Grammatical Subject meant ʻthat of which something is predicatedʼ. It was called ʻgrammaticalʼ because at that time the construction of Subject and Predicate was thought of as purely formal grammar relationship; it was seen to determine various other grammatical features, such as the case of the noun or pronoun that was functioning as Subject, and its concord of person and number with the verb, but it was not thought to express any particular meaning.
- Halliday (1985), a pag.33-34

[...] The term ʻSubjectʼ as we are using it corresponds to the ʻgrammatical Subjectʼ of earlier terminology; but it is being reinterpreted here in functional terms. The label ʻgrammatical Subjectʼ seems to imply a grammatical function whose only function is to be a grammatical function; whereas the element in question is semantic in origin, like all other elements of the clause. The Subject is not an arbitrary grammatical category; being the Subject of a clause means something.
- Halliday (1985), a pag.73

The Subject is a function in the CLAUSE AS AN EXCHANGE. It is the element that is held responsible: in which is vested the success of the clause in whatever is its particular speech function.
- Halliday (1985), a pag.36-37