diff -r 2bc119fc8657 -r 94824659f6d7 progs/scala/re.scala
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/progs/scala/re.scala	Fri Aug 15 14:10:58 2014 +0100
@@ -0,0 +1,231 @@
+import scala.language.implicitConversions    
+import scala.language.reflectiveCalls
+import scala.annotation.tailrec   
+
+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(n: Int, v: Val) extends Val
+case class Right(n: Int, v: Val) extends Val
+case class Stars(vs: List[Val]) extends Val
+case class Rec(x: String, v: Val) extends Val
+   
+// 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)
+  def $ (r: Rexp) = RECD(s, r)
+}
+
+// size of a regular expressions - for testing purposes 
+def size(r: Rexp) : Int = r match {
+  case NULL => 1
+  case EMPTY => 1
+  case CHAR(_) => 1
+  case ALT(r1, r2) => 1 + size(r1) + size(r2)
+  case SEQ(r1, r2) => 1 + size(r1) + size(r2)
+  case STAR(r) => 1 + size(r)
+  case RECD(_, r) => 1 + size(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 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)
+}
+
+// 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 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)
+}
+
+// derivative w.r.t. a string (iterates der)
+def ders (s: List[Char], r: Rexp) : Rexp = s match {
+  case Nil => r
+  case c::s => ders(s, der(c, r))
+}
+
+// extracts a string from value
+def flatten(v: Val) : String = v match {
+  case Void => ""
+  case Chr(c) => c.toString
+  case Left(n, v) => flatten(v)
+  case Right(n, v) => flatten(v)
+  case Sequ(v1, v2) => flatten(v1) + flatten(v2)
+  case Stars(vs) => vs.map(flatten).mkString
+  case Rec(_, v) => flatten(v)
+}
+
+// extracts an environment from a value
+def env(v: Val) : List[(String, String)] = v match {
+  case Void => Nil
+  case Chr(c) => Nil
+  case Left(n, v) => env(v)
+  case Right(n, v) => env(v)
+  case Sequ(v1, v2) => env(v1) ::: env(v2)
+  case Stars(vs) => vs.flatMap(env)
+  case Rec(x, v) => (x, flatten(v))::env(v)
+}
+
+def left_inc(v: Val) = v match {
+  case Left(v, n) => Left(v, n + 1)
+  case v => Left(v, 1)
+}
+
+def right_inc(v: Val) = v match {
+  case Right(v, n) => Right(v, n + 1)
+  case v => Right(v, 1)
+}
+
+def mkeps(r: Rexp) : Val = r match {
+  case EMPTY => Void
+  case ALT(r1, r2) => 
+    if (nullable(r1)) left_inc(mkeps(r1)) else right_inc(mkeps(r2))
+  case SEQ(r1, r2) => Sequ(mkeps(r1), mkeps(r2))
+  case STAR(r) => Stars(Nil)
+  case RECD(x, r) => Rec(x, mkeps(r))
+}
+
+def inj(r: Rexp, c: Char, v: Val) : Val = (r, v) match {
+  case (STAR(r), Sequ(v1, Stars(vs))) => Stars(inj(r, c, v1)::vs)
+  case (SEQ(r1, r2), Sequ(v1, v2)) => Sequ(inj(r1, c, v1), v2)
+  case (SEQ(r1, r2), Left(Sequ(v1, v2))) => Sequ(inj(r1, c, v1), v2)
+  case (SEQ(r1, r2), Right(v2)) => Sequ(mkeps(r1), inj(r2, c, v2))
+  case (ALT(r1, r2), Left(v1), 1) => Left(inj(r1, c, v1), 1)
+  case (ALT(r1, r2), Left(v1), n) => inc_left(inj(r1, c, Left(v1, n - 1)))
+  case (ALT(r1, r2), Right(v2)) => Right(inj(r2, c, v2))
+  case (CHAR(d), Void) => Chr(d) 
+  case (RECD(x, r1), _) => Rec(x, inj(r1, c, v))
+}
+
+
+// main lexing function (produces a value)
+def lex(r: Rexp, s: List[Char]) : Val = s match {
+  case Nil => if (nullable(r)) mkeps(r) else throw new Exception("Not matched")
+  case c::cs => inj(r, c, lex(der(c, r), cs))
+}
+
+def lexing(r: Rexp, s: String) : Val = lex(r, s.toList)
+
+
+// Lexing Rules for a Small While Language
+
+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 WHILE_REGS = (("k" $ KEYWORD) | 
+                  ("i" $ ID) | 
+                  ("o" $ OP) | 
+                  ("n" $ NUM) | 
+                  ("s" $ SEMI) | 
+                  ("p" $ (LPAREN | RPAREN)) | 
+                  ("b" $ (BEGIN | END)) | 
+                  ("w" $ WHITESPACE)).%
+*/
+
+val WHILE_REGS = (KEYWORD | 
+                  ID | 
+                  OP | 
+                  NUM | 
+                  SEMI | 
+                  LPAREN | RPAREN | 
+                  BEGIN | END | 
+                  WHITESPACE).%
+
+
+// Some Tests
+//============
+
+def time[T](code: => T) = {
+  val start = System.nanoTime()
+  val result = code
+  val end = System.nanoTime()
+  println((end - start)/1.0e9)
+  result
+}
+
+val prog0 = """read n"""
+env (lexing_simp(WHILE_REGS, prog0))
+
+println("Next test")
+/*
+val prog1 = """read  n; write (n)"""
+env (lexing_simp(WHILE_REGS, prog1))
+
+val prog2 = """
+i := 2;
+max := 100;
+while i < max do {
+  isprime := 1;
+  j := 2;
+  while (j * j) <= i + 1  do {
+    if i % j == 0 then isprime := 0  else skip;
+    j := j + 1
+  };
+  if isprime == 1 then write i else skip;
+  i := i + 1
+}"""
+lexing_acc(WHILE_REGS, prog2)
+
+for (i <- 1 to 228 by 1) {
+  print(i.toString + ":  ")
+  time(lexing_acc(WHILE_REGS, prog2 * i))
+}
+
+for (i <- 1 to 100 by 10) {
+  print(i.toString + ":  ")
+  time(lexing_simp(WHILE_REGS, prog2 * i))
+}
+*/