C3线性化

描述

一个类的C3超类线性化是这个类，再加上它的各个父类的线性化与各个父类形成列表的唯一合并的结果。父类列表作为合并过程的最后实参，保持了直接父类的本地前趋序。
各个父类的线性化与各个父类形成列表的合并算法，首先选择不出现在各个列表的尾部（指除了第一个元素外的其他元素）的第一个元素，该元素可能同时出现在多个列表的头部。被选中元素从各个列表中删除并追加到输出列表中。这个选择再删除、追加元素的过程迭代下去直到各个列表被耗尽。如果在某个时候无法选出元素，说明这个类继承体系的依赖序是不一致的，因而无法线性化。

例子

给定
class O
class A extends O
class B extends O
class C extends O
class D extends O
class E extends O
class K1 extends A, B, C
class K2 extends D, B, E
class K3 extends D, A
class Z extends K1, K2, K3
Z的线性化计算：
L(O)  := [O]                                                // the linearization of O is trivially the singleton list [O], because O has no parents

L(A)  := [A] + merge(L(O), [O])                             // the linearization of A is A plus the merge of its parents' linearizations with the list of parents...
       = [A] + merge([O], [O])
       = [A, O]                                             // ...which simply prepends A to its single parent's linearization

L(B)  := [B, O]                                             // linearizations of B, C, D and E are computed similar to that of A
L(C)  := [C, O]
L(D)  := [D, O]
L(E)  := [E, O]

L(K1) := [K1] + merge(L(A), L(B), L(C), [A, B, C])          // first, find the linearizations of K1's parents, L(A), L(B), and L(C), and merge them with the parent list [A, B, C]
       = [K1] + merge([A, O], [B, O], [C, O], [A, B, C])    // class A is a good candidate for the first merge step, because it only appears as the head of the first and last lists
       = [K1, A] + merge([O], [B, O], [C, O], [B, C])       // class O is not a good candidate for the next merge step, because it also appears in the tails of list 2 and 3; but class B is a good candidate
       = [K1, A, B] + merge([O], [O], [C, O], [C])          // class C is a good candidate; class O still appears in the tail of list 3
       = [K1, A, B, C] + merge([O], [O], [O])               // finally, class O is a valid candidate, which also exhausts all remaining lists
       = [K1, A, B, C, O]

L(K2) := [K2] + merge(L(D), L(B), L(E), [D, B, E])
       = [K2] + merge([D, O], [B, O], [E, O], [D, B, E])    // select D
       = [K2, D] + merge([O], [B, O], [E, O], [B, E])       // fail O, select B
       = [K2, D, B] + merge([O], [O], [E, O], [E])          // fail O, select E
       = [K2, D, B, E] + merge([O], [O], [O])               // select O
       = [K2, D, B, E, O]

L(K3) := [K3] + merge(L(D), L(A), [D, A])
       = [K3] + merge([D, O], [A, O], [D, A])               // select D
       = [K3, D] + merge([O], [A, O], [A])                  // fail O, select A
       = [K3, D, A] + merge([O], [O])                       // select O
       = [K3, D, A, O]

L(Z)  := [Z] + merge(L(K1), L(K2), L(K3), [K1, K2, K3])
       = [Z] + merge([K1, A, B, C, O], [K2, D, B, E, O], [K3, D, A, O], [K1, K2, K3])    // select K1
       = [Z, K1] + merge([A, B, C, O], [K2, D, B, E, O], [K3, D, A, O], [K2, K3])        // fail A, select K2
       = [Z, K1, K2] + merge([A, B, C, O], [D, B, E, O], [K3, D, A, O], [K3])            // fail A, fail D, select K3
       = [Z, K1, K2, K3] + merge([A, B, C, O], [D, B, E, O], [D, A, O])                  // fail A, select D
       = [Z, K1, K2, K3, D] + merge([A, B, C, O], [B, E, O], [A, O])                     // select A
       = [Z, K1, K2, K3, D, A] + merge([B, C, O], [B, E, O], [O])                        // select B
       = [Z, K1, K2, K3, D, A, B] + merge([C, O], [E, O], [O])                           // select C
       = [Z, K1, K2, K3, D, A, B, C] + merge([O], [E, O], [O])                           // fail O, select E
       = [Z, K1, K2, K3, D, A, B, C, E] + merge([O], [O], [O])                           // select O
       = [Z, K1, K2, K3, D, A, B, C, E, O]                                               // done

例子的Python实现

首先，metaclass允许对象通过名字简明表示而不用<class '__main__.A'>:
class Type(type):
    def __repr__(cls):
        return cls.__name__A = Type('A', (object,), {})
类A表示自身通过名字：
>>> AA
由于Python 3的metaclass语法改变了，为使例子兼任版本2与3，用metaclass创建对象，如同用type。
A = Type('A', (object,), {})B = Type('B', (object,), {})C = Type('C', (object,), {})D = Type('D', (object,), {})E = Type('E', (object,), {})K1 = Type('K1', (A, B, C), {})K2 = Type('K2', (D, B, E), {})K3 = Type('K3', (D, A), {})Z = Type('Z', (K1, K2, K3), {})
等价的Python 2 的类定义是：
class Z(K1, K2, K3):
    __metaclass__ = Type
对于Python 3是
class Z(K1, K2, K3, metaclass=Type):
    pass
最后有：
>>> Z.mro()[Z, K1, K2, K3, D, A, B, C, E, <type 'object'>]