diff -r 1fe44fb6d0a4 -r 4e00dd2398ac progs/scala/re-bit.scala
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/progs/scala/re-bit.scala	Fri Apr 01 16:29:33 2016 +0100
@@ -0,0 +1,213 @@
+import scala.language.implicitConversions    
+import scala.language.reflectiveCalls
+import scala.annotation.tailrec   
+
+abstract class Rexp 
+case object ZERO extends Rexp
+case object ONE 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 ARexp 
+case object AZERO extends ARexp
+case class AONE(bs: List[Boolean]) extends ARexp
+case class ACHAR(bs: List[Boolean], c: Char) extends ARexp
+case class AALT(bs: List[Boolean], r1: ARexp, r2: ARexp) extends ARexp 
+case class ASEQ(bs: List[Boolean], r1: ARexp, r2: ARexp) extends ARexp 
+case class ASTAR(bs: List[Boolean], r: ARexp) extends ARexp 
+
+abstract class Val
+case object Empty 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
+   
+// some convenience for typing in regular expressions
+def charlist2rexp(s : List[Char]): Rexp = s match {
+  case Nil => ONE
+  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)
+}
+
+// translation into ARexps
+def fuse(bs: List[Boolean], r: ARexp) : ARexp = r match {
+  case AZERO => AZERO
+  case AONE(cs) => AONE(bs ++ cs)
+  case ACHAR(cs, c) => ACHAR(bs ++ cs, c)
+  case AALT(cs, r1, r2) => AALT(bs ++ cs, r1, r2)
+  case ASEQ(cs, r1, r2) => ASEQ(bs ++ cs, r1, r2)
+  case ASTAR(cs, r) => ASTAR(bs ++ cs, r)
+}
+
+def internalise(r: Rexp) : ARexp = r match {
+  case ZERO => AZERO
+  case ONE => AONE(Nil)
+  case CHAR(c) => ACHAR(Nil, c)
+  case ALT(r1, r2) => AALT(Nil, fuse(List(false), internalise(r1)), fuse(List(true), internalise(r2)))
+  case SEQ(r1, r2) => ASEQ(Nil, internalise(r1), internalise(r2))
+  case STAR(r) => ASTAR(Nil, internalise(r))
+}
+
+internalise(("a" | "ab") ~ ("b" | ""))
+
+
+def decode_aux(r: Rexp, bs: List[Boolean]) : (Val, List[Boolean]) = (r, bs) match {
+  case (ONE, bs) => (Empty, bs)
+  case (CHAR(c), bs) => (Chr(c), bs)
+  case (ALT(r1, r2), false::bs) => {
+    val (v, bs1) = decode_aux(r1, bs)
+    (Left(v), bs1)
+  }
+  case (ALT(r1, r2), true::bs) => {
+    val (v, bs1) = decode_aux(r2, bs)
+    (Right(v), bs1)
+  }
+  case (SEQ(r1, r2), bs) => {
+    val (v1, bs1) = decode_aux(r1, bs)
+    val (v2, bs2) = decode_aux(r2, bs1)
+    (Sequ(v1, v2), bs2)
+  }
+  case (STAR(r), false::bs) => {
+    val (v, bs1) = decode_aux(r, bs)
+    val (Stars(vs), bs2) = decode_aux(STAR(r), bs1)
+    (Stars(v::vs), bs2)
+  }
+  case (STAR(r), true::bs) => (Stars(Nil), bs)
+}
+
+def decode(r: Rexp, bs: List[Boolean]) = decode_aux(r, bs) match {
+  case (v, Nil) => v
+  case _ => throw new Exception("Not decodable")
+}
+
+// nullable function: tests whether the aregular 
+// expression can recognise the empty string
+def nullable (r: ARexp) : Boolean = r match {
+  case AZERO => false
+  case AONE(_) => true
+  case ACHAR(_,_) => false
+  case AALT(_, r1, r2) => nullable(r1) || nullable(r2)
+  case ASEQ(_, r1, r2) => nullable(r1) && nullable(r2)
+  case ASTAR(_, _) => true
+}
+
+def mkepsBC(r: ARexp) : List[Boolean] = r match {
+  case AONE(bs) => bs
+  case AALT(bs, r1, r2) => 
+    if (nullable(r1)) bs ++ mkepsBC(r1) else bs ++ mkepsBC(r2)
+  case ASEQ(bs, r1, r2) => bs ++ mkepsBC(r1) ++ mkepsBC(r2)
+  case ASTAR(bs, r) => bs ++ List(true)
+}
+
+// derivative of a regular expression w.r.t. a character
+def der (c: Char, r: ARexp) : ARexp = r match {
+  case AZERO => AZERO
+  case AONE(_) => AZERO
+  case ACHAR(bs, d) => if (c == d) AONE(bs) else AZERO
+  case AALT(bs, r1, r2) => AALT(bs, der(c, r1), der(c, r2))
+  case ASEQ(bs, r1, r2) => 
+    if (nullable(r1)) AALT(bs, ASEQ(Nil, der(c, r1), r2), fuse(mkepsBC(r1), der(c, r2)))
+    else ASEQ(bs, der(c, r1), r2)
+  case ASTAR(bs, r) => ASEQ(bs, fuse(List(false), der(c, r)), ASTAR(Nil, r))
+}
+
+// derivative w.r.t. a string (iterates der)
+@tailrec
+def ders (s: List[Char], r: ARexp) : ARexp = s match {
+  case Nil => r
+  case c::s => ders(s, der(c, r))
+}
+
+// main unsimplified lexing function (produces a value)
+def lex(r: ARexp, s: List[Char]) : List[Boolean] = s match {
+  case Nil => if (nullable(r)) mkepsBC(r) else throw new Exception("Not matched")
+  case c::cs => lex(der(c, r), cs)
+}
+
+def lexing(r: Rexp, s: String) : Val = decode(r, lex(internalise(r), s.toList))
+
+// Some Tests
+//============
+
+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)
+}
+
+
+
+
+val r0 = ("a" | "ab") ~ ("b" | "")
+println(lexing(r0, "ab"))
+
+val r1 = ("a" | "ab") ~ ("bcd" | "cd")
+println(lexing(r1, "abcd"))
+
+println(lexing((("" | "a") ~ ("ab" | "b")), "ab"))
+println(lexing((("" | "a") ~ ("b" | "ab")), "ab"))
+println(lexing((("" | "a") ~ ("c" | "ab")), "ab"))
+
+
+
+// Two Simple Tests for the While Language
+//========================================
+
+// Lexing Rules 
+
+def PLUS(r: Rexp) = r ~ r.%
+val SYM = "a" | "b" | "c" | "d" | "e" | "f" | "g" | "h" | "i" | "j" | "k" | "l" | "m" | "n" | "o" | "p" | "q" | "r" | "s" | "t" | "u" | "v" | "w" | "x" | "y" | "z"
+val DIGIT = "0" | "1" | "2" | "3" | "4" | "5" | "6" | "7" | "8" | "9"
+val ID = SYM ~ (SYM | DIGIT).% 
+val NUM = PLUS(DIGIT)
+val KEYWORD : Rexp = "skip" | "while" | "do" | "if" | "then" | "else" | "read" | "write" | "true" | "false"
+val SEMI: Rexp = ";"
+val OP: Rexp = ":=" | "==" | "-" | "+" | "*" | "!=" | "<" | ">" | "<=" | ">=" | "%" | "/"
+val WHITESPACE = PLUS(" " | "\n" | "\t")
+val RPAREN: Rexp = ")"
+val LPAREN: Rexp = "("
+val BEGIN: Rexp = "{"
+val END: Rexp = "}"
+val STRING: Rexp = "\"" ~ SYM.% ~ "\""
+
+val WHILE_REGS = (KEYWORD | 
+                  ID | 
+                  OP | 
+                  NUM | 
+                  SEMI | 
+                  LPAREN | RPAREN | 
+                  BEGIN | END | 
+                  WHITESPACE).%
+
+
+println("prog0 test")
+
+val prog0 = """read n"""
+println(lexing(WHILE_REGS, prog0))
+
+println("prog1 test")
+
+val prog1 = """read  n; write (n)"""
+println(lexing(WHILE_REGS, prog1))
+
+