diff -r e66bd5c563eb -r b5b5583a3a08 Attic/re0.scala
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/Attic/re0.scala	Thu Jul 30 13:50:54 2020 +0100
@@ -0,0 +1,119 @@
+import scala.annotation.tailrec
+import scala.language.implicitConversions
+
+abstract class Rexp
+
+case object NULL extends Rexp
+case object EMPTY extends Rexp
+case object ALLCHAR extends Rexp
+case class CHAR(c: Char) extends Rexp
+case class STR(s: String) 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 NOT(r: Rexp) extends Rexp
+case class REP(r: Rexp, n: Int) extends Rexp 
+
+// some convenience for typing in regular expressions
+implicit def string2rexp(s : String) : Rexp = STR(s)
+
+implicit def RexpOps(r: Rexp) : Rexp = new {
+  def | (s: Rexp) = ALT(r, s)
+  def % = STAR(r)
+  def %(n: Int) = REP(r, n) 
+  def %%(n: Int) = SEQ(REP(r, n), STAR(r)) 
+  def ? = ALT(EMPTY, r)
+  def unary_! = NOT(r)
+  def ~ (s: Rexp) = SEQ(r, s)
+}
+
+implicit def stringOps(s: String) : Rexp = new {
+  def | (r: Rexp) = ALT(s, r)
+  def | (r: String) = ALT(s, r)
+  def % = STAR(s)
+  def %(n: Int) = REP(s, n)
+  def %%(n: Int) = SEQ(REP(s, n), STAR(s)) 
+  def ? = ALT(EMPTY, s)
+  def unary_! = NOT(s)
+  def ~ (r: Rexp) = SEQ(s, r)
+  def ~ (r: String) = SEQ(s, r)
+}
+
+
+// nullable function: tests whether the regular 
+// expression can recognise the empty string
+
+def nullable (r: Rexp) : Boolean = r match {
+  case NULL => false
+  case EMPTY => true
+  case ALLCHAR => false
+  case CHAR(_) => false
+  case STR(s) => s.isEmpty
+  case ALT(r1, r2) => nullable(r1) || nullable(r2)
+  case SEQ(r1, r2) => nullable(r1) && nullable(r2)
+  case STAR(_) => true
+  case NOT(r) => !(nullable(r))
+  case REP(r, i) => if (i == 0) true else nullable(r)
+}
+
+// derivative of a regular expression w.r.t. a character
+def der (c: Char, r: Rexp) : Rexp = r match {
+  case NULL => NULL
+  case EMPTY => NULL
+  case ALLCHAR => EMPTY
+  case CHAR(d) => if (c == d) EMPTY else NULL
+  case STR(s) => if (s.isEmpty || s.head != c) NULL else STR(s.tail)
+  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 NOT(r) => NOT(der (c, r))
+  case REP(r, i) => 
+    if (i == 0) NULL else SEQ(der(c, r), REP(r, i - 1))
+}
+
+
+// derivative w.r.t. a string (iterates der)
+@tailrec
+def ders (s: List[Char], r: Rexp) : Rexp = s match {
+  case Nil => r
+  case c::s => ders(s, der(c, r))
+}
+
+// main matcher function
+def matcher(r: Rexp, s: String) : Boolean = nullable(ders(s.toList, r))
+
+//examples
+val digit = "0" | "1" | "2" | "3" | "4" | "5" | "6" | "7" | "8" | "9"
+val int = ("+" | "-").? ~ digit.%%(1)
+val real = ("+" | "-").? ~ digit.%%(1) ~ ("." ~ digit.%%(1)).? ~ (("e" | "E") ~ ("+" | "-").? ~ digit.%%(1)).?
+
+val ints = List("0", "-4534", "+049", "99")
+val reals = List("0.9", "-12.8", "+91.0", "9e12", "+9.21E-12", "-512E+01")
+val errs = List("", "-", "+", "+-1", "-+2", "2-")
+
+ints.map(s => matcher(int, s))
+reals.map(s => matcher(int, s))
+errs.map(s => matcher(int, s))
+
+ints.map(s => matcher(real, s))
+reals.map(s => matcher(real, s))
+errs.map(s => matcher(real, s))
+
+
+
+def RTEST(n: Int) = ("a".? %(n)) ~ ("a" %(n))
+
+def time_needed[T](i: Int, code: => T) = {
+  val start = System.nanoTime()
+  for (j <- 1 to i) code
+  val end = System.nanoTime()
+  (end - start)/(i * 1.0e9)
+}
+
+for (i <- 1 to 12000 by 500) {
+  println(i + ": " + "%.5f".format(time_needed(1, matcher(RTEST(i), "a" * i))))
+}
+
+