diff -r e66bd5c563eb -r b5b5583a3a08 progs/re-sulzmann.scala --- a/progs/re-sulzmann.scala Mon Jul 27 11:02:48 2020 +0100 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,164 +0,0 @@ -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") -