added technical Overview section, almost done introduction
package POSIXobject PosixAlgo { abstract class Rexp case object NULL extends Rexp case object EMPTY extends Rexp case class CHAR(c: Char) extends Rexp case class ALT(r1: Rexp, r2: Rexp) extends Rexp case class SEQ(r1: Rexp, r2: Rexp) extends Rexp case class STAR(r: Rexp) extends Rexp case class RECD(x: String, r: Rexp) extends Rexp abstract class Val case object Void extends Val case class Chr(c: Char) extends Val case class Sequ(v1: Val, v2: Val) extends Val case class Left(v: Val) extends Val case class Right(v: Val) extends Val case class Stars(vs: List[Val]) extends Val case class Rec(x: String, v: Val) extends Val def nullable(r: Rexp): Boolean = r match { case NULL => false case EMPTY => true case CHAR(_) => false case ALT(r1, r2) => nullable(r1) || nullable(r2) case SEQ(r1, r2) => nullable(r1) && nullable(r2) case STAR(_) => true case RECD(_, r1) => nullable(r1) } //> nullable: (r: POSIX.PosixAlgo.Rexp)Boolean def der(c: Char, r: Rexp): Rexp = r match { case NULL => NULL case EMPTY => NULL case CHAR(d) => if (c == d) EMPTY else NULL 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)) case RECD(_, r1) => der(c, r1) } //> der: (c: Char, r: POSIX.PosixAlgo.Rexp)POSIX.PosixAlgo.Rexp}