6.4 Inheritance

Inheritance refers to properties. For example, if we have

   A ≤ B

then A has all the properties of B. A is said to inherit the properties of B. Thus, whatever can be said of B can also be said of A.

For example, since

   Mammal ≤ Animal

Mammal is said to inherit all the properties of Animal. Whatever is true of any instance of Animal is also true of any instance of Mammal. For example, all animals reproduce; therefore, a Mammal reproduces.

However, the converse does not hold. Not everything that can be said about a Mammal can be said about an Animal. For example, while it can be said that a Mammal breastfeeds its young, this cannot be said of every Animal.


The concept of inheritance can also be used to talk about types that are defined in terms of more than one supertype. We discuss this next.

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