multiple inheritance - Method resolution order in C++

Question

Consider the following class hierarchy:

• base class Object with a virtual method foo()
• an arbitrary hierarchy with multiple inheritance (virtual and non-virtual); each class is a subtype of Object; some of them override foo(), some don't
• a class X from this hierarchy, not overriding foo()

How to determine which method will be executed upon a call of foo() on an object of class X in C++?

(I'm looking for the algorithm, not any specific case.)

Answer 1

There is no MRO in C++ like Python. If a method is ambiguous, it is a compile-time error. Whether a method is virtual or not doesn't affect it, but virtual inheritance will.

---

The algorithm is described in the C++ standard §[class.member.lookup] (10.2). Basically it will find the closest unambiguous implementation in the superclass graph. The algorithm works like this:

1. Suppose you want to look up a function f in class C.

2. We define a look-up set S(f, C) being a pair of sets (Δ, Σ) representing all possibilities. _(§10.2/3)

   • The set Δ is called the declaration set, which is basically all the possible f's.

   • The set Σ is called the subobject set, which contain the classes that these f's are found.

3. Let S(f, C) include all f directly defined (or using-ed) in C, if any _(§10.2/4):

   Δ = {f in C};
   if (Δ != empty)
     Σ = {C};
   else
     Σ = empty;
   S(f, C) = (Δ, Σ);
   

4. If S(f, C) is empty _(§10.2/5),

   • Compute S(f, B_i) where B_i is a base class of C, for all i.

   • Merge each S(f, B_i) into S(f, C) one by one.

     if (S(f, C) == (empty, empty)) {
       B = base classes of C;
       for (Bi in B)
         S(f, C) = S(f, C) .Merge. S(f, Bi);
     }
     

5. Finally the declaration set is returned as the result of name resolution _(§10.2/7).

   return S(f, C).Δ;
   

6. The merge between two look-up sets (Δ₁, Σ₁) and (Δ₂, Σ₂) is defined as _(§10.2/6):

   • If every class in Σ₁ is a base class of at least one class in Σ₂, return (Δ₂, Σ₂).
     (Similar for the reverse.)
   • Else if Δ₁ ≠ Δ₂, return (ambiguous, Σ₁ ∪ Σ₂).

   • Otherwise, return (Δ₁, Σ₁ ∪ Σ₂)

     function Merge ( (Δ1, Σ1), (Δ2, Σ2) ) {
     
        function IsBaseOf(Σp, Σq) {
          for (B1 in Σp) {
            if (not any(B1 is base of C for (C in Σq)))
              return false;
          }
          return true;
        }
     
        if      (Σ1 .IsBaseOf. Σ2) return (Δ2, Σ2);
        else if (Σ2 .IsBaseOf. Σ1) return (Δ1, Σ1);
        else {
           Σ = Σ1 union Σ2;
           if (Δ1 != Δ2)
             Δ = ambiguous; 
           else
             Δ = Δ1;
           return (Δ, Σ);
        }
     }
     

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For example _(§10.2/10),

struct V { int f(); };
struct W { int g(); };
struct B : W, virtual V { int f(); int g(); };
struct C : W, virtual V { };

struct D : B, C {
   void glorp () {
     f();
     g();
   }
};

We compute that

S(f, D) = S(f, B from D) .Merge. S(f, C from D)
        = ({B::f}, {B from D}) .Merge. S(f, W from C from D) .Merge. S(f, V)
        = ({B::f}, {B from D}) .Merge. empty .Merge. ({V::f}, {V})
        = ({B::f}, {B from D})   // fine, V is a base class of B.

and

S(g, D) = S(g, B from D) .Merge. S(g, C from D)
        = ({B::g}, {B from D}) .Merge. S(g, W from C from D) .Merge. S(g, V)
        = ({B::g}, {B from D}) .Merge. ({W::g}, {W from C from D}) .Merge. empty
        = (ambiguous, {B from D, W from C from D})  // the W from C is unrelated to B.