Subtyping polymorphism

wikipedia Subtyping

NOTE: subtype是事物之间固有的、天然的relation的 is-a relation，就像下面的duck和bird之间的relation，作为programmer，我们往往是基于事物的这种固有的、天然的relation来进行model。

Example of subtypes: where bird is the supertype and all others are subtypes as denoted by the arrow in UML notation

In programming language theory, subtyping (also subtype polymorphism or inclusion polymorphism) is a form of type polymorphism in which a subtype is a datatype that is related to another datatype (the supertype) by some notion of substitutability, meaning that program elements, typically subroutines or functions, written to operate on elements of the supertype can also operate on elements of the subtype. If S is a subtype of T, the subtyping relation is often written S <: T, to mean that any term of type S can be safely used in a context where a term of type T is expected. The precise semantics of subtyping crucially(至关重要的) depends on the particulars(细节) of what "safely used in a context where" means in a given programming language. The type system of a programming language essentially defines its own subtyping relation, which may well be trivial should the language support no (or very little) conversion mechanisms.

NOTE: 上述 "substitutability" 所链接的是Liskov substitution principle。

Due to the subtyping relation, a term may belong to more than one type. Subtyping is therefore a form of type polymorphism. In object-oriented programming the term 'polymorphism' is commonly used to refer solely to this subtype polymorphism, while the techniques of parametric polymorphism would be considered generic programming.

NOTE: programming paradigm and polymorphism

The concept of subtyping is related to the linguistic notions of hyponymy and holonymy. It is also related to the concept of bounded quantification in mathematical logic.

Subsumption

NOTE: 意思是: "包含"

Relationship with inheritance

NOTE: 放到了./Subtyping-VS-inheritance中

wikipedia Behavioral subtyping

How to implementation subtyping in OOP?

现代programming language，往往使用inheritance + override 来供programmer使用subtyping polymorphism。

在programming language实现层，不同的programming language使用的实现方式是不同的。

Subtyping polymorphism is based on behavior

本节标题的是含义是: Subtyping polymorphism是基于behavior的，意思是: Subtyping polymorphism中能够polymorphism的只有behavior，data member是无法polymorphism；关于behavior，参见Theory\Programming-paradigm\Object-oriented-programming\Behaivor.md。关于这个观点，下面是例证:

文章
C++\Language-reference\Classes\Subtype-polymorphism\index.md	在C++，dynamic polymorphism是behavior（function），只有virtual method（virtual table），而不是data/value的
wikipedia Behavioral subtyping	TODO