Groovy type conversion

In Groovy you can do surprising type conversions using either the as operator or the asType method. Examples include

Short s = new Integer(6) as Short
List collection = new HashSet().asType(List)

I'm surprised that I can convert from an Integer to a Short and from a Set to a List, because there is no "is a" relationship between these types, although they do share a common ancestor.

For example, the following code is equivalent to the Integer/Short example in terms of the relationship between the types involved in the conversion

class Parent {}
class Child1 extends Parent {}
class Child2 extends Parent {}

def c = new Child1() as Child2

But of course this example fails. What exactly are the type conversion rules behind the as operator and the asType method?