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 and use map to solve 1.4.
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.
3.1. 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.
4.1. 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.