Modeling higher-kinded types in a language without them.

HigherKindedJava.java

class Option<A> {
  protected Option() { }
}
interface App<F, A> {
  F proof();
}
class OptionF  {
  private OptionF() {}
  
  private static class AppOption<A> implements App<OptionF, A> {
    public final Option<A> value;
    
    AppOption(Option<A> value) {
      this.value = value;
    }
  
    public OptionF proof() {
      return new OptionF();
    }
  }
  
  public static <A> App<OptionF, A> fromOption(Option<A> v) {
    return new AppOption(v);
  }
  
  public static <A> Option<A> toOption(App<OptionF, A> v) {
    return (((AppOption<A>)v).value);
  }
}
interface Function<A, B> {
  B apply(A a);
}
interface Functor<F> {
  <A, B> App<F, B> map(Function<A, B> f, App<F, A> fa);
}

@jdegoes, I don't think so. My original counter-example still produce a ClassCastException:
https://gist.github.com/jdegoes/6842d471e7b8849f90d5bb5644ecb3b2#gistcomment-1818237

Damn access methods. If only Java had protected[this]! Or an abstract private method that could be implemented and seen only by subclasses...