Here's a lemma that helps to prove D(n) is well-defined: LEMMA: D(pq•r) = D(p•qr): D(pq•r) = pq D(r) + r D(pq) = pq D(r) + rp D(q) + qr D(p) = p (q D(r) + r

Here's a lemma that helps to prove D(n) is well-defined: LEMMA: D(pq•r) = D(p•qr): D(pq•r) = pq D(r) + r D(pq) = pq D(r) + rp D(q) + qr D(p) = p (q D(r) + r D(q)) + qr D(p) = p D(qr) + qr D(p) = D(p•qr) There are a number of generalizations of the notion of "derivative"; in particular, you can take the derivative of a regular expression: https://github.com/scythe/dreg/blob/master/re-deriv.pdf https://github.com/scythe/dreg/blob/master/re-deriv.pdf ...which I've been slowly turning into a regex matcher.