Halliday & Matthiessen (2014: 630-1):
Consider the following examples:(a) The sun was shining on the sea.
(b) This is the house that Jack built.
(c) Algy met a bear. The bear was bulgy. The bulge was Algy.
In (a) we know which ‘sun’ and which ‘sea’ are being referred to even if we are not standing on the beach with the sun above our heads; there is only one sun, and for practical purposes only one sea. There may be other seas in different parts of the globe, and even other suns in the heavens; but they are irrelevant. In (b) we know which ‘house’ is being referred to, because we are told – it is the one built by Jack; and notice that the information comes after the occurrence of the the. In (c) we know which bear – the one that Algy met; and we know which bulge – the one displayed by the bear; but in this case the information had already been given before the the occurred. Only in (c), therefore, is the anaphoric.
Like the personals, and the other demonstratives, the has a specifying function; it signals ‘you know which one(s) I mean’. But there is an important difference. The other items not only signal that the identity is known, or knowable; they state explicitly how the identity is to be established. …
In other words, the merely announces that the identity is specific; it does not specify it. The information is available elsewhere. It may be in the preceding text (anaphoric), like (c) above; in the following text (cataphoric), like (b); or in the air, so to speak, like (a). Type (a) are self-specifying; there is only one – or at least only one that makes sense in the context, as in Have you fed the cat? (homophoric).