type Integer {
  init();

  Integer pred;

  Integer succ();
  Integer plus(Integer y);
  Integer times(Integer y);
}

class Zero : Integer imp Integer {
  init() {
    my.pred = this;
  }
  
  Integer pred;

  Integer plus(Integer y) {
    return y;
  }

  Integer times(Integer y) {
    return this;
  }
  
  Integer succ() {
    Integer that = new Positive : Integer();
    that.pred = this;
    return that;
  }

  export Integer : pred as pred, plus as plus, times as times, succ as succ;
}

class Positive : Integer imp Integer {

  init() {
    my.pred = null;
  }

  Integer pred;

  Integer plus(Integer y) {
    return pred.plus(y.succ());
  }

  Integer times(Integer y) {
    return pred.times(y).plus(y);
  }

  Integer succ() {
    Integer that = new Positive : Integer();
    that.pred = this;
    return that;
  }

  export Integer : pred as pred, plus as plus, times as times, succ as succ;
}