Assignment help: Union between sets

Question

I am taking a Coursera Functional Programming in Scala class. This is the second week and I hit a wall. In the assignment we are working with Sets, but not the kind of Set we all meet in Java, for example. It is a Set that returns true if the value is in there and false otherwise. They say it's not a container, it's just a function.

To get it clear, I need your help. I don't want you to solve my assignment, it's just an example that I want to get the idea of what I should do.

/**
   * We represent a set by its characteristic function, i.e.
   * its `contains` predicate.
   */
  type Set = Int => Boolean

 /**
   * Indicates whether a set contains a given element.
   */
  def contains(s: Set, elem: Int): Boolean = s(elem)

 /**
   * Returns the set of the one given element.
   */
  def singletonSet(elem: Int): Set = Set(elem)

 /**
   * Returns the union of the two given sets,
   * the sets of all elements that are in either `s` or `t`.
   */
  def union(s: Set, t: Set): Set = ???  

This is the code. In the singletonSet I guess the way to solve it is to return the Set(elem), right?

If that is good, how am I supposed to make the union between the two? I am not new to programming but I can't see any way to do it. Since I shouldn't return a "set" of numbers.

This is what another student told me about sets: "But all a "Set" is is a function that takes an Int and returns a Boolean (Int => Boolean). Any function that takes an Int and returns a Boolean fits the type 'Set'."

What I tried in the union function is to have something like:

def union(s: Set, t: Set): Set = (s | t) //value | not a member of Int => Boolean  

Any help would be appreciated :)

Answer 1

It seems the wall you are hitting is that you are unfamiliar with defining functions in Scala. In this particular case you need to define functions of type Int => Boolean, they take an Int and return a Boolean.

Here are some examples of function literals of type Int => Boolean. Try them in the Scala console or the Scala IDE worksheet:

(x: Int) => true
(x: Int) => false
(x: Int) => x == 2
(x: Int) => x == 10
(x: Int) => x == 2 || x == 10
(x: Int) => x % 2 == 0

Then all you have to do for the assignment is to use the same syntax, starting with (x: Int) => and then translate the meaning of union, intersect, ... into the right hand side of the expression.

Part of learning is giving it a genuine effort. I believe you can resubmit the solution multiple times, so don't hesitate to submit and iterate if you don't get 10/10 on the first try. All you need is compiling code. Good luck!