// uses bitcode sequences and annotated regular 

// expressions

//

// for basic regular expressions and RECD

//

// uses a non-standard extraction method for generating

// tokens (this is tail-recursive) 

//

// can match 60 copies of the fib-program (size 10500)

// in about 20 secs

import scala.language.implicitConversions    

import scala.language.reflectiveCalls

import scala.annotation.tailrec   

// standard regular expressions

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 Bit

case object Z extends Bit

case object S extends Bit

type Bits = List[Bit]

// annotated regular expressions

abstract class ARexp 

case object AZERO extends ARexp

case class AONE(bs: Bits) extends ARexp

case class ACHAR(bs: Bits, c: 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 

// an abbreviation for binary alternatives

def AALT(bs: Bits, r1: ARexp, r2: ARexp) = AALTS(bs, List(r1, r2))

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 Recd(x: String, v: Val) extends Val

abstract class BTree

case object LZ extends BTree

case class L(bs: Bits) extends BTree

case class LALTS(bs: Bits, bts: List[BTree]) extends BTree 

case class LSEQ(bs: Bits, bt1: BTree, bt2: BTree) extends BTree 

case class LSTAR(bs: Bits, bt: BTree) extends BTree

def ext(r: ARexp): BTree = r match {

  case AZERO => LZ

  case AONE(bs) => L(bs)

  case ACHAR(bs, _) => L(bs)

  case AALTS(bs, rs) => LALTS(bs, rs.map(ext))

  case ASEQ(bs, r1, r2) => LSEQ(bs, ext(r1), ext(r2))

  case ASTAR(bs, r) => LSTAR(bs, ext(r))

}

// annotated regular expressions

abstract class BRexp 

case object BZERO extends BRexp

case object BONE extends BRexp

case class BCHAR(c: Char) extends BRexp

case class BALTS(rs: List[BRexp]) extends BRexp 

case class BSEQ(r1: BRexp, r2: BRexp) extends BRexp 

case class BSTAR(r: BRexp) extends BRexp 

def ex(r: ARexp): BRexp = r match {

  case AZERO => BZERO

  case AONE(_) => BONE

  case ACHAR(_, c) => BCHAR(c)

  case AALTS(_, rs) => BALTS(rs.map(ex))

  case ASEQ(_, r1, r2) => BSEQ(ex(r1), ex(r2))

  case ASTAR(_, r) => BSTAR(ex(r))

}

// 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)

}

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)

}

// Bitcoded + Annotation

//=======================

//erase function: extracts the Rexp from ARexp

def erase(r:ARexp): Rexp = r match{

  case AZERO => ZERO

  case AONE(_) => ONE

  case ACHAR(bs, c) => CHAR(c)

  case AALTS(bs, Nil) => ZERO

  case AALTS(bs, r::Nil) => erase(r)

  case AALTS(bs, r::rs) => ALT(erase(r), erase(AALTS(bs, rs)))

  case ASEQ(bs, r1, r2) => SEQ (erase(r1), erase(r2))

  case ASTAR(cs, r)=> STAR(erase(r))

}

def fuse(bs: Bits, r: ARexp) : ARexp = r match {

  case AZERO => AZERO

  case AONE(cs) => AONE(bs ++ cs)

  case ACHAR(cs, c) => ACHAR(bs ++ cs, c)

  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 ALT(r1, r2) => AALT(Nil, fuse(List(Z), internalise(r1)), fuse(List(S), internalise(r2)))

  case SEQ(r1, r2) => ASEQ(Nil, internalise(r1), internalise(r2))

  case STAR(r) => ASTAR(Nil, internalise(r))

  case RECD(_, r) => internalise(r)

}

// example

// internalise(("a" | "ab") ~ ("b" | ""))

// decoding of a value from a bitsequence

// (this is not tail-recursive and therefore a potential bottleneck)

def vdecode_aux(r: Rexp, bs: Bits) : (Val, Bits) = (r, bs) match {

  case (ONE, bs) => (Empty, bs)

  case (CHAR(c), bs) => (Chr(c), bs)

  case (ALT(r1, r2), Z::bs) => {

    val (v, bs1) = vdecode_aux(r1, bs)

    (Left(v), bs1)

  }

  case (ALT(r1, r2), S::bs) => {

    val (v, bs1) = vdecode_aux(r2, bs)

    (Right(v), bs1)

  }

  case (SEQ(r1, r2), bs) => {

    val (v1, bs1) = vdecode_aux(r1, bs)

    val (v2, bs2) = vdecode_aux(r2, bs1)

    (Sequ(v1, v2), bs2)

  }

  case (STAR(r1), Z::bs) => {

    val (v, bs1) = vdecode_aux(r1, bs)

    val (Stars(vs), bs2) = vdecode_aux(STAR(r1), bs1)

    (Stars(v::vs), bs2)

  }

  case (STAR(_), S::bs) => (Stars(Nil), bs)

  case (RECD(s, r1), bs) => 

    val (v, bs1) = vdecode_aux(r1, bs)

    (Recd(s, v), bs1)

}

def vdecode(r: Rexp, bs: Bits) = vdecode_aux(r, bs) match {

  case (v, Nil) => v

  case _ => throw new Exception("Not decodable")

}

// decoding of sequence of string tokens from a bitsequence

// tail-recursive version using an accumulator (alternative for 

// vdecode)

@tailrec

def sdecode_aux(rs: List[Rexp], bs: Bits, acc: List[String]) : List[String] = (rs, bs) match {

  case (Nil, _) => acc

  case (_, Nil) => acc

  case (ONE::rest, bs) => sdecode_aux(rest, bs, acc)

  case (CHAR(c)::rest, bs) => 

    sdecode_aux(rest, bs, (acc.head ++ c.toString)::acc.tail)

  case (ALT(r1, r2)::rest, Z::bs) => sdecode_aux(r1::rest, bs, acc)

  case (ALT(r1, r2)::rest, S::bs) => sdecode_aux(r2::rest, bs, acc)

  case (SEQ(r1, r2)::rest, bs) => sdecode_aux(r1::r2::rest, bs, acc)

  case (STAR(r1)::rest, Z::bs) => sdecode_aux(r1::STAR(r1)::rest, bs, acc)

  case (STAR(_)::rest, S::bs) => sdecode_aux(rest, bs, acc)

  case (RECD(s, r1)::rest, bs) => 

    sdecode_aux(r1::rest, bs, s"$s:"::acc)

}

def sdecode(r: Rexp, bs: Bits) : List[String] = 

  sdecode_aux(List(r), bs, List("")).reverse.tail

// nullable function: tests whether the an (annotated) 

// regular 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 bmkeps(r: ARexp) : Bits = r match {

  case AONE(bs) => bs

  case AALTS(bs, r::Nil) => bs ++ bmkeps(r) 

  case AALTS(bs, r::rs) => 

    if (bnullable(r)) bs ++ bmkeps(r) else bmkeps(AALTS(bs, rs))  

  case ASEQ(bs, r1, r2) => bs ++ bmkeps(r1) ++ bmkeps(r2)

  case ASTAR(bs, r) => bs ++ List(S)

}

// 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, d) => if (c == d) AONE(bs) 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(bmkeps(r1), bder(c, r2)))

    else ASEQ(bs, bder(c, r1), r2)

  case ASTAR(bs, r) => ASEQ(bs, fuse(List(Z), bder(c, r)), ASTAR(Nil, 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))

}

// main unsimplified lexing function (produces a bitsequence)

def blex(r: ARexp, s: List[Char]) : Bits = s match {

  case Nil => if (bnullable(r)) bmkeps(r) else throw new Exception("Not matched")

  case c::cs => blex(bder(c, r), cs)

}

// calls blex and decodes the value

def blexing(r: Rexp, s: String) : Val = 

  vdecode(r, blex(internalise(r), s.toList))

// example by Tudor

//val reg = (STAR("a") ~ ("b" | "c")).%

//println(blexing(reg, "aab"))

//=======================

// simplification 

//

def flts(rs: List[ARexp]) : List[ARexp] = rs match {

  case Nil => Nil

  case AZERO :: rs => flts(rs)

  case AALTS(bs, rs1) :: rs => rs1.map(fuse(bs, _)) ++ flts(rs)

  case r1 :: rs => r1 :: flts(rs)

}

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)

      // needed in order to keep the size down

      case (AALTS(bs, rs), r2) => AALTS(bs1 ++ bs, rs.map(ASEQ(Nil, _, r2)))

      case (r1s, r2s) => ASEQ(bs1, r1s, r2s)

  }

  // distinctBy deletes copies of the same  "erased" regex

  case AALTS(bs1, rs) => (flts(rs.map(bsimp))).distinctBy(erase) match {

      case Nil => AZERO

      case r::Nil => fuse(bs1, r)

      case rs => AALTS(bs1, rs)

  }

  case r => r

}

def blex_simp(r: ARexp, s: List[Char]) : Bits = s match {

  case Nil => if (bnullable(r)) bmkeps(r) 

              else throw new Exception("Not matched")

  case c::cs => blex_simp(bsimp(bder(c, r)), cs)

}

// blexing_simp decodes a value from the bitsequence (potentially slow)

// blexing2_simp decodes a string-list from the bitsequence

def blexing_simp(r: Rexp, s: String) : Val = 

  vdecode(r, blex_simp(internalise(r), s.toList))

def blexing2_simp(r: Rexp, s: String) : List[String] = 

  sdecode(r, blex_simp(internalise(r), s.toList))

//println(blexing_simp(reg, "aab"))

// 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

}

// 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 Recd(x, v) => (x, flatten(v))::env(v)

}

def bsize(a: ARexp) = size(erase(a))

// Some Tests

//============

def time_needed[T](i: Int, code: => T) = {

  val start = System.nanoTime()

  for (j <- 1 to i) code

  val end = System.nanoTime()

  (end - start)/(i * 1.0e9)

}

/*

val evil1 = STAR(STAR("a")) ~ "b"

val evil2 = STAR(STAR(STAR("a"))) ~ "b"

val evil3 = STAR("aa" | "a")

for(i <- 0 to 10000 by 1000) {

    println(time_needed(1, blexing2_simp(evil1, "a"*i ++ "b")))

}

for(i <- 0 to 10000 by 1000) {

    println(time_needed(1, blexing2_simp(evil2, "a"*i ++ "b")))

}

for(i <- 0 to 10000 by 1000) {

    println(time_needed(1, blexing2_simp(evil3, "a"*i)))

}

*/

// WHILE LANGUAGE

//================

def PLUS(r: Rexp) = r ~ r.%

def Range(s : List[Char]) : Rexp = s match {

  case Nil => ZERO

  case c::Nil => CHAR(c)

  case c::s => ALT(CHAR(c), Range(s))

}

def RANGE(s: String) = Range(s.toList)

val SYM = RANGE("ABCDEFGHIJKLMNOPQRSTUVXYZabcdefghijklmnopqrstuvwxyz_")

val DIGIT = RANGE("0123456789")

val ID = SYM ~ (SYM | DIGIT).% 

val NUM = PLUS(DIGIT)

val KEYWORD : Rexp = "skip" | "while" | "do" | "if" | "then" | "else" | "read" | "write" 

val SEMI: Rexp = ";"

val OP: Rexp = ":=" | "=" | "-" | "+" | "*" | "!=" | "<" | ">"

val WHITESPACE = PLUS(" " | "\n" | "\t")

val RPAREN: Rexp = "{"

val LPAREN: Rexp = "}"

val STRING: Rexp = "\"" ~ SYM.% ~ "\""

val WHILE_REGS = (("k" $ KEYWORD) | 

                  ("i" $ ID) | 

                  ("o" $ OP) | 

                  ("n" $ NUM) | 

                  ("s" $ SEMI) | 

                  ("str" $ STRING) |

                  ("p" $ (LPAREN | RPAREN)) | 

                  ("w" $ WHITESPACE)).%

// Some Simple While Tests

//========================

val prog0 = """read n"""

println(s"test: $prog0")

println(env(blexing_simp(WHILE_REGS, prog0)))

println(blexing2_simp(WHILE_REGS, prog0))

val prog1 = """read  n; write n"""  

println(s"test: $prog1")

println(env(blexing_simp(WHILE_REGS, prog1)))

println(blexing2_simp(WHILE_REGS, prog1))

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

"""

println("lexing fib program (once)")

println(blexing2_simp(WHILE_REGS, prog2).filter(s => s == "" || !s.startsWith("w")))

val n = 60

println(s"lexing fib program ($n times, size ${prog2.length * n})")

println(time_needed(1, blexing2_simp(WHILE_REGS, prog2 * n)))