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package RexpRelated
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import scala.language.implicitConversions
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import scala.language.reflectiveCalls
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import scala.annotation.tailrec
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import scala.util.Try
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abstract class Bit
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case object Z extends Bit
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case object S extends Bit
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case class C(c: Char) extends Bit
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abstract class Rexp
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case object ZERO extends Rexp
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case object ONE extends Rexp
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case class CHAR(c: Char) extends Rexp
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case class ALTS(rs: List[Rexp]) extends Rexp
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case class SEQ(r1: Rexp, r2: Rexp) extends Rexp
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case class STAR(r: Rexp) extends Rexp
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case class RECD(x: String, r: Rexp) extends Rexp
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object Rexp{
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type Bits = List[Bit]
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// abbreviations
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type Mon = (Char, Rexp)
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type Lin = Set[Mon]
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def ALT(r1: Rexp, r2: Rexp) = ALTS(List(r1, r2))
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def PLUS(r: Rexp) = SEQ(r, STAR(r))
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def AALT(bs: Bits, r1: ARexp, r2: ARexp) = AALTS(bs, List(r1, r2))
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def distinctBy[B, C](xs: List[B], f: B => C, acc: List[C] = Nil): List[B] = xs match {
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case Nil => Nil
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case (x::xs) => {
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val res = f(x)
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if (acc.contains(res)) distinctBy(xs, f, acc)
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else x::distinctBy(xs, f, res::acc)
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}
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}
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// some convenience for typing in regular expressions
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def charlist2rexp(s : List[Char]): Rexp = s match {
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case Nil => ONE
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case c::Nil => CHAR(c)
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case c::s => SEQ(CHAR(c), charlist2rexp(s))
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}
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implicit def string2rexp(s : String) : Rexp = charlist2rexp(s.toList)
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implicit def RexpOps(r: Rexp) = new {
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def | (s: Rexp) = ALT(r, s)
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def % = STAR(r)
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def ~ (s: Rexp) = SEQ(r, s)
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}
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implicit def stringOps(s: String) = new {
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def | (r: Rexp) = ALT(s, r)
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def | (r: String) = ALT(s, r)
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def % = STAR(s)
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def ~ (r: Rexp) = SEQ(s, r)
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def ~ (r: String) = SEQ(s, r)
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def $ (r: Rexp) = RECD(s, r)
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}
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// translation into ARexps
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def fuse(bs: Bits, r: ARexp) : ARexp = r match {
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case AZERO => AZERO
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case AONE(cs) => AONE(bs ++ cs)
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case ACHAR(cs, f) => ACHAR(bs ++ cs, f)
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case AALTS(cs, rs) => AALTS(bs ++ cs, rs)
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case ASEQ(cs, r1, r2) => ASEQ(bs ++ cs, r1, r2)
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case ASTAR(cs, r) => ASTAR(bs ++ cs, r)
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}
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def internalise(r: Rexp) : ARexp = r match {
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case ZERO => AZERO
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case ONE => AONE(Nil)
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case CHAR(c) => ACHAR(Nil, c)
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case ALTS(List(r1, r2)) =>
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AALTS(Nil, List(fuse(List(Z), internalise(r1)), fuse(List(S), internalise(r2))))
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case ALTS(r1::rs) => {
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val AALTS(Nil, rs2) = internalise(ALTS(rs))
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AALTS(Nil, fuse(List(Z), internalise(r1)) :: rs2.map(fuse(List(S), _)))
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}
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case SEQ(r1, r2) => ASEQ(Nil, internalise(r1), internalise(r2))
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case STAR(r) => ASTAR(Nil, internalise(r))
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case RECD(x, r) => internalise(r)
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}
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internalise(("a" | "ab") ~ ("b" | ""))
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3
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/*
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0
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def decode_aux(r: Rexp, bs: Bits) : (Val, Bits) = (r, bs) match {
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case (ONE, bs) => (Empty, bs)
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case (PRED(f), C(c)::bs) => (Chr(c), bs)
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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
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case (ALTS(rs), bs) => bs match {
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case Z::bs1 => {
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val (v, bs2) = decode_aux(rs.head, bs1)
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(Left(v), bs2)
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}
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case S::bs1 => {
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val (v, bs2) = decode_aux(ALTS(rs.tail), bs1)
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(Right(v), bs2)
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}
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}
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case (SEQ(r1, r2), bs) => {
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val (v1, bs1) = decode_aux(r1, bs)
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val (v2, bs2) = decode_aux(r2, bs1)
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(Sequ(v1, v2), bs2)
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}
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case (STAR(r1), S::bs) => {
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val (v, bs1) = decode_aux(r1, bs)
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//println(v)
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val (Stars(vs), bs2) = decode_aux(STAR(r1), bs1)
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(Stars(v::vs), bs2)
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}
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case (STAR(_), Z::bs) => (Stars(Nil), bs)
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case (RECD(x, r1), bs) => {
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val (v, bs1) = decode_aux(r1, bs)
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(Rec(x, v), bs1)
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}
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}
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def decode(r: Rexp, bs: Bits) = decode_aux(r, bs) match {
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case (v, Nil) => v
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case _ => throw new Exception("Not decodable")
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}
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3
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*/
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//erase function: extracts the regx from Aregex
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def erase(r:ARexp): Rexp = r match{
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case AZERO => ZERO
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case AONE(_) => ONE
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case ACHAR(bs, f) => CHAR(f)
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case AALTS(bs, rs) => ALTS(rs.map(erase(_)))
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case ASEQ(bs, r1, r2) => SEQ (erase(r1), erase(r2))
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case ASTAR(cs, r)=> STAR(erase(r))
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}
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//--------------------------------------------------------------------------------------------------------START OF NON-BITCODE PART
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// nullable function: tests whether the regular
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// expression can recognise the empty string
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def nullable (r: Rexp) : Boolean = r match {
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case ZERO => false
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case ONE => true
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case CHAR(_) => false
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case ALTS(rs) => rs.exists(nullable)
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case SEQ(r1, r2) => nullable(r1) && nullable(r2)
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case STAR(_) => true
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case RECD(_, r) => nullable(r)
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//case PLUS(r) => nullable(r)
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}
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// derivative of a regular expression w.r.t. a character
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def der (c: Char, r: Rexp) : Rexp = r match {
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case ZERO => ZERO
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case ONE => ZERO
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case CHAR(f) => if (c == f) ONE else ZERO
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case ALTS(List(r1, r2)) => ALTS(List(der(c, r1), der(c, r2)))
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case SEQ(r1, r2) =>
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if (nullable(r1)) ALTS(List(SEQ(der(c, r1), r2), der(c, r2)))
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else SEQ(der(c, r1), r2)
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case STAR(r) => SEQ(der(c, r), STAR(r))
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case RECD(_, r1) => der(c, r1)
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//case PLUS(r) => SEQ(der(c, r), STAR(r))
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}
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def flatten(v: Val) : String = v match {
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case Empty => ""
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case Chr(c) => c.toString
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case Left(v) => flatten(v)
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case Right(v) => flatten(v)
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case Sequ(v1, v2) => flatten(v1) + flatten(v2)
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case Stars(vs) => vs.map(flatten).mkString
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case Rec(_, v) => flatten(v)
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}
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// extracts an environment from a value
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def env(v: Val) : List[(String, String)] = v match {
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case Empty => Nil
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case Chr(c) => Nil
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case Left(v) => env(v)
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case Right(v) => env(v)
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case Sequ(v1, v2) => env(v1) ::: env(v2)
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case Stars(vs) => vs.flatMap(env)
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case Rec(x, v) => (x, flatten(v))::env(v)
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}
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// injection part
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def mkeps(r: Rexp) : Val = r match {
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case ONE => Empty
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case ALTS(List(r1, r2)) =>
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if (nullable(r1)) Left(mkeps(r1)) else Right(mkeps(r2))
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case SEQ(r1, r2) => Sequ(mkeps(r1), mkeps(r2))
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case STAR(r) => Stars(Nil)
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case RECD(x, r) => Rec(x, mkeps(r))
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//case PLUS(r) => Stars(List(mkeps(r)))
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}
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def inj(r: Rexp, c: Char, v: Val) : Val = (r, v) match {
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case (STAR(r), Sequ(v1, Stars(vs))) => Stars(inj(r, c, v1)::vs)
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case (SEQ(r1, r2), Sequ(v1, v2)) => Sequ(inj(r1, c, v1), v2)
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case (SEQ(r1, r2), Left(Sequ(v1, v2))) => Sequ(inj(r1, c, v1), v2)
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case (SEQ(r1, r2), Right(v2)) => Sequ(mkeps(r1), inj(r2, c, v2))
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case (ALTS(List(r1, r2)), Left(v1)) => Left(inj(r1, c, v1))
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case (ALTS(List(r1, r2)), Right(v2)) => Right(inj(r2, c, v2))
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case (CHAR(_), Empty) => Chr(c)
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case (RECD(x, r1), _) => Rec(x, inj(r1, c, v))
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//case (PLUS(r), Sequ(v1, Stars(vs))) => Stars(inj(r, c, v1)::vs)
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}
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def lex(r: Rexp, s: List[Char]) : Val = s match {
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case Nil => if (nullable(r)) mkeps(r) else throw new Exception("Not matched")
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case c::cs => inj(r, c, lex(der(c, r), cs))
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}
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def lexing(r: Rexp, s: String) : Val = lex(r, s.toList)
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// some "rectification" functions for simplification
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def F_ID(v: Val): Val = v
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def F_RIGHT(f: Val => Val) = (v:Val) => Right(f(v))
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def F_LEFT(f: Val => Val) = (v:Val) => Left(f(v))
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def F_ALT(f1: Val => Val, f2: Val => Val) = (v:Val) => v match {
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case Right(v) => Right(f2(v))
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case Left(v) => Left(f1(v))
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}
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def F_SEQ(f1: Val => Val, f2: Val => Val) = (v:Val) => v match {
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case Sequ(v1, v2) => Sequ(f1(v1), f2(v2))
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}
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def F_SEQ_Empty1(f1: Val => Val, f2: Val => Val) =
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(v:Val) => Sequ(f1(Empty), f2(v))
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def F_SEQ_Empty2(f1: Val => Val, f2: Val => Val) =
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(v:Val) => Sequ(f1(v), f2(Empty))
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def F_RECD(f: Val => Val) = (v:Val) => v match {
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case Rec(x, v) => Rec(x, f(v))
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}
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def F_ERROR(v: Val): Val = throw new Exception("error")
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// simplification of regular expressions returning also an
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// rectification function; no simplification under STAR
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def simp(r: Rexp): (Rexp, Val => Val) = r match {
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case ALTS(List(r1, r2)) => {
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val (r1s, f1s) = simp(r1)
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val (r2s, f2s) = simp(r2)
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(r1s, r2s) match {
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case (ZERO, _) => (r2s, F_RIGHT(f2s))
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case (_, ZERO) => (r1s, F_LEFT(f1s))
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case _ => if (r1s == r2s) (r1s, F_LEFT(f1s))
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else (ALTS(List(r1s, r2s)), F_ALT(f1s, f2s))
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}
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}
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case SEQ(r1, r2) => {
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val (r1s, f1s) = simp(r1)
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val (r2s, f2s) = simp(r2)
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(r1s, r2s) match {
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case (ZERO, _) => (ZERO, F_ERROR)
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case (_, ZERO) => (ZERO, F_ERROR)
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case (ONE, _) => (r2s, F_SEQ_Empty1(f1s, f2s))
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case (_, ONE) => (r1s, F_SEQ_Empty2(f1s, f2s))
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case _ => (SEQ(r1s,r2s), F_SEQ(f1s, f2s))
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}
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}
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case RECD(x, r1) => {
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val (r1s, f1s) = simp(r1)
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(RECD(x, r1s), F_RECD(f1s))
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}
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case r => (r, F_ID)
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}
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/*
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val each_simp_time = scala.collection.mutable.ArrayBuffer.empty[Long]
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val each_simp_timeb = scala.collection.mutable.ArrayBuffer.empty[Long]
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*/
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def lex_simp(r: Rexp, s: List[Char]) : Val = s match {
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case Nil => {
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if (nullable(r)) {
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mkeps(r)
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}
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else throw new Exception("Not matched")
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}
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case c::cs => {
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val (r_simp, f_simp) = simp(der(c, r))
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inj(r, c, f_simp(lex_simp(r_simp, cs)))
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}
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}
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def lexing_simp(r: Rexp, s: String) : Val = lex_simp(r, s.toList)
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//println(lexing_simp(("a" | "ab") ~ ("b" | ""), "ab"))
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// filters out all white spaces
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def tokenise(r: Rexp, s: String) =
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env(lexing_simp(r, s)).filterNot { _._1 == "w"}
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//reads the string from a file
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def fromFile(name: String) : String =
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io.Source.fromFile(name).mkString
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def tokenise_file(r: Rexp, name: String) =
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tokenise(r, fromFile(name))
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// Testing
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//============
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def time[T](code: => T) = {
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306 |
val start = System.nanoTime()
|
|
|
307 |
val result = code
|
|
|
308 |
val end = System.nanoTime()
|
|
|
309 |
println((end - start)/1.0e9)
|
|
|
310 |
result
|
|
|
311 |
}
|
|
|
312 |
|
|
|
313 |
//--------------------------------------------------------------------------------------------------------END OF NON-BITCODE PART
|
|
|
314 |
|
|
|
315 |
// bnullable function: tests whether the aregular
|
|
|
316 |
// expression can recognise the empty string
|
|
|
317 |
def bnullable (r: ARexp) : Boolean = r match {
|
|
|
318 |
case AZERO => false
|
|
|
319 |
case AONE(_) => true
|
|
|
320 |
case ACHAR(_,_) => false
|
|
|
321 |
case AALTS(_, rs) => rs.exists(bnullable)
|
|
|
322 |
case ASEQ(_, r1, r2) => bnullable(r1) && bnullable(r2)
|
|
|
323 |
case ASTAR(_, _) => true
|
|
|
324 |
}
|
|
|
325 |
|
|
|
326 |
def mkepsBC(r: ARexp) : Bits = r match {
|
|
|
327 |
case AONE(bs) => bs
|
|
|
328 |
case AALTS(bs, rs) => {
|
|
|
329 |
val n = rs.indexWhere(bnullable)
|
|
|
330 |
bs ++ mkepsBC(rs(n))
|
|
|
331 |
}
|
|
|
332 |
case ASEQ(bs, r1, r2) => bs ++ mkepsBC(r1) ++ mkepsBC(r2)
|
|
|
333 |
case ASTAR(bs, r) => bs ++ List(Z)
|
|
|
334 |
}
|
|
|
335 |
|
|
|
336 |
// derivative of a regular expression w.r.t. a character
|
|
|
337 |
def bder(c: Char, r: ARexp) : ARexp = r match {
|
|
|
338 |
case AZERO => AZERO
|
|
|
339 |
case AONE(_) => AZERO
|
|
|
340 |
case ACHAR(bs, f) => if (c == f) AONE(bs:::List(C(c))) else AZERO
|
|
|
341 |
case AALTS(bs, rs) => AALTS(bs, rs.map(bder(c, _)))
|
|
|
342 |
case ASEQ(bs, r1, r2) =>
|
|
|
343 |
if (bnullable(r1)) AALT(bs, ASEQ(Nil, bder(c, r1), r2), fuse(mkepsBC(r1), bder(c, r2)))
|
|
|
344 |
else ASEQ(bs, bder(c, r1), r2)
|
|
|
345 |
case ASTAR(bs, r) => ASEQ(bs, fuse(List(S), bder(c, r)), ASTAR(Nil, r))
|
|
|
346 |
}
|
|
|
347 |
|
|
|
348 |
|
|
|
349 |
def ders (s: List[Char], r: Rexp) : Rexp = s match {
|
|
|
350 |
case Nil => r
|
|
|
351 |
case c::s => ders(s, der(c, r))
|
|
|
352 |
}
|
|
|
353 |
|
|
|
354 |
// derivative w.r.t. a string (iterates bder)
|
|
|
355 |
@tailrec
|
|
|
356 |
def bders (s: List[Char], r: ARexp) : ARexp = s match {
|
|
|
357 |
case Nil => r
|
|
|
358 |
case c::s => bders(s, bder(c, r))
|
|
|
359 |
}
|
|
|
360 |
|
|
|
361 |
def flats(rs: List[ARexp]): List[ARexp] = rs match {
|
|
|
362 |
case Nil => Nil
|
|
|
363 |
case AZERO :: rs1 => flats(rs1)
|
|
|
364 |
case AALTS(bs, rs1) :: rs2 => rs1.map(fuse(bs, _)) ::: flats(rs2)
|
|
|
365 |
case r1 :: rs2 => r1 :: flats(rs2)
|
|
|
366 |
}
|
|
|
367 |
def rflats(rs: List[Rexp]): List[Rexp] = rs match {
|
|
|
368 |
case Nil => Nil
|
|
|
369 |
case ZERO :: rs1 => rflats(rs1)
|
|
|
370 |
case ALTS(rs1) :: rs2 => rs1 ::: rflats(rs2)
|
|
|
371 |
case r1 :: rs2 => r1 :: rflats(rs2)
|
|
|
372 |
}
|
|
|
373 |
//val flats_time = scala.collection.mutable.ArrayBuffer.empty[Long]
|
|
|
374 |
//val dist_time = scala.collection.mutable.ArrayBuffer.empty[Long]
|
|
|
375 |
var flats_time = 0L
|
|
|
376 |
var dist_time = 0L
|
|
|
377 |
/*
|
|
|
378 |
def bsimp(r: ARexp, depth: Int): ARexp =
|
|
|
379 |
{
|
|
|
380 |
r match {
|
|
|
381 |
case ASEQ(bs1, r1, r2) => (bsimp(r1, depth), bsimp(r2, depth)) match {
|
|
|
382 |
case (AZERO, _) => AZERO
|
|
|
383 |
case (_, AZERO) => AZERO
|
|
|
384 |
case (AONE(bs2), r2s) => fuse(bs1 ++ bs2, r2s)
|
|
|
385 |
case (r1s, r2s) => ASEQ(bs1, r1s, r2s)
|
|
|
386 |
}
|
|
|
387 |
case AALTS(bs1, rs) => {
|
|
|
388 |
depth match {
|
|
|
389 |
case 0 => {
|
|
|
390 |
flats(distinctBy(rs, erase)) match {
|
|
|
391 |
case Nil => AZERO
|
|
|
392 |
case s :: Nil => fuse(bs1, s)
|
|
|
393 |
case rs => AALTS(bs1, rs)
|
|
|
394 |
}
|
|
|
395 |
}
|
|
|
396 |
case n => {
|
|
|
397 |
val rs_simp = rs.map(bsimp(_, n - 1))
|
|
|
398 |
val time2 = System.nanoTime()
|
|
|
399 |
val flat_res = flats(rs_simp)
|
|
|
400 |
val time3 = System.nanoTime()
|
|
|
401 |
val dist_res = distinctBy(flat_res, erase)
|
|
|
402 |
val time4 = System.nanoTime()
|
|
|
403 |
flats_time = flats_time + time3 - time2
|
|
|
404 |
dist_time = dist_time + time4 - time3
|
|
|
405 |
//flats_time += time3 - time2
|
|
|
406 |
//dist_time += time4 - time3
|
|
|
407 |
//distinctBy(flats(rs.map(bsimp)), erase) match {
|
|
|
408 |
dist_res match {
|
|
|
409 |
case Nil => AZERO
|
|
|
410 |
case s :: Nil => fuse(bs1, s)
|
|
|
411 |
case rs => AALTS(bs1, rs)
|
|
|
412 |
}
|
|
|
413 |
}
|
|
|
414 |
}
|
|
|
415 |
}
|
|
|
416 |
case r => r
|
|
|
417 |
}
|
|
|
418 |
}
|
|
|
419 |
*/
|
|
|
420 |
//----------------------------------------------------------------------------This bsimp is the original slow one
|
|
|
421 |
|
|
|
422 |
def bsimp(r: ARexp): ARexp = r match {
|
|
|
423 |
case ASEQ(bs1, r1, r2) => (bsimp(r1), bsimp(r2)) match {
|
|
|
424 |
case (AZERO, _) => AZERO
|
|
|
425 |
case (_, AZERO) => AZERO
|
|
|
426 |
case (AONE(bs2), r2s) => fuse(bs1 ++ bs2, r2s)
|
|
|
427 |
case (r1s, r2s) => ASEQ(bs1, r1s, r2s)
|
|
|
428 |
}
|
|
|
429 |
case AALTS(bs1, rs) => {
|
|
|
430 |
val rs_simp = rs.map(bsimp)
|
|
|
431 |
val time2 = System.nanoTime()
|
|
|
432 |
val flat_res = flats(rs_simp)
|
|
|
433 |
val time3 = System.nanoTime()
|
|
|
434 |
val dist_res = distinctBy(flat_res, erase)
|
|
|
435 |
val time4 = System.nanoTime()
|
|
|
436 |
flats_time = flats_time + time3 - time2
|
|
|
437 |
dist_time = dist_time + time4 - time3
|
|
|
438 |
dist_res match {
|
|
|
439 |
case Nil => AZERO
|
|
|
440 |
case s :: Nil => fuse(bs1, s)
|
|
|
441 |
case rs => AALTS(bs1, rs)
|
|
|
442 |
}
|
|
|
443 |
}
|
|
|
444 |
case ASTAR(bs, r) => ASTAR(bs, bsimp(r))
|
|
|
445 |
case r => r
|
|
|
446 |
}
|
|
|
447 |
|
|
|
448 |
def bsimp_weakened(r: ARexp): ARexp = r match {
|
|
|
449 |
case ASEQ(bs1, r1, r2) => (bsimp_weakened(r1), r2) match {
|
|
|
450 |
case (AZERO, _) => AZERO
|
|
|
451 |
case (_, AZERO) => AZERO
|
|
|
452 |
case (AONE(bs2), r2s) => fuse(bs1 ++ bs2, r2s)
|
|
|
453 |
case (r1s, r2s) => ASEQ(bs1, r1s, r2s)
|
|
|
454 |
}
|
|
|
455 |
case AALTS(bs1, rs) => {
|
|
|
456 |
val rs_simp = rs.map(bsimp_weakened)
|
|
|
457 |
val time2 = System.nanoTime()
|
|
|
458 |
val flat_res = flats(rs_simp)
|
|
|
459 |
val time3 = System.nanoTime()
|
|
|
460 |
val dist_res = distinctBy(flat_res, erase)
|
|
|
461 |
val time4 = System.nanoTime()
|
|
|
462 |
flats_time = flats_time + time3 - time2
|
|
|
463 |
dist_time = dist_time + time4 - time3
|
|
|
464 |
dist_res match {
|
|
|
465 |
case Nil => AZERO
|
|
|
466 |
case s :: Nil => fuse(bs1, s)
|
|
|
467 |
case rs => AALTS(bs1, rs)
|
|
|
468 |
}
|
|
|
469 |
}
|
|
|
470 |
case ASTAR(bs, r) => ASTAR(bs, bsimp_weakened(r))
|
|
|
471 |
case r => r
|
|
|
472 |
}
|
|
|
473 |
|
|
|
474 |
def simp_weakened(r: Rexp): Rexp = r match {
|
|
|
475 |
case SEQ(r1, r2) => (simp_weakened(r1), r2) match {
|
|
|
476 |
case (ZERO, _) => ZERO
|
|
|
477 |
case (_, ZERO) => ZERO
|
|
|
478 |
case (ONE, r2s) => r2s
|
|
|
479 |
case (r1s, r2s) => SEQ(r1s, r2s)
|
|
|
480 |
}
|
|
|
481 |
case ALTS(rs) => {
|
|
|
482 |
val rs_simp = rs.map(simp_weakened)
|
|
|
483 |
val flat_res = rflats(rs_simp)
|
|
|
484 |
val dist_res = rs_simp.distinct
|
|
|
485 |
dist_res match {
|
|
|
486 |
case Nil => ZERO
|
|
|
487 |
case s :: Nil => s
|
|
|
488 |
case rs => ALTS(rs)
|
|
|
489 |
}
|
|
|
490 |
}
|
|
|
491 |
case STAR(r) => STAR(simp_weakened(r))
|
|
|
492 |
case r => r
|
|
|
493 |
}
|
|
|
494 |
|
|
|
495 |
|
|
|
496 |
//----------------------------------------------------------------------------experiment bsimp
|
|
|
497 |
/*
|
|
|
498 |
def bders_simp (s: List[Char], r: ARexp) : ARexp = s match {
|
|
|
499 |
case Nil => r
|
|
|
500 |
case c::s => bders_simp(s, bsimp(bder(c, r)))
|
|
|
501 |
}
|
|
|
502 |
*/
|
|
|
503 |
/*
|
|
|
504 |
def time[T](code: => T) = {
|
|
|
505 |
val start = System.nanoTime()
|
|
|
506 |
val result = code
|
|
|
507 |
val end = System.nanoTime()
|
|
|
508 |
println((end - start)/1.0e9)
|
|
|
509 |
result
|
|
|
510 |
}
|
|
|
511 |
*/
|
|
|
512 |
// main unsimplified lexing function (produces a value)
|
|
|
513 |
def blex(r: ARexp, s: List[Char]) : Bits = s match {
|
|
|
514 |
case Nil => if (bnullable(r)) mkepsBC(r) else throw new Exception("Not matched")
|
|
|
515 |
case c::cs => {
|
|
|
516 |
val der_res = bder(c,r)
|
|
|
517 |
blex(der_res, cs)
|
|
|
518 |
}
|
|
|
519 |
}
|
|
|
520 |
|
|
|
521 |
def bpre_lexing(r: Rexp, s: String) = blex(internalise(r), s.toList)
|
|
|
522 |
//def blexing(r: Rexp, s: String) : Val = decode(r, blex(internalise(r), s.toList))
|
|
|
523 |
|
|
|
524 |
var bder_time = 0L
|
|
|
525 |
var bsimp_time = 0L
|
|
|
526 |
var mkepsBC_time = 0L
|
|
|
527 |
var small_de = 2
|
|
|
528 |
var big_de = 5
|
|
|
529 |
var usual_de = 3
|
|
|
530 |
|
|
|
531 |
def blex_simp(r: ARexp, s: List[Char]) : Bits = s match {
|
|
|
532 |
case Nil => {
|
|
|
533 |
if (bnullable(r)) {
|
|
|
534 |
//println(asize(r))
|
|
|
535 |
val time4 = System.nanoTime()
|
|
|
536 |
val bits = mkepsBC(r)
|
|
|
537 |
val time5 = System.nanoTime()
|
|
|
538 |
mkepsBC_time = time5 - time4
|
|
|
539 |
bits
|
|
|
540 |
}
|
|
|
541 |
else throw new Exception("Not matched")
|
|
|
542 |
}
|
|
|
543 |
case c::cs => {
|
|
|
544 |
val time1 = System.nanoTime()
|
|
|
545 |
val der_res = bder(c,r)
|
|
|
546 |
val time2 = System.nanoTime()
|
|
|
547 |
val simp_res = bsimp(der_res)
|
|
|
548 |
val time3 = System.nanoTime()
|
|
|
549 |
bder_time = bder_time + time2 - time1
|
|
|
550 |
bsimp_time = bsimp_time + time3 - time2
|
|
|
551 |
blex_simp(simp_res, cs)
|
|
|
552 |
}
|
|
|
553 |
}
|
|
|
554 |
def blex_real_simp(r: ARexp, s: List[Char]): ARexp = s match{
|
|
|
555 |
case Nil => r
|
|
|
556 |
case c::cs => blex_real_simp(bsimp(bder(c, r)), cs)
|
|
|
557 |
}
|
|
|
558 |
|
|
|
559 |
//-------------------------------------------------------------------------------------tests whether simp(simp(r)) == simp(r) holds true
|
|
|
560 |
/*
|
|
|
561 |
def blex_simp(r: ARexp, s: List[Char]) : Bits = s match {
|
|
|
562 |
case Nil => {
|
|
|
563 |
if (bnullable(r)) {
|
|
|
564 |
//println(asize(r))
|
|
|
565 |
mkepsBC(r)
|
|
|
566 |
}
|
|
|
567 |
else throw new Exception("Not matched")
|
|
|
568 |
}
|
|
|
569 |
case c::cs => {
|
|
|
570 |
val der_res = bder(c,r)
|
|
|
571 |
val simp_res = bsimp(der_res)
|
|
|
572 |
//val simp_res2 = bsimp(simp_res)
|
|
|
573 |
//println("Size reduction from "+asize(der_res)+ " to " +asize(simp_res)+" to " + asize(simp_res2))
|
|
|
574 |
blex_simp(simp_res, cs)
|
|
|
575 |
}
|
|
|
576 |
}
|
|
|
577 |
*/
|
|
|
578 |
/*
|
|
|
579 |
def lex_simp(r: Rexp, s: List[Char]) : Val = s match {
|
|
|
580 |
case Nil => {
|
|
|
581 |
if (nullable(r)) {
|
|
|
582 |
mkeps(r)
|
|
|
583 |
}
|
|
|
584 |
else throw new Exception("Not matched")
|
|
|
585 |
}
|
|
|
586 |
case c::cs => {
|
|
|
587 |
val start = System.nanoTime()
|
|
|
588 |
val (r_simp, f_simp) = simp(der(c, r))
|
|
|
589 |
val end = System.nanoTime()
|
|
|
590 |
println((end - start)/1.0e9)
|
|
|
591 |
inj(r, c, f_simp(lex_simp(r_simp, cs)))
|
|
|
592 |
}
|
|
|
593 |
}
|
|
|
594 |
*/
|
|
|
595 |
|
|
|
596 |
//size: of a Aregx for testing purposes
|
|
|
597 |
def size(r: Rexp) : Int = r match {
|
|
|
598 |
case ZERO => 1
|
|
|
599 |
case ONE => 1
|
|
|
600 |
case CHAR(_) => 1
|
|
|
601 |
case SEQ(r1, r2) => 1 + size(r1) + size(r2)
|
|
|
602 |
case ALTS(rs) => 1 + rs.map(size).sum
|
|
|
603 |
case STAR(r) => 1 + size(r)
|
|
|
604 |
}
|
|
|
605 |
|
|
|
606 |
def asize(a: ARexp) = size(erase(a))
|
|
|
607 |
|
|
|
608 |
|
|
|
609 |
// decoding does not work yet
|
|
|
610 |
def blexing_simp(r: Rexp, s: String) = {
|
|
|
611 |
//flats_time.clear()
|
|
|
612 |
//dist_time.clear()
|
|
|
613 |
flats_time = 0L
|
|
|
614 |
dist_time = 0L
|
|
|
615 |
bder_time = 0L
|
|
|
616 |
bsimp_time = 0L
|
|
|
617 |
mkepsBC_time = 0L
|
|
|
618 |
val start = System.nanoTime()
|
|
|
619 |
val bit_code = blex_simp(internalise(r), s.toList)
|
|
|
620 |
val end = System.nanoTime()
|
|
|
621 |
println("total time: "+ (end - start)/1.0e9)
|
|
|
622 |
println("spent on flats: " + (flats_time/(1.0e9)))
|
|
|
623 |
println("spent on distinctBy: " + (dist_time/(1.0e9)))
|
|
|
624 |
println("spent on bder: "+ bder_time/1.0e9)
|
|
|
625 |
println("spent on bsimp: " + bsimp_time/1.0e9)
|
|
|
626 |
println("spent on mkepsBC: " + mkepsBC_time/1.0e9)
|
|
|
627 |
//println(s"The length of the string ${s.length}; length of bit sequence:")
|
|
|
628 |
//println((bit_code.length))
|
|
|
629 |
//println(final_derivative)
|
|
|
630 |
//bit_code
|
|
|
631 |
//decode(r, bit_code)
|
|
|
632 |
}
|
|
|
633 |
|
|
|
634 |
|
|
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635 |
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636 |
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637 |
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638 |
// Lexing Rules for a Small While Language
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639 |
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640 |
//symbols
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641 |
/*
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642 |
val SYM = PRED("abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ".contains(_))
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643 |
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644 |
//digits
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645 |
val DIGIT = PRED("0123456789".contains(_))
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646 |
//identifiers
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647 |
val ID = SYM ~ (SYM | DIGIT).%
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648 |
//numbers
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649 |
val NUM = STAR(DIGIT)
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650 |
//keywords
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651 |
val KEYWORD : Rexp = "skip" | "while" | "do" | "if" | "then" | "else" | "read" | "write" | "true" | "false"
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652 |
val AKEYWORD: Rexp = ALTS(List("skip" , "while" , "do" , "if" , "then" , "else" , "read" , "write" , "true" , "false"))
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653 |
//semicolons
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654 |
val SEMI: Rexp = ";"
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655 |
//operators
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656 |
val OP: Rexp = ":=" | "==" | "-" | "+" | "*" | "!=" | "<" | ">" | "<=" | ">=" | "%" | "/"
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657 |
val AOP: Rexp = ALTS(List(":=" , "==" , "-" , "+" , "*" , "!=" , "<" , ">" , "<=" , ">=" , "%" , "/"))
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658 |
//whitespaces
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659 |
val WHITESPACE = PLUS(" " | "\n" | "\t")
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660 |
//parentheses
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661 |
val RPAREN: Rexp = ")"
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662 |
val LPAREN: Rexp = "("
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663 |
val BEGIN: Rexp = "{"
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|
664 |
val END: Rexp = "}"
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665 |
//strings...but probably needs not
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|
666 |
val STRING: Rexp = "\"" ~ SYM.% ~ "\""
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667 |
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668 |
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669 |
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670 |
val WHILE_REGS = (("k" $ KEYWORD) |
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671 |
("i" $ ID) |
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672 |
("o" $ OP) |
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673 |
("n" $ NUM) |
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674 |
("s" $ SEMI) |
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675 |
("str" $ STRING) |
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676 |
("p" $ (LPAREN | RPAREN)) |
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677 |
("b" $ (BEGIN | END)) |
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|
678 |
("w" $ WHITESPACE)).%
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679 |
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|
680 |
val AWHILE_REGS = (
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|
681 |
ALTS(
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682 |
List(
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|
683 |
("k" $ AKEYWORD),
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|
684 |
("i" $ ID),
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685 |
("o" $ AOP) ,
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686 |
("n" $ NUM) ,
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687 |
("s" $ SEMI) ,
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688 |
("str" $ STRING),
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689 |
("p" $ (LPAREN | RPAREN)),
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690 |
("b" $ (BEGIN | END)),
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691 |
("w" $ WHITESPACE)
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692 |
)
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693 |
)
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694 |
).%
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695 |
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696 |
*/
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697 |
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698 |
|
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699 |
//--------------------------------------------------------------------------------------------------------START OF NON-BITCODE PART (TESTING)
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|
700 |
/*
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|
701 |
// Two Simple While programs
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|
702 |
//========================
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703 |
println("prog0 test")
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704 |
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|
705 |
val prog0 = """read n"""
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706 |
println(env(lexing_simp(WHILE_REGS, prog0)))
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|
707 |
println(tokenise(WHILE_REGS, prog0))
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708 |
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|
709 |
println("prog1 test")
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710 |
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|
711 |
val prog1 = """read n; write (n)"""
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712 |
println(tokenise(WHILE_REGS, prog1))
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713 |
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|
714 |
*/
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715 |
// Bigger Tests
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|
716 |
//==============
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717 |
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|
718 |
def escape(raw: String): String = {
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|
719 |
import scala.reflect.runtime.universe._
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|
720 |
Literal(Constant(raw)).toString
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|
721 |
}
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722 |
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|
723 |
val prog2 = """
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|
724 |
write "Fib";
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725 |
read n;
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|
726 |
minus1 := 0;
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|
727 |
minus2 := 1;
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|
728 |
while n > 0 do {
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|
729 |
temp := minus2;
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|
730 |
minus2 := minus1 + minus2;
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|
731 |
minus1 := temp;
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|
732 |
n := n - 1
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|
733 |
};
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|
734 |
write "Result";
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|
735 |
write minus2
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|
736 |
"""
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737 |
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|
738 |
val prog3 = """
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|
739 |
start := 1000;
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|
740 |
x := start;
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|
741 |
y := start;
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|
742 |
z := start;
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|
743 |
while 0 < x do {
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|
744 |
while 0 < y do {
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|
745 |
while 0 < z do {
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|
746 |
z := z - 1
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|
747 |
};
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|
748 |
z := start;
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|
749 |
y := y - 1
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|
750 |
};
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|
751 |
y := start;
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|
752 |
x := x - 1
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|
753 |
}
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|
754 |
"""
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|
755 |
/*
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|
756 |
for(i <- 400 to 400 by 1){
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|
757 |
println(i+":")
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|
758 |
blexing_simp(WHILE_REGS, prog2 * i)
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|
759 |
} */
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|
760 |
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|
761 |
/*
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|
762 |
for (i <- 2 to 5){
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|
763 |
for(j <- 1 to 3){
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|
764 |
println(i,j)
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|
765 |
small_de = i
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|
766 |
usual_de = i + j
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|
767 |
big_de = i + 2*j
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|
768 |
blexing_simp(AWHILE_REGS, prog2 * 100)
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|
769 |
}
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|
770 |
}*/
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|
771 |
|
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|
772 |
/*
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|
773 |
println("Tokens of prog2")
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|
774 |
println(tokenise(WHILE_REGS, prog2).mkString("\n"))
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|
775 |
|
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|
776 |
val fib_tokens = tokenise(WHILE_REGS, prog2)
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|
777 |
fib_tokens.map{case (s1, s2) => (escape(s1), escape(s2))}.mkString(",\n")
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|
778 |
|
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|
779 |
|
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|
780 |
val test_tokens = tokenise(WHILE_REGS, prog3)
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|
781 |
test_tokens.map{case (s1, s2) => (escape(s1), escape(s2))}.mkString(",\n")
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|
782 |
*/
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|
783 |
|
|
|
784 |
/*
|
|
|
785 |
println("time test for blexing_simp")
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|
|
786 |
for (i <- 1 to 1 by 1) {
|
|
|
787 |
lexing_simp(WHILE_REGS, prog2 * i)
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|
|
788 |
blexing_simp(WHILE_REGS, prog2 * i)
|
|
|
789 |
for( j <- 0 to each_simp_timeb.length - 1){
|
|
|
790 |
if( each_simp_timeb(j)/each_simp_time(j) >= 10.0 )
|
|
|
791 |
println(j, each_simp_timeb(j), each_simp_time(j))
|
|
|
792 |
}
|
|
|
793 |
}
|
|
|
794 |
*/
|
|
|
795 |
|
|
|
796 |
|
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|
797 |
//--------------------------------------------------------------------------------------------------------END OF NON-BITCODE PART (TESTING)
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|
|
798 |
|
|
|
799 |
|
|
|
800 |
|
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|
801 |
def clear() = {
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|
|
802 |
print("")
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|
803 |
//print("\33[H\33[2J")
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|
|
804 |
}
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|
805 |
|
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|
806 |
//testing the two lexings produce the same value
|
|
|
807 |
//enumerates strings of length n over alphabet cs
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|
|
808 |
def strs(n: Int, cs: String) : Set[String] = {
|
|
|
809 |
if (n == 0) Set("")
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|
|
810 |
else {
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|
|
811 |
val ss = strs(n - 1, cs)
|
|
|
812 |
ss ++
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|
|
813 |
(for (s <- ss; c <- cs.toList) yield c + s)
|
|
|
814 |
}
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|
|
815 |
}
|
|
|
816 |
def enum(n: Int, s: String) : Stream[Rexp] = n match {
|
|
|
817 |
case 0 => ZERO #:: ONE #:: s.toStream.map(CHAR)
|
|
|
818 |
case n => {
|
|
|
819 |
val rs = enum(n - 1, s)
|
|
|
820 |
rs #:::
|
|
|
821 |
(for (r1 <- rs; r2 <- rs) yield ALT(r1, r2)) #:::
|
|
|
822 |
(for (r1 <- rs; r2 <- rs) yield SEQ(r1, r2)) #:::
|
|
|
823 |
(for (r1 <- rs) yield STAR(r1))
|
|
|
824 |
}
|
|
|
825 |
}
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|
|
826 |
|
|
|
827 |
//tests blexing and lexing
|
|
|
828 |
def tests_blexer_simp(ss: Set[String])(r: Rexp) = {
|
|
|
829 |
clear()
|
|
|
830 |
//println(s"Testing ${r}")
|
|
|
831 |
for (s <- ss.par) yield {
|
|
|
832 |
val res1 = Try(Some(lexing_simp(r, s))).getOrElse(None)
|
|
|
833 |
val res2 = Try(Some(blexing_simp(r, s))).getOrElse(None)
|
|
|
834 |
if (res1 != res2) println(s"Disagree on ${r} and ${s}")
|
|
|
835 |
if (res1 != res2) println(s" ${res1} != ${res2}")
|
|
|
836 |
if (res1 != res2) Some((r, s)) else None
|
|
|
837 |
}
|
|
|
838 |
}
|
|
|
839 |
|
|
|
840 |
|
|
|
841 |
|
|
|
842 |
//enum(3, "abc").map(tests_blexer_simp(strs(3, "abc"))).toSet
|
|
|
843 |
/*
|
|
|
844 |
def single_expression_explorer(ar: ARexp, ss: Set[String]): Unit = {
|
|
|
845 |
for (s <- ss){
|
|
|
846 |
|
|
|
847 |
val der_res = bder(c, ar)
|
|
|
848 |
val simp_res = bsimp(der_res)
|
|
|
849 |
println(asize(der_res))
|
|
|
850 |
println(asize(simp_res))
|
|
|
851 |
single_expression_explorer(simp_res, (sc - c))
|
|
|
852 |
}
|
|
|
853 |
}*/
|
|
|
854 |
|
|
|
855 |
//single_expression_explorer(internalise(("c"~("a"+"b"))%) , Set('a','b','c'))
|
|
|
856 |
|
|
|
857 |
|
|
|
858 |
}
|
|
|
859 |
|
|
|
860 |
import Rexp.Bits
|
|
|
861 |
abstract class ARexp
|
|
|
862 |
case object AZERO extends ARexp
|
|
|
863 |
case class AONE(bs: Bits) extends ARexp
|
|
|
864 |
case class ACHAR(bs: Bits, f: Char) extends ARexp
|
|
|
865 |
case class AALTS(bs: Bits, rs: List[ARexp]) extends ARexp
|
|
|
866 |
case class ASEQ(bs: Bits, r1: ARexp, r2: ARexp) extends ARexp
|
|
|
867 |
case class ASTAR(bs: Bits, r: ARexp) extends ARexp
|
|
|
868 |
|
|
|
869 |
|
|
|
870 |
|
|
|
871 |
abstract class Val
|
|
|
872 |
case object Empty extends Val
|
|
|
873 |
case class Chr(c: Char) extends Val
|
|
|
874 |
case class Sequ(v1: Val, v2: Val) extends Val
|
|
|
875 |
case class Left(v: Val) extends Val
|
|
|
876 |
case class Right(v: Val) extends Val
|
|
|
877 |
case class Stars(vs: List[Val]) extends Val
|
|
|
878 |
case class Rec(x: String, v: Val) extends Val
|
|
|
879 |
//case class Pos(i: Int, v: Val) extends Val
|
|
|
880 |
case object Prd extends Val
|