Type Inheritance and Relational Theory

\(T^\prime\) is a subtype of type \(T\) if and only if, both of the following conditions are satisfied:

1. Every value of type \(T^\prime\) is a value of type \(T\) (i.e., "\(T^\prime\) is a subset of \(T\)").
2. A value of type \(T\) is a value of type \(T^\prime\) if and only if it satisfies a certain constraint, where the constraint in question is such that it can be tested for any given value of type \(T\) by examining just those properties that are intrinsic to values of type \(T\) in general.

(Date 2016, 5 chap.1)