Halliday & Matthiessen (2014: 368-9):
Thus the so-called ‘articles’ of English, ‘definite article’ the and ‘indefinite article’ a(n), are determiners realising terms in, respectively, the specific and non-specific systems of nominal deixis. They enter into a proportional pattern as follows: see Table 6-4.
Historically the and a(n) are reduced forms of (respectively) that and one; it is also a reduced form of that (but preserving the final part, since it functions as Head, where the preserves the initial part). there is a reduced form of locative there.