A lot of people resist the idea that programming is intrinsically mathematical, but this is one of the places it pops out. The power of programming lies precisely in the way it brings together text that "represents" something with text that "does" something. That is, at the core, the source of its power. You can still draw the distinction philosophically, as you just did, but at the same time there is also a profound way in which there is in fact no difference between "using" computers and "representing" your use of computers.