import scala.language.implicitConversions    

import scala.language.reflectiveCalls

import scala.annotation.tailrec   

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 ARexp 

case object AZERO extends ARexp

case class AONE(bs: List[Boolean]) extends ARexp

case class ACHAR(bs: List[Boolean], c: Char) extends ARexp

case class AALT(bs: List[Boolean], r1: ARexp, r2: ARexp) extends ARexp 

case class ASEQ(bs: List[Boolean], r1: ARexp, r2: ARexp) extends ARexp 

case class ASTAR(bs: List[Boolean], 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

// 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: List[Boolean], r: ARexp) : ARexp = r match {

  case AZERO => AZERO

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

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

  case AALT(cs, r1, r2) => AALT(bs ++ cs, r1, r2)

  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(false), internalise(r1)), fuse(List(true), internalise(r2)))

  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: List[Boolean]) : (Val, List[Boolean]) = (r, bs) match {

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

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

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

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

    (Left(v), bs1)

  }

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

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

    (Right(v), bs1)

  }

  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), false::bs) => {

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

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

    (Stars(v::vs), bs2)

  }

  case (STAR(_), true::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: List[Boolean]) = decode_aux(r, bs) match {

  case (v, Nil) => v

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

}

// 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 ACHAR(_,_) => false

  case AALT(_, r1, r2) => nullable(r1) || nullable(r2)

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

  case ASTAR(_, _) => true

}

def mkepsBC(r: ARexp) : List[Boolean] = r match {

  case AONE(bs) => bs

  case AALT(bs, r1, r2) => 

    if (nullable(r1)) bs ++ mkepsBC(r1) else bs ++ mkepsBC(r2)

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

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

}

// 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 ACHAR(bs, d) => if (c == d) AONE(bs) else AZERO

  case AALT(bs, r1, r2) => AALT(bs, der(c, r1), der(c, r2))

  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(false), 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]) : List[Boolean] = s match {

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

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

}

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

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 AALT(bs1, r1, r2) => (simp(r1), simp(r2)) match {

      case (AZERO, r2s) => fuse(bs1, r2s)

      case (r1s, AZERO) => fuse(bs1, r1s)

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

  }

  case r => r

}

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

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

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

}

def lexing_simp(r: Rexp, s: String) : Val = decode(r, lex_simp(internalise(r), s.toList))

// 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

  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 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 r0 = ("a" | "ab") ~ ("b" | "")

println(lexing(r0, "ab"))

println(lexing_simp(r0, "ab"))

val r1 = ("a" | "ab") ~ ("bcd" | "cd")

println(lexing(r1, "abcd"))

println(lexing_simp(r1, "abcd"))

println(lexing((("" | "a") ~ ("ab" | "b")), "ab"))

println(lexing_simp((("" | "a") ~ ("ab" | "b")), "ab"))

println(lexing((("" | "a") ~ ("b" | "ab")), "ab"))

println(lexing_simp((("" | "a") ~ ("b" | "ab")), "ab"))

println(lexing((("" | "a") ~ ("c" | "ab")), "ab"))

println(lexing_simp((("" | "a") ~ ("c" | "ab")), "ab"))

// Two Simple Tests for the While Language

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

// Lexing Rules 

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

val SYM = "a" | "b" | "c" | "d" | "e" | "f" | "g" | "h" | "i" | "j" | "k" | "l" | "m" | "n" | "o" | "p" | "q" | "r" | "s" | "t" | "u" | "v" | "w" | "x" | "y" | "z"

val DIGIT = "0" | "1" | "2" | "3" | "4" | "5" | "6" | "7" | "8" | "9"

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

val NUM = PLUS(DIGIT)

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

val SEMI: Rexp = ";"

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

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

val RPAREN: Rexp = ")"

val LPAREN: Rexp = "("

val BEGIN: Rexp = "{"

val END: Rexp = "}"

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)).%

println("prog0 test")

val prog0 = """read n"""

println(env(lexing(WHILE_REGS, prog0)))

println(env(lexing_simp(WHILE_REGS, prog0)))

println("prog1 test")

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

println(env(lexing(WHILE_REGS, prog1)))

println(env(lexing_simp(WHILE_REGS, prog1)))

// Sulzmann's tests

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

val sulzmann = ("a" | "b" | "ab").%

println(lexing(sulzmann, "a" * 10))

println(lexing_simp(sulzmann, "a" * 10))

for (i <- 1 to 6501 by 500) {

  println(i + ": " + "%.5f".format(time_needed(1, lexing_simp(sulzmann, "a" * i))))

}

for (i <- 1 to 16 by 5) {

  println(i + ": " + "%.5f".format(time_needed(1, lexing_simp(sulzmann, "ab" * i))))

}