Templated operator overloading

[XavierAP]

I've been trying some things to template operator overloads. The 
reason is that I want very similar code for different types, but 
I can't use polymorphism, as they're structs rather than classes. 
Perhaps this choice is not as advantageous as I think, and I may 
change this design from structs to classes, or else the code 
duplication would be small and never subject to change. But now 
I'm just trying for the sake of learning to find out what works 
or not in terms of templated operator overloading, and whether 
the reason something doesn't work is by design and if mentioned 
in the specification, or just an arbitraty result of some 
unspecified parsing/lowering step order, or it depends on the 
compiler (I'm using dmd).

Since there are in my case two similar types (below just a 
minimal dumb proof of concept), I want the operator(s) to work 
within the same type, or also with the other. The following code 
actually works, including type parameter inferrence, and const 
ref to avoid struct copying:

/********************/
import std.stdio;

struct S1
{
	void opOpAssign(string op, T)(const ref T x)
	{
		writeln(this, op, x);
	}
}
struct S2
{}

void main()
{	
	S1 s1;
	S2 s2;
	s1 *= s2;
}
/********************/

When I want to have the same operator overloading code in both 
types however, I can't make it work:

/********************/
private mixin template operator(Tthis)
{
	void opOpAssign(string op, T)(ref Tthis, const ref T x)
	{
		writeln(this, op, x);
	}
}

struct S1
{
	mixin operator!S1;
}
struct S2
{
	mixin operator!S2;
}

void main()
{	
	S1 s1;
	S2 s2;
	s1 *= s2; // Error: s1 *= s2 is not a scalar
	s1.opOpAssign!"*"(s2); // Error: template 
test.S1.operator!(S1).opOpAssign cannot deduce function
}
/********************/

And a final try with a global templated function instead of a 
mixin template:

/********************/
private void opOpAssign(string op, Tthis, T)(ref Tthis that, 
const ref T x)
{
	writeln(that, op, x);
}

struct S1
{}
struct S2
{}

void main()
{	
	S1 s1;
	S2 s2;
	s1 *= s2; // Error: s1 *= s2 is not a scalar
	s1.opOpAssign!"*"(s2); // OK!
}
/********************/