Is there a way to implement algebraic types in Java?

Give class A a constructor with package-level accessibility (and no other constructors).

^{Thanks, Dave L., for the bit about no other constructors.}

You probably want an enum (Java >= 1.5). An enum type can have a set of fixed values. And it has all the goodies of a class: they can have fields and properties, and can make them implement an interface. An enum cannot be extended.

Example:

enum A {

  B,
  C,
  D;

  public int someField;

  public void someMethod() {
  }


}