Halliday & Matthiessen (2014: 149):
So the Subject is a thick, well-rounded category along with all the other elements in the structure of the clause. The fact that it proves difficult to define does not distinguish it from Theme or Actor or Medium or many other equally pregnant categories. All are subject to the general principle of ineffability – they mean themselves (see Halliday, 1984b). The guiding axiom is the metafunctional one: just as the Theme is best understood by starting from the concept of the clause as message, so the Subject is best understood by starting from the concept of the clause as exchange, a move in dialogic interaction. Each of the two can be thought of as an anchor; … the Medium plays an analogous rôle in the clause as representation.