We attach meaning to symbols. I doubt that many people on this list would read the expression "a == b" as "a and b are operated on by some function with the name == that has some result".
That really depends on the underlying types.
It should not. Equality should mean equality. I don't see why this should be so distasteful.
bind(&foo, _1) == 2
as "the object which bind returns is equal to 2"; operator== on lambda-type objects is not an equivalence relation but instead returns "some result" (that happens to be a proxy for possibly evaluating an equivalence relation later).
I think if you read this using std::bind I think its actually interpreted as its written: "the bound unary function is equal to 2". Not only is that meaningless, it should be a compiler error. Refusing to legitimize meaningless or ambiguously interpreted syntax is, I tend to think, a good thing. Obviously, you can hijack the syntax to change the meaning to whatever you want, but that's not generic, and its not specific to the algorithms being discussed. That's a specific interpretation of syntax that you happen to be using to generate a function.