This could be interesting. One would have to define what hash math should mean. Personally, I would expect (based on my naive assumptions here) that:

    {1: "A"} + {} == {1: "A"}

but

    {1: "A"} + {} + {1: "B", 2: "Z"} + {1: "C"} + {}

should reduce to:

    {1: ("A" + "B" + "C"), 2: "Z"}

Whether you can add "A", "B", and "C" would depend on string functions (could be "ABC" or raise an exception that these cannot be added for example).