--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/lex_blex_Frankensteined.scala Wed Mar 13 13:14:38 2019 +0000
@@ -0,0 +1,880 @@
+package RexpRelated
+import scala.language.implicitConversions
+import scala.language.reflectiveCalls
+import scala.annotation.tailrec
+import scala.util.Try
+
+abstract class Bit
+case object Z extends Bit
+case object S extends Bit
+case class C(c: Char) extends Bit
+
+
+abstract class Rexp
+case object ZERO extends Rexp
+case object ONE extends Rexp
+case class CHAR(c: Char) extends Rexp
+case class ALTS(rs: List[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
+
+
+
+object Rexp{
+ type Bits = List[Bit]
+ // abbreviations
+ type Mon = (Char, Rexp)
+ type Lin = Set[Mon]
+ def ALT(r1: Rexp, r2: Rexp) = ALTS(List(r1, r2))
+ def PLUS(r: Rexp) = SEQ(r, STAR(r))
+ def AALT(bs: Bits, r1: ARexp, r2: ARexp) = AALTS(bs, List(r1, r2))
+
+
+ def distinctBy[B, C](xs: List[B], f: B => C, acc: List[C] = Nil): List[B] = xs match {
+ case Nil => Nil
+ case (x::xs) => {
+ val res = f(x)
+ if (acc.contains(res)) distinctBy(xs, f, acc)
+ else x::distinctBy(xs, f, res::acc)
+ }
+ }
+ // 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)
+ }
+
+ // translation into ARexps
+ def fuse(bs: Bits, r: ARexp) : ARexp = r match {
+ case AZERO => AZERO
+ case AONE(cs) => AONE(bs ++ cs)
+ case ACHAR(cs, f) => ACHAR(bs ++ cs, f)
+ case AALTS(cs, rs) => AALTS(bs ++ cs, rs)
+ case ASEQ(cs, r1, r2) => ASEQ(bs ++ cs, r1, r2)
+ case ASTAR(cs, r) => ASTAR(bs ++ cs, r)
+ }
+
+ def internalise(r: Rexp) : ARexp = r match {
+ case ZERO => AZERO
+ case ONE => AONE(Nil)
+ case CHAR(c) => ACHAR(Nil, c)
+ case ALTS(List(r1, r2)) =>
+ AALTS(Nil, List(fuse(List(Z), internalise(r1)), fuse(List(S), internalise(r2))))
+ case ALTS(r1::rs) => {
+ val AALTS(Nil, rs2) = internalise(ALTS(rs))
+ AALTS(Nil, fuse(List(Z), internalise(r1)) :: rs2.map(fuse(List(S), _)))
+ }
+ case SEQ(r1, r2) => ASEQ(Nil, internalise(r1), internalise(r2))
+ case STAR(r) => ASTAR(Nil, internalise(r))
+ case RECD(x, r) => internalise(r)
+ }
+
+ internalise(("a" | "ab") ~ ("b" | ""))
+
+ def decode_aux(r: Rexp, bs: Bits) : (Val, Bits) = (r, bs) match {
+ case (ONE, bs) => (Empty, bs)
+ case (PRED(f), C(c)::bs) => (Chr(c), bs)
+ case (ALTS(r::Nil), bs) => decode_aux(r, bs)//this case seems tailor made for those who want to simplify the regex before der or simp
+ case (ALTS(rs), bs) => bs match {
+ case Z::bs1 => {
+ val (v, bs2) = decode_aux(rs.head, bs1)
+ (Left(v), bs2)
+ }
+ case S::bs1 => {
+ val (v, bs2) = decode_aux(ALTS(rs.tail), bs1)
+ (Right(v), bs2)
+ }
+ }
+ case (SEQ(r1, r2), bs) => {
+ val (v1, bs1) = decode_aux(r1, bs)
+ val (v2, bs2) = decode_aux(r2, bs1)
+ (Sequ(v1, v2), bs2)
+ }
+ case (STAR(r1), S::bs) => {
+ val (v, bs1) = decode_aux(r1, bs)
+ //println(v)
+ val (Stars(vs), bs2) = decode_aux(STAR(r1), bs1)
+ (Stars(v::vs), bs2)
+ }
+ case (STAR(_), Z::bs) => (Stars(Nil), bs)
+ case (RECD(x, r1), bs) => {
+ val (v, bs1) = decode_aux(r1, bs)
+ (Rec(x, v), bs1)
+ }
+ }
+
+ def decode(r: Rexp, bs: Bits) = decode_aux(r, bs) match {
+ case (v, Nil) => v
+ case _ => throw new Exception("Not decodable")
+ }
+
+
+ //erase function: extracts the regx from Aregex
+ def erase(r:ARexp): Rexp = r match{
+ case AZERO => ZERO
+ case AONE(_) => ONE
+ case ACHAR(bs, f) => CHAR(f)
+ case AALTS(bs, rs) => ALTS(rs.map(erase(_)))
+ case ASEQ(bs, r1, r2) => SEQ (erase(r1), erase(r2))
+ case ASTAR(cs, r)=> STAR(erase(r))
+ }
+
+ //--------------------------------------------------------------------------------------------------------START OF NON-BITCODE PART
+ // 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 ALTS(rs) => rs.exists(nullable)
+ case SEQ(r1, r2) => nullable(r1) && nullable(r2)
+ case STAR(_) => true
+ case RECD(_, r) => nullable(r)
+ //case PLUS(r) => nullable(r)
+ }
+
+ // 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(f) => if (c == f) ONE else ZERO
+ case ALTS(List(r1, r2)) => ALTS(List(der(c, r1), der(c, r2)))
+ case SEQ(r1, r2) =>
+ if (nullable(r1)) ALTS(List(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)
+ //case PLUS(r) => SEQ(der(c, r), STAR(r))
+ }
+
+ 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)
+ }
+
+
+ // injection part
+ def mkeps(r: Rexp) : Val = r match {
+ case ONE => Empty
+ case ALTS(List(r1, r2)) =>
+ if (nullable(r1)) Left(mkeps(r1)) else Right(mkeps(r2))
+ case SEQ(r1, r2) => Sequ(mkeps(r1), mkeps(r2))
+ case STAR(r) => Stars(Nil)
+ case RECD(x, r) => Rec(x, mkeps(r))
+ //case PLUS(r) => Stars(List(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)
+ 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 (ALTS(List(r1, r2)), Left(v1)) => Left(inj(r1, c, v1))
+ case (ALTS(List(r1, r2)), Right(v2)) => Right(inj(r2, c, v2))
+ case (CHAR(_), Empty) => Chr(c)
+ case (RECD(x, r1), _) => Rec(x, inj(r1, c, v))
+ //case (PLUS(r), Sequ(v1, Stars(vs))) => Stars(inj(r, c, v1)::vs)
+ }
+ 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)
+
+ // 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_Empty1(f1: Val => Val, f2: Val => Val) =
+ (v:Val) => Sequ(f1(Empty), f2(v))
+ def F_SEQ_Empty2(f1: Val => Val, f2: Val => Val) =
+ (v:Val) => Sequ(f1(v), f2(Empty))
+ 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")
+
+ // simplification of regular expressions returning also an
+ // rectification function; no simplification under STAR
+ def simp(r: Rexp): (Rexp, Val => Val) = r match {
+ case ALTS(List(r1, r2)) => {
+ val (r1s, f1s) = simp(r1)
+ val (r2s, f2s) = simp(r2)
+ (r1s, r2s) match {
+ case (ZERO, _) => (r2s, F_RIGHT(f2s))
+ case (_, ZERO) => (r1s, F_LEFT(f1s))
+ case _ => if (r1s == r2s) (r1s, F_LEFT(f1s))
+ else (ALTS(List(r1s, r2s)), F_ALT(f1s, f2s))
+ }
+ }
+ case SEQ(r1, r2) => {
+ val (r1s, f1s) = simp(r1)
+ val (r2s, f2s) = simp(r2)
+ (r1s, r2s) match {
+ case (ZERO, _) => (ZERO, F_ERROR)
+ case (_, ZERO) => (ZERO, F_ERROR)
+ case (ONE, _) => (r2s, F_SEQ_Empty1(f1s, f2s))
+ case (_, ONE) => (r1s, F_SEQ_Empty2(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)
+ }
+ /*
+ val each_simp_time = scala.collection.mutable.ArrayBuffer.empty[Long]
+ val each_simp_timeb = scala.collection.mutable.ArrayBuffer.empty[Long]
+ */
+ 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)
+
+ //println(lexing_simp(("a" | "ab") ~ ("b" | ""), "ab"))
+
+ // filters out all white spaces
+ def tokenise(r: Rexp, s: String) =
+ env(lexing_simp(r, s)).filterNot { _._1 == "w"}
+
+
+ //reads the string from a file
+ def fromFile(name: String) : String =
+ io.Source.fromFile(name).mkString
+
+ def tokenise_file(r: Rexp, name: String) =
+ tokenise(r, fromFile(name))
+
+ // Testing
+ //============
+
+ def time[T](code: => T) = {
+ val start = System.nanoTime()
+ val result = code
+ val end = System.nanoTime()
+ println((end - start)/1.0e9)
+ result
+ }
+
+ //--------------------------------------------------------------------------------------------------------END OF NON-BITCODE PART
+
+ // bnullable function: tests whether the aregular
+ // expression can recognise the empty string
+ def bnullable (r: ARexp) : Boolean = r match {
+ case AZERO => false
+ case AONE(_) => true
+ case ACHAR(_,_) => false
+ case AALTS(_, rs) => rs.exists(bnullable)
+ case ASEQ(_, r1, r2) => bnullable(r1) && bnullable(r2)
+ case ASTAR(_, _) => true
+ }
+
+ def mkepsBC(r: ARexp) : Bits = r match {
+ case AONE(bs) => bs
+ case AALTS(bs, rs) => {
+ val n = rs.indexWhere(bnullable)
+ bs ++ mkepsBC(rs(n))
+ }
+ case ASEQ(bs, r1, r2) => bs ++ mkepsBC(r1) ++ mkepsBC(r2)
+ case ASTAR(bs, r) => bs ++ List(Z)
+ }
+
+ // derivative of a regular expression w.r.t. a character
+ def bder(c: Char, r: ARexp) : ARexp = r match {
+ case AZERO => AZERO
+ case AONE(_) => AZERO
+ case ACHAR(bs, f) => if (c == f) AONE(bs:::List(C(c))) else AZERO
+ case AALTS(bs, rs) => AALTS(bs, rs.map(bder(c, _)))
+ case ASEQ(bs, r1, r2) =>
+ if (bnullable(r1)) AALT(bs, ASEQ(Nil, bder(c, r1), r2), fuse(mkepsBC(r1), bder(c, r2)))
+ else ASEQ(bs, bder(c, r1), r2)
+ case ASTAR(bs, r) => ASEQ(bs, fuse(List(S), bder(c, r)), ASTAR(Nil, r))
+ }
+
+
+ def ders (s: List[Char], r: Rexp) : Rexp = s match {
+ case Nil => r
+ case c::s => ders(s, der(c, r))
+ }
+
+ // derivative w.r.t. a string (iterates bder)
+ @tailrec
+ def bders (s: List[Char], r: ARexp) : ARexp = s match {
+ case Nil => r
+ case c::s => bders(s, bder(c, r))
+ }
+
+ def flats(rs: List[ARexp]): List[ARexp] = rs match {
+ case Nil => Nil
+ case AZERO :: rs1 => flats(rs1)
+ case AALTS(bs, rs1) :: rs2 => rs1.map(fuse(bs, _)) ::: flats(rs2)
+ case r1 :: rs2 => r1 :: flats(rs2)
+ }
+ def rflats(rs: List[Rexp]): List[Rexp] = rs match {
+ case Nil => Nil
+ case ZERO :: rs1 => rflats(rs1)
+ case ALTS(rs1) :: rs2 => rs1 ::: rflats(rs2)
+ case r1 :: rs2 => r1 :: rflats(rs2)
+ }
+ //val flats_time = scala.collection.mutable.ArrayBuffer.empty[Long]
+ //val dist_time = scala.collection.mutable.ArrayBuffer.empty[Long]
+ var flats_time = 0L
+ var dist_time = 0L
+ /*
+ def bsimp(r: ARexp, depth: Int): ARexp =
+ {
+ r match {
+ case ASEQ(bs1, r1, r2) => (bsimp(r1, depth), bsimp(r2, depth)) match {
+ case (AZERO, _) => AZERO
+ case (_, AZERO) => AZERO
+ case (AONE(bs2), r2s) => fuse(bs1 ++ bs2, r2s)
+ case (r1s, r2s) => ASEQ(bs1, r1s, r2s)
+ }
+ case AALTS(bs1, rs) => {
+ depth match {
+ case 0 => {
+ flats(distinctBy(rs, erase)) match {
+ case Nil => AZERO
+ case s :: Nil => fuse(bs1, s)
+ case rs => AALTS(bs1, rs)
+ }
+ }
+ case n => {
+ val rs_simp = rs.map(bsimp(_, n - 1))
+ val time2 = System.nanoTime()
+ val flat_res = flats(rs_simp)
+ val time3 = System.nanoTime()
+ val dist_res = distinctBy(flat_res, erase)
+ val time4 = System.nanoTime()
+ flats_time = flats_time + time3 - time2
+ dist_time = dist_time + time4 - time3
+ //flats_time += time3 - time2
+ //dist_time += time4 - time3
+ //distinctBy(flats(rs.map(bsimp)), erase) match {
+ dist_res match {
+ case Nil => AZERO
+ case s :: Nil => fuse(bs1, s)
+ case rs => AALTS(bs1, rs)
+ }
+ }
+ }
+ }
+ case r => r
+ }
+ }
+ */
+ //----------------------------------------------------------------------------This bsimp is the original slow one
+
+ def bsimp(r: ARexp): ARexp = r match {
+ case ASEQ(bs1, r1, r2) => (bsimp(r1), bsimp(r2)) match {
+ case (AZERO, _) => AZERO
+ case (_, AZERO) => AZERO
+ case (AONE(bs2), r2s) => fuse(bs1 ++ bs2, r2s)
+ case (r1s, r2s) => ASEQ(bs1, r1s, r2s)
+ }
+ case AALTS(bs1, rs) => {
+ val rs_simp = rs.map(bsimp)
+ val time2 = System.nanoTime()
+ val flat_res = flats(rs_simp)
+ val time3 = System.nanoTime()
+ val dist_res = distinctBy(flat_res, erase)
+ val time4 = System.nanoTime()
+ flats_time = flats_time + time3 - time2
+ dist_time = dist_time + time4 - time3
+ dist_res match {
+ case Nil => AZERO
+ case s :: Nil => fuse(bs1, s)
+ case rs => AALTS(bs1, rs)
+ }
+ }
+ case ASTAR(bs, r) => ASTAR(bs, bsimp(r))
+ case r => r
+ }
+
+ def bsimp_weakened(r: ARexp): ARexp = r match {
+ case ASEQ(bs1, r1, r2) => (bsimp_weakened(r1), r2) match {
+ case (AZERO, _) => AZERO
+ case (_, AZERO) => AZERO
+ case (AONE(bs2), r2s) => fuse(bs1 ++ bs2, r2s)
+ case (r1s, r2s) => ASEQ(bs1, r1s, r2s)
+ }
+ case AALTS(bs1, rs) => {
+ val rs_simp = rs.map(bsimp_weakened)
+ val time2 = System.nanoTime()
+ val flat_res = flats(rs_simp)
+ val time3 = System.nanoTime()
+ val dist_res = distinctBy(flat_res, erase)
+ val time4 = System.nanoTime()
+ flats_time = flats_time + time3 - time2
+ dist_time = dist_time + time4 - time3
+ dist_res match {
+ case Nil => AZERO
+ case s :: Nil => fuse(bs1, s)
+ case rs => AALTS(bs1, rs)
+ }
+ }
+ case ASTAR(bs, r) => ASTAR(bs, bsimp_weakened(r))
+ case r => r
+ }
+
+ def simp_weakened(r: Rexp): Rexp = r match {
+ case SEQ(r1, r2) => (simp_weakened(r1), r2) match {
+ case (ZERO, _) => ZERO
+ case (_, ZERO) => ZERO
+ case (ONE, r2s) => r2s
+ case (r1s, r2s) => SEQ(r1s, r2s)
+ }
+ case ALTS(rs) => {
+ val rs_simp = rs.map(simp_weakened)
+ val flat_res = rflats(rs_simp)
+ val dist_res = rs_simp.distinct
+ dist_res match {
+ case Nil => ZERO
+ case s :: Nil => s
+ case rs => ALTS(rs)
+ }
+ }
+ case STAR(r) => STAR(simp_weakened(r))
+ case r => r
+ }
+
+
+ //----------------------------------------------------------------------------experiment bsimp
+ /*
+ def bders_simp (s: List[Char], r: ARexp) : ARexp = s match {
+ case Nil => r
+ case c::s => bders_simp(s, bsimp(bder(c, r)))
+ }
+ */
+ /*
+ def time[T](code: => T) = {
+ val start = System.nanoTime()
+ val result = code
+ val end = System.nanoTime()
+ println((end - start)/1.0e9)
+ result
+ }
+ */
+ // main unsimplified lexing function (produces a value)
+ def blex(r: ARexp, s: List[Char]) : Bits = s match {
+ case Nil => if (bnullable(r)) mkepsBC(r) else throw new Exception("Not matched")
+ case c::cs => {
+ val der_res = bder(c,r)
+ blex(der_res, cs)
+ }
+ }
+
+ def bpre_lexing(r: Rexp, s: String) = blex(internalise(r), s.toList)
+ //def blexing(r: Rexp, s: String) : Val = decode(r, blex(internalise(r), s.toList))
+
+ var bder_time = 0L
+ var bsimp_time = 0L
+ var mkepsBC_time = 0L
+ var small_de = 2
+ var big_de = 5
+ var usual_de = 3
+
+ def blex_simp(r: ARexp, s: List[Char]) : Bits = s match {
+ case Nil => {
+ if (bnullable(r)) {
+ //println(asize(r))
+ val time4 = System.nanoTime()
+ val bits = mkepsBC(r)
+ val time5 = System.nanoTime()
+ mkepsBC_time = time5 - time4
+ bits
+ }
+ else throw new Exception("Not matched")
+ }
+ case c::cs => {
+ val time1 = System.nanoTime()
+ val der_res = bder(c,r)
+ val time2 = System.nanoTime()
+ val simp_res = bsimp(der_res)
+ val time3 = System.nanoTime()
+ bder_time = bder_time + time2 - time1
+ bsimp_time = bsimp_time + time3 - time2
+ blex_simp(simp_res, cs)
+ }
+ }
+ def blex_real_simp(r: ARexp, s: List[Char]): ARexp = s match{
+ case Nil => r
+ case c::cs => blex_real_simp(bsimp(bder(c, r)), cs)
+ }
+
+ //-------------------------------------------------------------------------------------tests whether simp(simp(r)) == simp(r) holds true
+ /*
+ def blex_simp(r: ARexp, s: List[Char]) : Bits = s match {
+ case Nil => {
+ if (bnullable(r)) {
+ //println(asize(r))
+ mkepsBC(r)
+ }
+ else throw new Exception("Not matched")
+ }
+ case c::cs => {
+ val der_res = bder(c,r)
+ val simp_res = bsimp(der_res)
+ //val simp_res2 = bsimp(simp_res)
+ //println("Size reduction from "+asize(der_res)+ " to " +asize(simp_res)+" to " + asize(simp_res2))
+ blex_simp(simp_res, cs)
+ }
+ }
+ */
+ /*
+ 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 start = System.nanoTime()
+ val (r_simp, f_simp) = simp(der(c, r))
+ val end = System.nanoTime()
+ println((end - start)/1.0e9)
+ inj(r, c, f_simp(lex_simp(r_simp, cs)))
+ }
+ }
+ */
+
+ //size: of a Aregx for testing purposes
+ def size(r: Rexp) : Int = r match {
+ case ZERO => 1
+ case ONE => 1
+ case CHAR(_) => 1
+ case SEQ(r1, r2) => 1 + size(r1) + size(r2)
+ case ALTS(rs) => 1 + rs.map(size).sum
+ case STAR(r) => 1 + size(r)
+ }
+
+ def asize(a: ARexp) = size(erase(a))
+
+
+ // decoding does not work yet
+ def blexing_simp(r: Rexp, s: String) = {
+ //flats_time.clear()
+ //dist_time.clear()
+ flats_time = 0L
+ dist_time = 0L
+ bder_time = 0L
+ bsimp_time = 0L
+ mkepsBC_time = 0L
+ val start = System.nanoTime()
+ val bit_code = blex_simp(internalise(r), s.toList)
+ val end = System.nanoTime()
+ println("total time: "+ (end - start)/1.0e9)
+ println("spent on flats: " + (flats_time/(1.0e9)))
+ println("spent on distinctBy: " + (dist_time/(1.0e9)))
+ println("spent on bder: "+ bder_time/1.0e9)
+ println("spent on bsimp: " + bsimp_time/1.0e9)
+ println("spent on mkepsBC: " + mkepsBC_time/1.0e9)
+ //println(s"The length of the string ${s.length}; length of bit sequence:")
+ //println((bit_code.length))
+ //println(final_derivative)
+ //bit_code
+ //decode(r, bit_code)
+ }
+
+
+
+
+
+ // Lexing Rules for a Small While Language
+
+ //symbols
+ /*
+ val SYM = PRED("abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ".contains(_))
+
+ //digits
+ val DIGIT = PRED("0123456789".contains(_))
+ //identifiers
+ val ID = SYM ~ (SYM | DIGIT).%
+ //numbers
+ val NUM = STAR(DIGIT)
+ //keywords
+ val KEYWORD : Rexp = "skip" | "while" | "do" | "if" | "then" | "else" | "read" | "write" | "true" | "false"
+ val AKEYWORD: Rexp = ALTS(List("skip" , "while" , "do" , "if" , "then" , "else" , "read" , "write" , "true" , "false"))
+ //semicolons
+ val SEMI: Rexp = ";"
+ //operators
+ val OP: Rexp = ":=" | "==" | "-" | "+" | "*" | "!=" | "<" | ">" | "<=" | ">=" | "%" | "/"
+ val AOP: Rexp = ALTS(List(":=" , "==" , "-" , "+" , "*" , "!=" , "<" , ">" , "<=" , ">=" , "%" , "/"))
+ //whitespaces
+ val WHITESPACE = PLUS(" " | "\n" | "\t")
+ //parentheses
+ val RPAREN: Rexp = ")"
+ val LPAREN: Rexp = "("
+ val BEGIN: Rexp = "{"
+ val END: Rexp = "}"
+ //strings...but probably needs not
+ val STRING: Rexp = "\"" ~ SYM.% ~ "\""
+
+
+
+ val WHILE_REGS = (("k" $ KEYWORD) |
+ ("i" $ ID) |
+ ("o" $ OP) |
+ ("n" $ NUM) |
+ ("s" $ SEMI) |
+ ("str" $ STRING) |
+ ("p" $ (LPAREN | RPAREN)) |
+ ("b" $ (BEGIN | END)) |
+ ("w" $ WHITESPACE)).%
+
+ val AWHILE_REGS = (
+ ALTS(
+ List(
+ ("k" $ AKEYWORD),
+ ("i" $ ID),
+ ("o" $ AOP) ,
+ ("n" $ NUM) ,
+ ("s" $ SEMI) ,
+ ("str" $ STRING),
+ ("p" $ (LPAREN | RPAREN)),
+ ("b" $ (BEGIN | END)),
+ ("w" $ WHITESPACE)
+ )
+ )
+ ).%
+
+*/
+
+
+ //--------------------------------------------------------------------------------------------------------START OF NON-BITCODE PART (TESTING)
+ /*
+ // Two Simple While programs
+ //========================
+ println("prog0 test")
+
+ val prog0 = """read n"""
+ println(env(lexing_simp(WHILE_REGS, prog0)))
+ println(tokenise(WHILE_REGS, prog0))
+
+ println("prog1 test")
+
+ val prog1 = """read n; write (n)"""
+ println(tokenise(WHILE_REGS, prog1))
+
+ */
+ // Bigger Tests
+ //==============
+
+ def escape(raw: String): String = {
+ import scala.reflect.runtime.universe._
+ Literal(Constant(raw)).toString
+ }
+
+ val prog2 = """
+ write "Fib";
+ read n;
+ minus1 := 0;
+ minus2 := 1;
+ while n > 0 do {
+ temp := minus2;
+ minus2 := minus1 + minus2;
+ minus1 := temp;
+ n := n - 1
+ };
+ write "Result";
+ write minus2
+ """
+
+ val prog3 = """
+ start := 1000;
+ x := start;
+ y := start;
+ z := start;
+ while 0 < x do {
+ while 0 < y do {
+ while 0 < z do {
+ z := z - 1
+ };
+ z := start;
+ y := y - 1
+ };
+ y := start;
+ x := x - 1
+ }
+ """
+ /*
+ for(i <- 400 to 400 by 1){
+ println(i+":")
+ blexing_simp(WHILE_REGS, prog2 * i)
+ } */
+
+ /*
+ for (i <- 2 to 5){
+ for(j <- 1 to 3){
+ println(i,j)
+ small_de = i
+ usual_de = i + j
+ big_de = i + 2*j
+ blexing_simp(AWHILE_REGS, prog2 * 100)
+ }
+ }*/
+
+ /*
+ println("Tokens of prog2")
+ println(tokenise(WHILE_REGS, prog2).mkString("\n"))
+
+ val fib_tokens = tokenise(WHILE_REGS, prog2)
+ fib_tokens.map{case (s1, s2) => (escape(s1), escape(s2))}.mkString(",\n")
+
+
+ val test_tokens = tokenise(WHILE_REGS, prog3)
+ test_tokens.map{case (s1, s2) => (escape(s1), escape(s2))}.mkString(",\n")
+ */
+
+ /*
+ println("time test for blexing_simp")
+ for (i <- 1 to 1 by 1) {
+ lexing_simp(WHILE_REGS, prog2 * i)
+ blexing_simp(WHILE_REGS, prog2 * i)
+ for( j <- 0 to each_simp_timeb.length - 1){
+ if( each_simp_timeb(j)/each_simp_time(j) >= 10.0 )
+ println(j, each_simp_timeb(j), each_simp_time(j))
+ }
+ }
+ */
+
+
+ //--------------------------------------------------------------------------------------------------------END OF NON-BITCODE PART (TESTING)
+
+
+
+ def clear() = {
+ print("")
+ //print("\33[H\33[2J")
+ }
+
+ //testing the two lexings produce the same value
+ //enumerates strings of length n over alphabet cs
+ def strs(n: Int, cs: String) : Set[String] = {
+ if (n == 0) Set("")
+ else {
+ val ss = strs(n - 1, cs)
+ ss ++
+ (for (s <- ss; c <- cs.toList) yield c + s)
+ }
+ }
+ def enum(n: Int, s: String) : Stream[Rexp] = n match {
+ case 0 => ZERO #:: ONE #:: s.toStream.map(CHAR)
+ case n => {
+ val rs = enum(n - 1, s)
+ rs #:::
+ (for (r1 <- rs; r2 <- rs) yield ALT(r1, r2)) #:::
+ (for (r1 <- rs; r2 <- rs) yield SEQ(r1, r2)) #:::
+ (for (r1 <- rs) yield STAR(r1))
+ }
+ }
+
+ //tests blexing and lexing
+ def tests_blexer_simp(ss: Set[String])(r: Rexp) = {
+ clear()
+ //println(s"Testing ${r}")
+ for (s <- ss.par) yield {
+ val res1 = Try(Some(lexing_simp(r, s))).getOrElse(None)
+ val res2 = Try(Some(blexing_simp(r, s))).getOrElse(None)
+ if (res1 != res2) println(s"Disagree on ${r} and ${s}")
+ if (res1 != res2) println(s" ${res1} != ${res2}")
+ if (res1 != res2) Some((r, s)) else None
+ }
+ }
+
+
+
+ //enum(3, "abc").map(tests_blexer_simp(strs(3, "abc"))).toSet
+ /*
+ def single_expression_explorer(ar: ARexp, ss: Set[String]): Unit = {
+ for (s <- ss){
+
+ val der_res = bder(c, ar)
+ val simp_res = bsimp(der_res)
+ println(asize(der_res))
+ println(asize(simp_res))
+ single_expression_explorer(simp_res, (sc - c))
+ }
+ }*/
+
+ //single_expression_explorer(internalise(("c"~("a"+"b"))%) , Set('a','b','c'))
+
+
+}
+
+import Rexp.Bits
+abstract class ARexp
+case object AZERO extends ARexp
+case class AONE(bs: Bits) extends ARexp
+case class ACHAR(bs: Bits, f: Char) extends ARexp
+case class AALTS(bs: Bits, rs: List[ARexp]) extends ARexp
+case class ASEQ(bs: Bits, r1: ARexp, r2: ARexp) extends ARexp
+case class ASTAR(bs: Bits, r: ARexp) extends ARexp
+
+
+
+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
+//case class Pos(i: Int, v: Val) extends Val
+case object Prd extends Val