A good example for overloading are set operations, because the logic is "compatible".

• X * Y intersection
• X + Y join
• X - Y difference
• - X complement

I don't see how the logic is compatible, unary - as complement means X - Y is different from X + (-Y). And there's just no relation between * and + anymore. At least with + for concatenation (which I already don't like much), you can have STRING * 3 to be equivalent to STRING + STRING + STRING.

And actually now that I think of it, the best operator to overload to append to a file is .=. With the dot you have both the append and string semantic, and the = makes it ok for the operation to have an effect on the left operand. And it makes chaining more consistent:
file("path") .= "First string" . "Second string";

> I don't see how the logic is compatible

Set operations have a natural analogy to Boolean operations.

And in mathematics and CS and and or are often replaced with * and + notations, especially in pre-LaTeX documents.

That's because the truth tables are the same

*/AND
  0 1
0 0 0
1 0 1

+/OR
  0 1
0 0 1
1 1 2 (2 is true here)
[download]

Arithmetic operators + - * / are also "close" in precedence, associativity and context (see perlop ) and the grouping rules are well known.

Furthermore is comparison with < > => <= obvious here.

Also the duplicity of == and eq for comparison comes handy (same "set object" or same "set elements")

> STRING * 3 to be equivalent to STRING + STRING + STRING.

not sure what you mean set elements are unique, if you refer to power-sets the cross operator x or power ** may be the better choice.

Cheers Rolf
_{(addicted to the Perl Programming Language :)
Wikisyntax for the Monastery}