I'm a bit lost with the way how e.g. the + operator is implemented in Mathematica as binary (infix) and unary (prefix) operator depending on the context, since I would like to define a similiar behaviour e.g. for the CirclePlus operator.
If one uses the $+$ operator as $+a$ then one gets the expected result $a$.
Since $+$ is by definition a Binary operator the expression $a+b$ is translated into $Plus[a,b]$.
Now how could I specify a similar behavior for e.g the $\oplus$ binary operator? Obviously $a \oplus b$ is translating nicely into CirclePlus[a,b] as expected.
However if I try $\oplus a$ I get a syntax error "$\oplus a$ is incomplete; more input is needed."
I'm sure I miss here some additional definition or rule necessary to get this behavior.