Why are Super-class and Sub-class reversed?

Question

In set theory, a set is a superset if it contains everything in the original set and possibly more. A subset however is does not contain everything of the initial set.

W

Answer 1

The subclass has all the [members] of its superclass [and more]. Isn't this backwards?

This issue crops up all over programming languages, and it always makes my head hurt. (Subtyping especially.)

Here are the rules:

• When you are considering obejcts, the subclass/child/subtype has more methods and members. It can be used in more contexts. This seems counterintuitive.

• When you are considering contexts, or interfaces, or arguments, roles are reversed. For example, a method expecting an argument of the supertype/parent/superclass can accept more arguments than a method expecting an argument of the subtype.

Which one is on top depends entirely on whether you think objects are primary or whether you think contexts expecting objects are primary. I have studied this subject for almost 15 years and still my intuition betrays me.

If a class declaration is considered as a specification, then the superclass specification is satisifed by more objects, and the subclass specification is satisfied by fewer objects. I believe this is the reason for the nomenclature. (It is a little clearer if you talk about subtypes and supertypes—a subtype is inhabited by fewer values than its supertype, because every value of the subtype is also a value of the supertype, and the supertype is likely inhabited by additional values that are not members of the subtype.)

Did I mention that the whole topic makes my head hurt?