ''[2, 4, 2]'' and ''[6, 7, 8]'' should yield ''[8, 11, 10]''

4.3. Write a method that takes a list and returns a new list with the square of each element.

4.4. (!) Identify a generic function which can replace all the above, and implement it. Solve 4.3. using it.