import scala.language.implicitConversions    

import scala.language.reflectiveCalls

import scala.annotation.tailrec   

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]

abstract class Rexp 

case object ZERO extends Rexp

case object ONE extends Rexp

case class PRED(f: Char => Boolean) 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

// abbreviations

def CHAR(c: Char) = PRED(_ == c)

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

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

abstract class ARexp 

case object AZERO extends ARexp

case class AONE(bs: Bits) extends ARexp

case class APRED(bs: Bits, f: Char => Boolean) 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 

// abbreviations

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

// some convenience for typing in regular expressions

def charlist2rexp(s : List[Char]): Rexp = s match {

  case Nil => ONE

  case c::Nil => CHAR(c)

  case c::s => SEQ(CHAR(c), charlist2rexp(s))

}

implicit def string2rexp(s : String) : Rexp = charlist2rexp(s.toList)

implicit def RexpOps(r: Rexp) = new {

  def | (s: Rexp) = ALT(r, s)

  def % = STAR(r)

  def ~ (s: Rexp) = SEQ(r, s)

}

implicit def stringOps(s: String) = new {

  def | (r: Rexp) = ALT(s, r)

  def | (r: String) = ALT(s, r)

  def % = STAR(s)

  def ~ (r: Rexp) = SEQ(s, r)

  def ~ (r: String) = SEQ(s, r)

  def $ (r: Rexp) = RECD(s, r)

}

// translation into ARexps

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

  case AZERO => AZERO

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

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

  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)

  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)

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

}

// nullable function: tests whether the aregular 

// expression can recognise the empty string

def nullable (r: ARexp) : Boolean = r match {

  case AZERO => false

  case AONE(_) => true

  case APRED(_,_) => false

  case AALTS(_, rs) => rs.exists(nullable)

  case ASEQ(_, r1, r2) => nullable(r1) && nullable(r2)

  case ASTAR(_, _) => true

}

def mkepsBC(r: ARexp) : Bits = r match {

  case AONE(bs) => bs

  case AALTS(bs, rs) => {

    val n = rs.indexWhere(nullable)

    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 der(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(der(c, _)))

  case ASEQ(bs, r1, r2) => 

    if (nullable(r1)) AALT(bs, ASEQ(Nil, der(c, r1), r2), fuse(mkepsBC(r1), der(c, r2)))

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

  case ASTAR(bs, r) => ASEQ(bs, fuse(List(S), der(c, r)), ASTAR(Nil, r))

}

// derivative w.r.t. a string (iterates der)

@tailrec

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

  case Nil => r

  case c::s => ders(s, der(c, r))

}

// main unsimplified lexing function (produces a value)

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

  case Nil => if (nullable(r)) mkepsBC(r) else throw new Exception("Not matched")

  case c::cs => lex(der(c, r), cs)

}

def pre_lexing(r: Rexp, s: String) = lex(internalise(r), s.toList)

//def lexing(r: Rexp, s: String) : Val = decode(r, lex(internalise(r), s.toList))

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 simp(r: ARexp): ARexp = r match {

  case ASEQ(bs1, r1, r2) => (simp(r1), simp(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(simp)), erase) match {

    case Nil => AZERO

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

    case rs => AALTS(bs1, rs)  

  }

  case r => r

}

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

  case Nil => r

  case c::s => ders_simp(s, simp(der(c, r)))

}

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

  case Nil => {

    if (nullable(r)) {

      //println(asize(r))

      mkepsBC(r)

    }

   else throw new Exception("Not matched")

  }

  case c::cs => lex_simp(simp(der(c, r)), cs)

}

//size: of a Aregx 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)

}

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

// decoding does not work yet

def lexing_simp(r: Rexp, s: String) = {

  val final_derivative = lex_simp(internalise(r), s.toList)

  println("The length of bit sequence:")

  println((final_derivative.length))

  //println(final_derivative)

  decode(r, final_derivative) 

  //println(vsize(value))

}

// 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 = PLUS(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)).%

// 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))

// Some Tests

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

println("simple tests:")

println(lexing_simp((SYM.%), "abcd"))

println(lexing_simp(((SYM.%) | NUM), "12345"))

println(lexing_simp((WHILE_REGS), "abcd"))

println(lexing_simp((WHILE_REGS), "12345"))

println(lexing_simp((WHILE_REGS), """write "Fib";"""))

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

  val start = System.nanoTime()

  val result = code

  val end = System.nanoTime()

  println((end - start)/1.0e9)

  result

}

val prog2 = """

write "Fib";

read n;

minus1 := 0;

minus2 := 1;

while n > 0 do {

  temp := minus2;

  minus2 := minus1 + minus2;

  minus1 := temp;

  n := n -x 1

};

write "Result";

write minus2

"""

/*

val prog2 = """

write "Fib";

"""

*/

println("Iteration test with fib")

for (i <- 900 to 1000 by 50) {

  print(i.toString + ":  ")

  time(lexing_simp((WHILE_REGS), (prog2 * i)))

  //time(lex_simp(internalise(WHILE_REGS), (prog2 * i).toList))

}