import scala.language.implicitConversions    

import scala.language.reflectiveCalls

import scala.annotation.tailrec   

import scala.util.Try

// for escaping strings

def escape(raw: String) : String = {

  import scala.reflect.runtime.universe._

  Literal(Constant(raw)).toString

}

def esc2(r: (String, String)) = (escape(r._1), escape(r._2))

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)

  }

} 

abstract class Bit

case object Z extends Bit

case object S extends Bit

case class C(c: Char) extends Bit

type Bits = List[Bit]

// usual regular expressions with predicates

abstract class Rexp 

case object ZERO extends Rexp

case object ONE extends Rexp

case class PRED(f: Char => Boolean, s: String = "_") extends Rexp {

  override def toString = s"PRED(${s})"

}

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

// abbreviations

def CHAR(c: Char) = PRED(_ == c, c.toString)

def ALT(r1: Rexp, r2: Rexp) = ALTS(List(r1, r2))

def PLUS(r: Rexp) = SEQ(r, STAR(r))

val ANYCHAR = PRED(_ => true, ".")

// annotated regular expressions

abstract class ARexp 

case object AZERO extends ARexp

case class AONE(bs: Bits) extends ARexp

case class APRED(bs: Bits, f: Char => Boolean, s: String = "_") extends ARexp {

  override def toString = s"APRED(${bs}, ${s})"

}

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 

// abbreviations

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

// values

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

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)

}

// 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)

}

// string of a regular expression - for testing purposes

def string(r: Rexp): String = r match {

  case ZERO => "0"

  case ONE => "1"

  case PRED(_, s) => s

  case ALTS(rs) => rs.map(string).mkString("[", "|", "]")

  case SEQ(r1, r2) => s"(${string(r1)} ~ ${string(r2)})"

  case STAR(r) => s"{${string(r)}}*"

  case RECD(x, r) => s"(${x}! ${string(r)})"

}

// string of an annotated regular expression - for testing purposes

def astring(a: ARexp): String = a match {

  case AZERO => "0"

  case AONE(_) => "1"

  case APRED(_, _, s) => s

  case AALTS(_, rs) => rs.map(astring).mkString("[", "|", "]")

  case ASEQ(_, r1, r2) => s"(${astring(r1)} ~ ${astring(r2)})"

  case ASTAR(_, r) => s"{${astring(r)}}*"

}

//--------------------------------------------------------------------

// BITCODED PART

def retrieve(r: ARexp, v: Val) : Bits = (r, v) match {

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

  case (APRED(bs, _, _), Chr(d)) => bs

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

  case (AALTS(bs, r::rs), Left(v)) => bs ++ retrieve(r, v)

  case (AALTS(bs, r::rs), Right(v)) => bs ++ retrieve(AALTS(Nil, rs), v)

  case (ASEQ(bs, r1, r2), Sequ(v1, v2)) => 

    bs ++ retrieve(r1, v1) ++ retrieve(r2, v2)

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

  case (ASTAR(bs, r), Stars(v::vs)) => 

     bs ++ List(Z) ++ retrieve(r, v) ++ retrieve(ASTAR(Nil, r), Stars(vs))

}

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

  case AZERO => AZERO

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

  case APRED(cs, f, s) => APRED(bs ++ cs, f, s)

  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)

}

// translation into ARexps

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

  case ZERO => AZERO

  case ONE => AONE(Nil)

  case PRED(f, s) => APRED(Nil, f, s)

  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" | ""))

// decoding of values from bit sequences

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)

  case (ALTS(rs), Z::bs1) => {

      val (v, bs2) = decode_aux(rs.head, bs1)

      (Left(v), bs2)

    }

  case (ALTS(rs), 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)

    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")

}

def encode(v: Val) : Bits = v match {

  case Empty => Nil

  case Chr(c) => Nil

  case Left(v) => Z :: encode(v)

  case Right(v) => S :: encode(v)

  case Sequ(v1, v2) => encode(v1) ::: encode(v2)

  case Stars(Nil) => List(S)

  case Stars(v::vs) => Z :: encode(v) ::: encode(Stars(vs))

}

//erase function: extracts a Rexp from Arexp

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

  case AZERO => ZERO

  case AONE(_) => ONE

  case APRED(bs, f, s) => PRED(f, s)

  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))

}

// 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 APRED(_,_,_) => 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, rs) => {

    val n = rs.indexWhere(bnullable)

    bs ++ bmkeps(rs(n))

  }

  case ASEQ(bs, r1, r2) => bs ++ bmkeps(r1) ++ bmkeps(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 APRED(bs, f, _) => if (f(c)) 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(bmkeps(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 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)

}

def preblexing(r: ARexp, s: String) : Val = 

 decode(erase(r), blex(r, s.toList))

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

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

// 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 vsimp(r: ARexp, v: Val): Val = (r, v) match {

  case (ASEQ(bs1, r1, r2), Sequ(v1, v2)) => 

    (bsimp(r1), bsimp(r2), vsimp(r1, v1), vsimp(r2, v2)) match {

      case (AZERO, _, _, _) => throw new Exception("error")

      case (_, AZERO, _, _) => throw new Exception("error")

      case (AONE(_), _, _, vp2) => vp2

      case (r1s, r2s, vp1, vp2) => Sequ(vp1, vp2) 

  }

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

    case Nil => throw new Exception("error")

    case r :: Nil => throw new Exception("error")

    case rs => throw new Exception("error")

  }

  case _ => v

}

*/

def vsimp(v: Val, a: ARexp): Val = (v, bsimp(a)) match {

  case (Sequ(v1, v2), ASEQ(_, a1, a2)) => 

    (vsimp(v1, a1), vsimp(v2, a2)) match {

        case (Empty, vp2) => vp2

        case (vp1, vp2) => Sequ(vp1, vp2) 

    }

  case (Left(Left(v1)), AALTS(_, r::rs)) => Left(vsimp(v1, r)) 

  case (Left(v1), AALTS(_, rs)) => 

    if (rs.length == 1) vsimp(v1, rs.head) else Left(vsimp(v1, rs.head)) 

  case (Right(v1), AALTS(bs, rs)) => 

    if (rs.length == 1) vsimp(v1, rs.head) else Right(vsimp(v1, AALTS(bs, rs.tail)))

  case _ => v

}

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) => distinctBy(flats(rs.map(bsimp)), erase) match {

    case Nil => AZERO

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

    case rs => AALTS(bs1, rs)  

  }

  case r => r

}

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 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)

}

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

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

def btokenise_simp(r: Rexp, s: String) = 

  env(blexing_simp(r, s)).map(esc2)

// Quick example

val r : Rexp = ZERO | "a" 

lexing(r, "a")

val a0 = internalise(r)

val a1 = bder('a', a0)

val a1s = bsimp(bder('a', a0))

val a2 = bmkeps(a1)

val a2s = bmkeps(a1s)

val v  = decode(r, a2)

val vs  = decode(r, a2s)

val Rr : Rexp = ONE ~ "a" 

lexing(Rr, "a")

val Ra0 = internalise(Rr)

astring(Ra0)

val Ra1 = bder('a', Ra0)

astring(Ra1)

val Ra1s = bsimp(bder('a', Ra0))

astring(Ra1s)

val Ra2 = bmkeps(Ra1)

val Ra2s = bmkeps(Ra1s)

val Rv  = decode(Rr, Ra2)

val Rvs  = decode(Rr, Ra2s)

//   Testing

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

def time[T](code: => T) = {

  val start = System.nanoTime()

  val result = code

  val end = System.nanoTime()

  ((end - start)/1.0e9).toString

}

def timeR[T](code: => T) = {

  val start = System.nanoTime()

  for (i <- 1 to 10) code

  val result = code

  val end = System.nanoTime()

  (result, (end - start))

}

//size: of a Rrexp and ARexp for testing purposes 

def size(r: Rexp) : Int = r match {

  case ZERO => 1

  case ONE => 1

  case PRED(_,_) => 1

  case SEQ(r1, r2) => 1 + size(r1) + size(r2)

  case ALTS(rs) => 1 + rs.map(size).sum

  case STAR(r) => 1 + size(r)

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

}

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

// Lexing Rules for a Small While Language

//symbols

val SYM = PRED("abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ".contains(_), "SYM")

//digits

val DIGIT = PRED("0123456789".contains(_), "NUM")

//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"

//semicolons

val SEMI: Rexp = ";"

//operators

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

//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)).%

// Some Small Tests

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

println("Small tests")

val re1 = STAR("a" | "aa")

println(astring(bders_simp("".toList, internalise(re1))))

println(astring(bders_simp("a".toList, internalise(re1))))

println(astring(bders_simp("aa".toList, internalise(re1))))

println(astring(bders_simp("aaa".toList, internalise(re1))))

println(astring(bders_simp("aaaaaa".toList, internalise(re1))))

println(astring(bders_simp("aaaaaaaaa".toList, internalise(re1))))

println(astring(bders_simp("aaaaaaaaaaaa".toList, internalise(re1))))

println(astring(bders_simp("aaaaaaaaaaaaaaaaaaaaaaaaa".toList, internalise(re1))))

println(astring(bders_simp("aaaaaabaaaabbbbbaaaaaaaaaaaaaaa".toList, internalise(re1))))

for (i <- 0 to 100 by 5) {

  //print("Old: " + time(tokenise_simp(re1, "a" * i)))

  print(" Bit: " + time(btokenise_simp(re1, "a" * i)))

  print(" Bit full simp: " + time(btokenise_simp_full(re1, "a" * i)))

  println(" Bit2: " + time(btokenise2_simp(re1, "a" * i)))

}

Console.readLine

// Bigger Tests

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

println("Big tests")

val fib_prog = """

write "Fib";