Reflexive - x.equals(x) must return true.

Symmetric - if x.equals(y), then y.equals(x)

• e.g. implementing the equals() method of CaseInsensitiveString to interoperate with String is futile, because ((String) y).equals((CaseInsensitiveString) x) will not work.

Transitive - if x.equals(y) and y.equals(z), then x.equals(z).

• example that violates transitivity

  @Override
  public boolean equals(Object o) {
      if (!(o instanceof Point))
          return false
      if (!(o instanceof ColorPoint))
          return o.equals(this)
      return super.equals(o) && ((ColorPoint) o).color == color;
  }
  
  ColorPoint p1 = new ColorPoint(1, 2, Color.RED);
  Point p2 = new Point(1, 2);
  ColorPoint p3 = new ColorPoint(1, 2, Color.BLUE);
  
  p1.equals(p2); // true
  p2.equals(p3); // true
  p1.equals(p3); // false

• In general, "[T]here is no way to extend an instantiable class and add a value component while preserving the equals contract."

• "Favor composition over inheritance." (item 18)

• It is possible to add a value component to a subclass of an abstract class without violating the equals contract.

Consistent - if x.equals(y) now, then x.equals(y) later if x and y are not modified.

• e.g. if URL's equality depends on IP provided by DNS, update in DNS might violate consistency.

Non-nullity - x.equals(null) must return false.

• Using instanceof operator implicitly takes care of null, i.e. o instanceof MyType returns if o is null.