Is There Really Multiple Types of Addition on Integers?

There's essentially no way of hiding this aspect of your implementation. You cannot in any way wrap it up such that the particular choices you made about type classes in the middle of your program aren't exposed. It's sort of anti-modular in a fairly in-your-face way. Addition is maybe not the most compelling example, although I'm sure there are good cases where you really do want to have different forms of addition on what is an underlying level the same type.

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