--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/progs/re-sulzmann.scala Wed Aug 07 17:31:42 2013 +0100
@@ -0,0 +1,164 @@
+import scala.language.implicitConversions
+import scala.language.reflectiveCalls
+
+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
+
+abstract class Pat
+
+case class VAR(x: String, w: String, r: Rexp) extends Pat
+case class GRP(x: String, w: String, p: Pat) extends Pat
+case class PSEQ(p1: Pat, p2: Pat) extends Pat
+case class PALT(p1: Pat, p2: Pat) extends Pat
+case class PSTAR(p: Pat) extends Pat
+
+object VAR { def apply(x: String, r: Rexp) : VAR = VAR(x, "", r) }
+object GRP { def apply(x: String, p: Pat) : GRP = GRP(x, "", p) }
+
+
+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
+}
+
+// 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))
+}
+
+def down(p: Pat) : Rexp = p match {
+ case VAR(x: String, w: String, r: Rexp) => r
+ case GRP(x: String, w: String, p: Pat) => down(p)
+ case PSEQ(p1: Pat, p2: Pat) => SEQ(down(p1), down(p2))
+ case PALT(p1: Pat, p2: Pat) => ALT(down(p1), down(p2))
+ case PSTAR(p: Pat) => STAR(down(p))
+}
+
+def empty(p: Pat) : Pat = p match {
+ case VAR(x: String, w: String, r: Rexp) =>
+ if (nullable(r)) VAR(x, w, EMPTY)
+ else VAR(x, w, NULL)
+ case GRP(x: String, w: String, p: Pat) => GRP(x, w, empty(p))
+ case PSEQ(p1: Pat, p2: Pat) => PSEQ(empty(p1), empty(p2))
+ case PALT(p1: Pat, p2: Pat) => PALT(empty(p1), empty(p2))
+ case PSTAR(p: Pat) => PSTAR(empty(p))
+}
+
+def patder(c: Char, p: Pat) : Pat = p match {
+ case VAR(x: String, w: String, r: Rexp) => VAR(x, w + c, der(c, r))
+ case GRP(x: String, w: String, p: Pat) => GRP(x, w + c, patder(c, p))
+ case PSEQ(p1: Pat, p2: Pat) =>
+ if (nullable(down(p1))) PALT(PSEQ(patder(c, p1), p2), PSEQ(empty(p1), patder(c, p2)))
+ else PSEQ(patder(c, p1), p2)
+ case PALT(p1: Pat, p2: Pat) => PALT(patder(c, p1), patder(c, p2))
+ case PSTAR(p: Pat) => PSEQ(patder(c, p), PSTAR(p))
+}
+
+def patders (s: List[Char], p: Pat) : Pat = s match {
+ case Nil => p
+ case c::s => patders(s, patder(c, p))
+}
+
+type Env = Set[List[(String, String)]]
+
+def special(p: Pat, env: Env) : Env =
+ if (env == Set() && nullable(down(p))) Set(Nil) else env
+
+
+def env(p: Pat) : Env = p match {
+ case VAR(x: String, w: String, r: Rexp) =>
+ if (nullable(r)) Set(List((x, w))) else Set()
+ case GRP(x: String, w: String, p1: Pat) =>
+ special(p, for (e <- env(p1)) yield List((x, w)) ++ e)
+ case PSEQ(p1: Pat, p2: Pat) =>
+ special(p, for (e1 <- env(p1); e2 <- env(p2)) yield (e1 ++ e2))
+ case PALT(p1: Pat, p2: Pat) => special(p, env(p1) ++ env(p2))
+ case PSTAR(p1: Pat) => special(p, env(p1))
+}
+
+def matcher(p: Pat, s: String) = env(empty(patders(s.toList, p)))
+
+
+// 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)
+}
+
+implicit def PatOps(p: Pat) = new {
+ def | (q: Pat) = PALT(p, q)
+ def % = PSTAR(p)
+ def ~ (q: Pat) = PSEQ(p, q)
+}
+
+
+val p0 = VAR("x", "A")
+
+patders("A".toList, p0)
+matcher(p0, "A")
+
+val p1 = VAR("x", "A") | VAR("y", "A") | VAR("z", "B")
+
+patders("A".toList, p1)
+matcher(p1, "A")
+matcher(p1, "B")
+
+val p2 = VAR("x", "AB")
+matcher(p2, "AB")
+matcher(p2, "AA")
+
+val p3 = VAR("x", "A" ~ "B")
+matcher(p3, "AB")
+matcher(p3, "AA")
+
+val p4 = VAR("x", "A") ~ VAR("y", "B")
+matcher(p4, "AB")
+matcher(p4, "AA")
+
+val p5 = VAR("x", "A".%)
+matcher(p5, "A")
+matcher(p5, "AA")
+matcher(p5, "")
+matcher(p5, "AAA")
+
+val p6 = VAR("x", "A").%
+matcher(p6, "A")
+matcher(p6, "AA")
+matcher(p6, "")
+matcher(p6, "AAA")
+
+val p7 = (VAR("x", "A") | VAR("y", "AB") | VAR("z", "B")).%
+matcher(p7, "AB")