--- a/progs/scala/re.scala	Sun Oct 26 16:42:28 2014 +0000
+++ b/progs/scala/re.scala	Tue Oct 28 15:36:14 2014 +0000
@@ -54,6 +54,7 @@
   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 {
@@ -107,7 +108,6 @@
   case Rec(x, v) => (x, flatten(v))::env(v)
 }
 
-
 def mkeps(r: Rexp) : Val = r match {
   case EMPTY => Void
   case ALT(r1, r2) => 
@@ -117,6 +117,7 @@
   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)
@@ -124,11 +125,10 @@
   case (SEQ(r1, r2), Right(v2)) => Sequ(mkeps(r1), inj(r2, c, v2))
   case (ALT(r1, r2), Left(v1)) => Left(inj(r1, c, v1))
   case (ALT(r1, r2), Right(v2)) => Right(inj(r2, c, v2))
-  case (CHAR(d), Void) => Chr(d) 
+  case (CHAR(d), Void) => Chr(c) 
   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")
@@ -138,11 +138,66 @@
 def lexing(r: Rexp, s: String) : Val = lex(r, s.toList)
 
 
-val r = (("1" $ "a") | (("2" $ "b") | ("3" $ "ab"))).% 
-env(lexing(r, "ba"))
+
+// some "rectification" functions for simplification
+def F_ID(v: Val): Val = v
+def F_RIGHT(f: Val => Val) = (v:Val) => Right(f(v))
+def F_LEFT(f: Val => Val) = (v:Val) => Left(f(v))
+def F_ALT(f1: Val => Val, f2: Val => Val) = (v:Val) => v match {
+  case Right(v) => Right(f2(v))
+  case Left(v) => Left(f1(v))
+}
+def F_SEQ(f1: Val => Val, f2: Val => Val) = (v:Val) => v match {
+  case Sequ(v1, v2) => Sequ(f1(v1), f2(v2))
+}
+def F_SEQ_Void1(f1: Val => Val, f2: Val => Val) = (v:Val) => Sequ(f1(Void), f2(v))
+def F_SEQ_Void2(f1: Val => Val, f2: Val => Val) = (v:Val) => Sequ(f1(v), f2(Void))
+def F_RECD(f: Val => Val) = (v:Val) => v match {
+  case Rec(x, v) => Rec(x, f(v))
+}
+def F_ERROR(v: Val): Val = throw new Exception("error")
 
-val r = "a" | "b"
-lexing(r,"a")
+// simplification of regular expressions returning also an
+// rectification function; no simplification under STAR 
+def simp(r: Rexp): (Rexp, Val => Val) = r match {
+  case ALT(r1, r2) => {
+    val (r1s, f1s) = simp(r1)
+    val (r2s, f2s) = simp(r2)
+    (r1s, r2s) match {
+      case (NULL, _) => (r2s, F_RIGHT(f2s))
+      case (_, NULL) => (r1s, F_LEFT(f1s))
+      case _ => if (r1s == r2s) (r1s, F_LEFT(f1s))
+                else (ALT (r1s, r2s), F_ALT(f1s, f2s)) 
+    }
+  }
+  case SEQ(r1, r2) => {
+    val (r1s, f1s) = simp(r1)
+    val (r2s, f2s) = simp(r2)
+    (r1s, r2s) match {
+      case (NULL, _) => (NULL, F_ERROR)
+      case (_, NULL) => (NULL, F_ERROR)
+      case (EMPTY, _) => (r2s, F_SEQ_Void1(f1s, f2s))
+      case (_, EMPTY) => (r1s, F_SEQ_Void2(f1s, f2s))
+      case _ => (SEQ(r1s,r2s), F_SEQ(f1s, f2s))
+    }
+  }
+  case RECD(x, r1) => {
+    val (r1s, f1s) = simp(r1)
+    (RECD(x, r1s), F_RECD(f1s))
+  }
+  case r => (r, F_ID)
+}
+
+def lex_simp(r: Rexp, s: List[Char]) : Val = s match {
+  case Nil => if (nullable(r)) mkeps(r) else throw new Exception("Not matched")
+  case c::cs => {
+    val (r_simp, f_simp) = simp(der(c, r))
+    inj(r, c, f_simp(lex_simp(r_simp, cs)))
+  }
+}
+
+def lexing_simp(r: Rexp, s: String) : Val = lex_simp(r, s.toList)
+
 
 // Lexing Rules for a Small While Language
 
@@ -193,12 +248,12 @@
 }
 
 val prog0 = """read n"""
-env (lexing_simp(WHILE_REGS, prog0))
+env (lexing(WHILE_REGS, prog0))
 
 println("Next test")
 /*
 val prog1 = """read  n; write (n)"""
-env (lexing_simp(WHILE_REGS, prog1))
+env (lexing(WHILE_REGS, prog1))
 
 val prog2 = """
 i := 2;
@@ -222,6 +277,6 @@
 
 for (i <- 1 to 100 by 10) {
   print(i.toString + ":  ")
-  time(lexing_simp(WHILE_REGS, prog2 * i))
+  time(lexing(WHILE_REGS, prog2 * i))
 }
 */