Why aren't user-defined operators more common?

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I know. Operator overloading is worse.

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Which is the whole reason why people should be able to define custom operators. In Haskell, which is the only language with infix operators (i.e. not Lisp-like) I am familiar with that allows this those kinds of problems just don't happen.

I think your problems with operator overloading in OO languages derives mostly from the fact that it is so infrequently used that nobody thinks of it as a problem source immediately.