diff -r 6a43ea9305ba -r 1fe44fb6d0a4 progs/scala/re2.scala --- a/progs/scala/re2.scala Sat Mar 19 23:27:29 2016 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,157 +0,0 @@ -import scala.language.implicitConversions -import scala.language.reflectiveCalls -import scala.annotation.tailrec - -abstract class Rexp -case object ZERO extends Rexp -case object ONE 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 Empty 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 => ONE - 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 ZERO => 1 - case ONE => 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 ZERO => false - case ONE => 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 ZERO => ZERO - case ONE => ZERO - case CHAR(d) => if (c == d) ONE else ZERO - 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 Empty => "" - 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 Empty => 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 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), Empty) => 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") - 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")) -