Category Theory for Programmers Chapter 6: Simple Algebraic Data Types

12 Sep 2018

1. Show the isomorphism between Maybe a and Either () a.

   maybeToEither :: Maybe a -> Either () a
   maybeToEither None = Left ()
   maybeToEither Just x = Right x
   
   eitherToMaybe :: Either () a -> Maybe a
   eitherToMaybe Left _ = None
   eitherToMaybe Right x = Just x
   

2. Implement Shape in C++ or Java as an interface and create two classes: Circle and Rect. Implement area as a virtual function.

   public class HelloWorld {
     interface Shape {
       double area();
     }
     static class Circle implements Shape {
       final double radius;
       Circle(double radius) {
         this.radius = radius;
       }
       @Override
       public double area() {
         return Math.PI * radius * radius;
       }
     }
     static class Rect implements Shape {
       final double height;
       final double width;
       Rect(double height, double width) {
         this.height = height;
         this.width = width;
       }
       @Override
       public double area() {
         return height * width;
       }
     }
     public static void printShape(Shape shape) {
       System.out.println(shape.area());
     }
     public static void main(String[] args) {
       printShape(new Circle(5.0));
       printShape(new Rect(5.0, 5.0));
     }
   }
   

3. Add circ to your C++ or Java implementation. What parts of the original code did you have to touch?

   Add double circ(); to the interface, then implement it in both the subclasses.

4. Adding Square in Java is just creating a new subclass.

5. a + a is represented by Either a a and 2 * a can be represented by (Bool, a). This works because you can assign either Left or Right one of the two values of Bool so then you create the mappings Left a => (true, a) and Right a => (false, a).