I would like to explain why covariance and contravariance are important, and why they apply to return types and parameter types respectively, and not the other way around.Covariance is probably easiest to understand, and is directly related to the Liskov Substitution Principle. Using the above example, let's say that we receive an `AnimalShelter` object, and then we want to use it by invoking its `adopt()` method. We know that it returns an `Animal` object, and no matter what exactly that object is, i.e. whether it is a `Cat` or a `Dog`, we can treat them the same. Therefore, it is OK to specialize the return type: we know at least the common interface of any thing that can be returned, and we can treat all of those values in the same way.Contravariance is slightly more complicated. It is related very much to the practicality of increasing the flexibility of a method. Using the above example again, perhaps the "base" method `eat()` accepts a specific type of food; however, a _particular_ animal may want to support a _wider range_ of food types. Maybe it, like in the above example, adds functionality to the original method that allows it to consume _any_ kind of food, not just that meant for animals. The "base" method in `Animal` already implements the functionality allowing it to consume food specialized for animals. The overriding method in the `Dog` class can check if the parameter is of type `AnimalFood`, and simply invoke `parent::eat($food)`. If the parameter is _not_ of the specialized type, it can perform additional or even completely different processing of that parameter - without breaking the original signature, because it _still_ handles the specialized type, but also more. That's why it is also related closely to the Liskov Substitution: consumers may still pass a specialized food type to the `Animal` without knowing exactly whether it is a `Cat` or `Dog`.

The gist of how the Liskov Substition Princple applies to class types is, basically: "If an object is an instance of something, it should be possible to use it wherever an instance of something is allowed". The Co- and Contravariance rules come from this expectation when you remember that "something" could be a parent class of the object.For the Cat/Animal example of the text, Cats are Animals, so it should be possible for Cats to go anywhere Animals can go. The variance rules formalise this.Covariance: A subclass can override a method in the parent class with one that has a narrower return type. (Return values can be more specific in more specific subclasses; they "vary in the same direction", hence "covariant").If an object has a method you expect to produce Animals, you should be able to replace it with an object where that method produces only Cats. You'll only get Cats from it but Cats are Animals, which are what you expected from the object.Contravariance: A subclass can override a method in the parent class with one that has a parameter with a wider type. (Parameters can be less specific in more specific subclasses; they "vary in the opposite direction", hence "contravariant").If an object has a method you expect to take Cats, you should be able to replace it with an object where that method takes any sort of Animal. You'll only be giving it Cats but Cats are Animals, which are what the object expected from you.So, if your code is working with an object of a certain class, and it's given an instance of a subclass to work with, it shouldn't cause any trouble:It might accept any sort of Animal where you're only giving it Cats, or it might only return Cats when you're happy to receive any sort of Animal, but LSP says "so what? Cats are Animals so you should both be satisfied."

Covariance also works with general type-hinting, note also the interface:interface xInterface{    public function y() : object;}abstract class x implements xInterface{    abstract public function y() : object;}class a extends x{    public function y() : \DateTime    {        return new \DateTime("now");    }}$a = new a;echo '<pre>';var_dump($a->y());echo '</pre>';