symmetric visitor pattern

Question

I'm using visitor pattern to define a set of operations on some classes.
Some operations are commutative, so I end up with duplication in the visitor pattern code.
Let's say I have classes A B C, and the operations: A*A, A*B, A*C, B*A, B*B, B*C, C*A, C*B, C*C.
A*A, B*B, C*C are unique.
A*B, B*A and friends will have code duplication I could implement A*B, and make B*A call A*B but I will end up asking myself: in which file did I implement the operation between A and B again, in A or in B? (there will be about 6 classes, so I will ask this question a lot. 15 pairs of possible operations)
There is a risk of someone in the future making an infinite loop of A*B calling B*A calling A*B when implementing a new operation.
It's unnatural to have a convention that decides which should be implemented A*B or B*A.
I could make a 3rd file with all the implemented functions which are called by either A*B and B*A, doesn't seem very object oriented.
How would you solve this issue?
Thanks
(I could list some code, but it's long and doesn't illustrate the point easily)

Answer 1

You are right, you should definitely refrain from implementing A*B as a call of B*A. In addition to a potential of creating an infinite chain of calls, that approach does not reflect the symmetry of the operation in your code, because the code is not symmetric.

A better approach is to implement a "symmetric" operation in a helper class or as a top-level function, depending on what is supported in your language, and then make both A*B and B*A call that helper implementation.

Answer 2

My suggestion would be use builder which will act as parameter Builder

new ParameterBuilder()
    .setFirst( "A" )
    .setSecond( "B" )
    .setThird( "C" )
    ...
    .build();

Then you will have only one method which takes ParameterBuilder as argument.