--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/progs/scala/re2.scala Tue Oct 28 15:36:14 2014 +0000
@@ -0,0 +1,172 @@
+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(v: Val) extends Val
+case class Right(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(v) => flatten(v)
+ case Right(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(v) => env(v)
+ case Right(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 mkeps_all(r: Rexp) : Set[Val] = r match {
+ case EMPTY => Set(Void)
+ case ALT(r1, r2) => (nullable(r1), nullable(r2)) match {
+ case (true, true) => mkeps_all(r1).map(Left) ++ mkeps_all(r2).map(Right)
+ case (true, false) => mkeps_all(r1).map(Left)
+ case (false, true) => mkeps_all(r2).map(Right)
+ }
+ case SEQ(r1, r2) => for (v1 <- mkeps_all(r1);
+ v2 <- mkeps_all(r2)) yield Sequ(v1, v2)
+ case STAR(r) => Set(Stars(Nil), Stars(List(mkeps(r))))
+ case RECD(x, r) => for (v <- mkeps_all(r)) yield Rec(x, v)
+}
+
+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)) => Left(inj(r1, c, v1))
+ case (ALT(r1, r2), Right(v2)) => Right(inj(r2, c, v2))
+ case (CHAR(d), Void) => Chr(c)
+ case (RECD(x, r1), _) => Rec(x, inj(r1, c, v))
+}
+
+def inj_all(r: Rexp, c: Char, vs: Set[Val]) : Set[Val] =
+ for (v <- vs) yield inj(r, 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)
+
+// Examples
+val K: Rexp = "a" | "b"
+val I: Rexp = "ab" | "ba"
+
+val R0 = (K | I).%
+
+lexing(R0, "abab")
+
+val K: Rexp = ("key" $ "a" | "b")
+val I: Rexp = ("id" $ ("ab" | "ba"))
+
+val R0 = (K | I).%
+lexing(R0, "abaa")
+env(lexing(R0, "abaa"))
+
+val r0: Rexp = (K | I).%
+val r1 = der('a', r0)
+val r1_simp = simp2(r1)
+val r2 = der('b', r1)
+val r2_simp = simp2(r2)
+nullable(r2)
+val v2 = mkeps(r2)
+val v1 = inj(r1, 'b', v2)
+val v0 = inj(r0, 'a', v1)
+env(v0)
+env(lexing(r0, "abab"))
+