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Subtyping VS inheritance

wikipedia Subtyping

Subtyping should not be confused with the notion of (class or object) inheritance from object-oriented languages;[1] subtyping is a relation between types (interfaces in object-oriented parlance) whereas inheritance is a relation between implementations stemming from a language feature that allows new objects to be created from existing ones. In a number of object-oriented languages, subtyping is called interface inheritance, with inheritance referred to as implementation inheritance.

Relationship with inheritance

Subtyping and inheritance are independent (orthogonal) relationships. They may coincide(碰巧一致), but none is a special case of the other. In other words, between two types S and T, all combinations of subtyping and inheritance are possible:

  1. S is neither a subtype nor a derived type of T
  2. S is a subtype but is not a derived type of T
  3. S is not a subtype but is a derived type of T
  4. S is both a subtype and a derived type of T

NOTE: 上面用到了两个词语:

subtype: 对应的是subtyping

derived type: 对应的是inheritance

显然这两个词语能够非常好的体现出subtyping和inheritance，后续使用使用它们更好。

The first case is illustrated by independent types, such as Boolean and Float.

The second case can be illustrated by the relationship between Int32 and Int64. In most object oriented programming languages, Int64 are unrelated by inheritance to Int32. However Int32 can be considered a subtype of Int64 since any 32 bit integer value can be promoted into a 64 bit integer value.

The third case is a consequence of function subtyping input contravariance. Assume a super class of type T having a method m returning an object of the same type (i.e. the type of m is T → T, also note that the first argument of m is this/self) and a derived class type S from T. By inheritance, the type of m in S is S → S. In order for S to be a subtype of T the type of m in S must be a subtype of the type of m in T, in other words: S → S ≤: T → T. By bottom-up application of the function subtyping rule, this means: S ≤: T and T ≤: S, which is only possible if S and T are the same. Since inheritance is an irreflexive relation, S can't be a subtype of T.

Subtyping and inheritance are compatible when all inherited fields and methods of the derived type have types which are subtypes of the corresponding fields and methods from the inherited type [1].

wikipedia Inheritance (object-oriented programming)

Inheritance should not be confused with subtyping.[3][4] In some languages inheritance and subtyping agree,[a] whereas in others they differ; in general, subtyping establishes an is-a relationship, whereas inheritance only reuses implementation and establishes a syntactic(语法) relationship, not necessarily a semantic(语义) relationship (inheritance does not ensure behavioral subtyping). To distinguish these concepts, subtyping is also known as interface inheritance, whereas inheritance as defined here is known as implementation inheritance or code inheritance.[5] Still, inheritance is a commonly used mechanism for establishing subtype relationships.[6]

Summary

需要注意的是，programming language并不是严谨的、严格的学术作品，所以不会严格的区分两者，而是会考虑programmer的学习成本、提供了非常灵活的，多种可能性的实现方式等多重因素来提供实现；因此，在现代programming language中，两者是存在一定的重叠的，但是作为programmer，我们应该要知道两者之间本质的区别。

如何区分?

Syntactic(语法) relationship VS semantic(语义) relationship

1) 通过inheritance而关联的两个class，建立了**syntactic(语法) relationship**，两者之间可能并没有语义上的subtyping关系；或者说:

2) "inheritance"是很多现代programming language用于实现subtyping的mechanism:

wikipedia Inheritance (object-oriented programming) 中有这样的描述: "inheritance is a commonly used mechanism for establishing subtype relationships"，这可能是导致很多programmer混淆两者的原因

3) 相比于 inheritance，subtyping更加强调implement interface语义。

Implementation

下面从 implementation 的角度来进行分析

NOTE: 这段分析，是我在阅读 wikipedia Modern C++ Design#Policy-based design 时，想到的。

Subtyping override interface，implementation是由subtype(下)实现/提供，它的主要目的是: subtyping polymorphism。

Inheritance inherit implementation，implementation是由derived type(上)实现提供，它的主要目的是code reuse；最能体现此的是Mixin、Policy-based design，在下面进行了介绍。

现代programming language的实现

现代programming language是如何来处理subtyping VS inheritance？或者说: 是否区分interface inheritance和implementation/code inheritance:

区分: Java，Java中提供了inheritance 和 implement 语义；可以显示定义interface，

未区分: C++，Python，没有区分；使用duck type，implicit interface

NOTE: 参见 wikipedia Modern C++ Design#Policy-based design

implicit VS explicit

体现 inheritance 和 subtyping 差异的example

Mixin和policy-based design都使用了inheritance，但是它们并不是 subtyping ，它们都符合前面"Summary 3)"中描述的内容

Mixin

参见 Theory\Programming-paradigm\Object-oriented-programming\Assemble\Mixin 章节。

Policy-based design

参见 C++\Idiom\Generic-programming\Policy-based-design 章节。