In CG, many grammatical concepts can only be defined recursively. Dowty  defines grammatical functions such as subject and object as being the ultimate and penultimate `argument-in' of a verbal category. Hoeksema  defines verbs as exocentric categories reducible to S. Lexical rules frequently refer to such concepts. For instance, a categorial lexical rule of passive applies to verbs selecting an object and must remove the subject.
In standard unification-based formalisms, these concepts and the rules referring to such concepts cannot be expressed directly.