--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/Attic/re-sulzmann-partial.scala	Thu Jul 30 13:50:54 2020 +0100
@@ -0,0 +1,136 @@
+import scala.language.implicitConversions
+import scala.language.reflectiveCalls
+
+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 
+
+abstract class Pat
+
+case class VAR(x: String, r: Rexp) extends Pat
+case class GRP(x: String, p: Pat) extends Pat
+case class PSEQ(p1: Pat, p2: Pat) extends Pat
+case class PALT(p1: Pat, p2: Pat) extends Pat
+case class PSTAR(p: Pat) extends Pat
+
+
+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
+}
+
+def down (p: Pat) : Rexp = p match {
+  case VAR(x: String, w: String, r: Rexp) => r
+  case GRP(x: String, w: String, p: Pat) => down(p)
+  case PSEQ(p1: Pat, p2: Pat) => SEQ(down(p1), down(p2))
+  case PALT(p1: Pat, p2: Pat) => ALT(down(p1), down(p2))
+  case PSTAR(p: Pat) => STAR(down(p))
+}
+
+def patnullable (p: Pat) : Boolean = p match {
+  case PVar(_, r) => nullable(r)
+  case PSEQ(p1, p2) => patnullable(p1) && patnullable(p2)
+  case PCHOICE(p1, p2) => patnullable(p1) || patnullable(p2)
+  case PSTAR(p) => true
+  case PatVar(_, p) => patnullable(p)
+}
+
+//type Env = Set[List[(String, String)]]
+type Env = Map[Int, String]
+
+def update(n: Int, c: Char) (env: Env) = 
+  env + (n -> (env.getOrElse(n, "") + c.toString))
+
+def pderivPat (p: Pat, c: Char) : Set[(Pat, Env => Env)] = p match {
+  case PVar(n: Int, r: Rexp) => {
+    val pds = pderiv(r, c)
+    if (pds.isEmpty) Set()
+    else Set((PVar(n, toRexp(pds.toList)), update(n, c)))
+  }
+  case PSEQ(p1: Pat, p2: Pat) => {
+    val pats : Set[(Pat, Env => Env)] = 
+      for ((p, f) <- pderivPat(p1, c)) yield (PSEQ(p, p2), f)
+    if (nullable(strip(p1))) pats ++ pderivPat(p2, c)  
+    else pats
+  }
+  case PCHOICE(p1: Pat, p2: Pat) => pderivPat(p1, c) ++ pderivPat(p2, c)
+  case PSTAR(p1: Pat) => 
+    for ((p, f) <- pderivPat(p1, c)) yield (PSEQ(p, PSTAR(p1)), f)
+  case PatVar(n: Int, p1: Pat) => 
+    for ((p, f) <- pderivPat(p1, c)) yield (PatVar(n, p), f compose (update (n, c)))
+}
+
+
+val p2 = PSEQ(PVar(1, STAR("A")), PVar(2, STAR("A")))
+pderivPat(p2, 'A').mkString("\n")
+
+
+def greedy_aux(env: Set[(Pat, Env)], w: List[Char]) : Set[Env] = w match {
+  case Nil => 
+    for ((p, e) <- env if patnullable(p)) yield e
+  case c::cs => {
+    val env2 = for ((p, e) <- env; (p1, f) <- pderivPat(p, c)) yield (p1, f(e))
+    greedy_aux(env2, cs)
+  }
+}
+
+def greedy(p: Pat, w: String) = {
+  val res = greedy_aux(Set((p, Map())), w.toList)
+  if (res.isEmpty) None else Some(res)
+}
+
+// some convenience for typing in regular expressions
+def charlist2rexp (s : List[Char]) : Rexp = s match {
+  case Nil => EMPTY
+  case c::Nil => CHAR(c)
+  case c::s => SEQ(CHAR(c), charlist2rexp(s))
+}
+implicit def string2rexp (s : String) : Rexp = charlist2rexp(s.toList)
+
+implicit def RexpOps (r: Rexp) = new {
+  def | (s: Rexp) = ALT(r, s)
+  def % = STAR(r)
+  def ~ (s: Rexp) = SEQ(r, s)
+}
+
+implicit def stringOps (s: String) = new {
+  def | (r: Rexp) = ALT(s, r)
+  def | (r: String) = ALT(s, r)
+  def % = STAR(s)
+  def ~ (r: Rexp) = SEQ(s, r)
+  def ~ (r: String) = SEQ(s, r)
+}
+
+implicit def PatOps (p: Pat) = new {
+  def | (q: Pat) = PALT(p, q)
+  def % = PSTAR(p)
+  def ~ (q: Pat) = PSEQ(p, q)
+}
+
+val p3 = PSTAR(PSEQ(PVar(1, "A"), PVar(2, "B")))
+
+greedy2(Set((p3, Map())), "ABAB".toList)
+
+
+val p4 = PVar(1, "A")
+greedy2(Set((p4, Map())), "A".toList)
+
+val p5 = PSEQ(PVar(1, "A"), PVar(1, "B"))
+greedy2(Set((p5, Map())), "AB".toList)
+
+val res = pderivPat(p5, 'A')
+for ((_, f) <- res) yield f(Map())
+
+
+val p6 = PatVar(4,PSTAR(PCHOICE(PCHOICE(PVar(1, "A"), PVar(2, "AB")), PVar(3, "B"))))
+
+greedy(p6, "ABA")