Reaction of CaO with C
Why would it not? C is a nonmetal, and it is common for nonmetals to form compounds with metals. Oxygen gives oxides, nitrogen gives nitrides (if you succeed in making him react, which may be not quite trivial, but that's another story), chlorine gives chlorides, etc. Now, C is less eager to take extra electrons than N or O, so it would form ionic carbides only with active metals. Well, Ca is pretty active.