def nullable (r: Rexp) : Boolean = r match { case ZERO => false case ONE => true case CHAR(_) => false case ALT(r1, r2) => nullable(r1) || nullable(r2) case SEQ(r1, r2) => nullable(r1) && nullable(r2) case STAR(_) => true}def der (c: Char, r: Rexp) : Rexp = r match { case ZERO => ZERO case ONE => ZERO case CHAR(d) => if (c == d) ONE else ZERO case ALT(r1, r2) => ALT(der(c, r1), der(c, r2)) case SEQ(r1, r2) => if (nullable(r1)) ALT(SEQ(der(c, r1), r2), der(c, r2)) else SEQ(der(c, r1), r2) case STAR(r) => SEQ(der(c, r), STAR(r))}def ders (s: List[Char], r: Rexp) : Rexp = s match { case Nil => r case c::s => ders(s, der(c, r))}def matches(r: Rexp, s: String) : Boolean = nullable(ders(s.toList, r))