Nat.java

public final class Nat {
  private final Nat predecessor;

  private Nat (Nat n) {
    predecessor = null;
  }

  public static Nat S(Nat n) {
    return new Nat(n);
  }

  public static Nat Z = new Nat(null);

  public interface Eliminator<A> {
    public A Z();
    public A S(A a);
  }

  public class Eliminate<A> {
    private Eliminator<A> eliminator;
    public Eliminate(Eliminator<A> e) {
      eliminator = e;
    }
    public A call(Nat n) {
      A v = eliminator.Z();
      while (n.predecessor != null) {
        v = eliminator.S(v);
        n = n.predecessor;
      }
      return v;
    }
  }

  public boolean equals(Nat n) {
    return predecessor == n.predecessor
        || predecessor.equals(n.predecessor);
  }

  private class ToInteger implements Eliminator<Integer> {
    public Integer Z() {
      return 0;
    }
    public Integer S(Integer n) {
      return n + 1;
    }
  }

  public Integer toInteger() {
    Eliminate<Integer> e = new Eliminate(new ToInteger());
    return e.call(this);
  }
}