/* lexer without simplification */

import scala.language.implicitConversions    

import scala.language.reflectiveCalls

import scala.annotation.tailrec   

import scala.io.Source

import scala.util._

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 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)

}

def Alts(rs: List[Rexp]) : Rexp = rs match {

  case Nil => ZERO

  case r::Nil => r

  case r::rs => ALT(r, Alts(rs))

}

def ALTS(rs: Rexp*) = Alts(rs.toList)

def Seqs(rs: List[Rexp]) : Rexp = rs match {

  case Nil => ONE

  case r::Nil => r

  case r::rs => SEQ(r, Seqs(rs))

}

def SEQS(rs: Rexp*) = Seqs(rs.toList)

// nullable function: tests whether the regular 

// expression can recognise the empty string

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

  case ZERO => false

  case ONE => true

  case CHAR(_) => false

  case ALT(r1, r2) => nullable(r1) || nullable(r2)

  case SEQ(r1, r2) => nullable(r1) && nullable(r2)

  case STAR(_) => true

  case RECD(_, r1) => nullable(r1)

}

// derivative of a regular expression w.r.t. a character

def der (c: Char, r: Rexp) : Rexp = r match {

  case ZERO => ZERO

  case ONE => ZERO

  case CHAR(d) => if (c == d) ONE else ZERO

  case ALT(r1, r2) => ALT(der(c, r1), der(c, r2))

  case SEQ(r1, r2) => 

    if (nullable(r1)) ALT(SEQ(der(c, r1), r2), der(c, r2))

    else SEQ(der(c, r1), r2)

  case STAR(r) => SEQ(der(c, r), STAR(r))

  case RECD(_, r1) => der(c, r1)

}

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

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

  case Nil => r

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

}

def closed_seq_ders()

def ders2(s: List[Char], r: Rexp) : Rexp = (s, r) match {

  case (Nil, r) => r

  case (s, ZERO) => ZERO

  case (s, ONE) => if (s == Nil) ONE else ZERO

  case (s, CHAR(c)) => if (s == List(c)) ONE else 

                       if (s == Nil) CHAR(c) else ZERO

  case (s, ALT(r1, r2)) => ALT(ders2(s, r1), ders2(s, r2))

  case (c::s, r) => ders2(s, simp(der(c, r)))

}

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

def cders (s: List[Char], r: Rexp) : Rexp = s match {

  case ZERO => ZERO

  case ONE => ZERO

  case CHAR(d) => if (s == List(d)) ONE else ZERO

  case ALT(r1, r2) => ALT(cders(s, r1), cders(s, r2))

  case SEQ(r1, r2) => closed_seq_ders(r1, r2, s)     ???

  case STAR(r) => SEQ(cders(s, r), STAR(r)) ???

  case RECD(_, r1) => cders(s, r1)

}

// 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)

}

// injection part

def mkeps(r: Rexp) : Val = r match {

  case ONE => Empty

  case ALT(r1, r2) => 

    if (nullable(r1)) Left(mkeps(r1)) else Right(mkeps(r2))

  case SEQ(r1, r2) => Sequ(mkeps(r1), mkeps(r2))

  case STAR(r) => Stars(Nil)

  case RECD(x, r) => Rec(x, mkeps(r))

}

def inj(r: Rexp, c: Char, v: Val) : Val = (r, v) match {

  case (STAR(r), Sequ(v1, Stars(vs))) => Stars(inj(r, c, v1)::vs)

  case (SEQ(r1, r2), Sequ(v1, v2)) => Sequ(inj(r1, c, v1), v2)

  case (SEQ(r1, r2), Left(Sequ(v1, v2))) => Sequ(inj(r1, c, v1), v2)

  case (SEQ(r1, r2), Right(v2)) => Sequ(mkeps(r1), inj(r2, c, v2))

  case (ALT(r1, r2), Left(v1)) => Left(inj(r1, c, v1))

  case (ALT(r1, r2), Right(v2)) => Right(inj(r2, c, v2))

  case (CHAR(d), Empty) => Chr(c) 

  case (RECD(x, r1), _) => Rec(x, inj(r1, c, v))

}

// main lexing function (produces a value)

def lex(r: Rexp, s: List[Char]) : Val = s match {

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

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

}

def lexing(r: Rexp, s: String) : Try[Val] = Try(lex(r, s.toList))

// Examples

val K: Rexp = "a" | "b"

val I: Rexp = "ab" | "ba"  

println(lexing((K | I).%, "abab"))

val K2: Rexp = ("key" $ "a" | "b")

val I2: Rexp = ("id" $ ("ab" | "ba"))  

println(lexing((K2 | I2).%, "abaa"))

println(env(lexing((K2 | I2).%, "abaa")))

val r1: Rexp = "abc"

val r2: Rexp = der('a', r1)

val r3: Rexp = der('b', r2)

val r4: Rexp = der('c', r3)

println(r1)

println(r2)

println(r3)

println(r4)

// time keeping

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)

}

// first benchmark regex 

val reWord = ALTS("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","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","0","1","2","3","4","5","6","7","8","9")

val reWordStar = STAR(reWord)

val reWordPlus = reWord ~ reWordStar

val optionSet1 = "-" | "+" | "."

val optionSet2 = "-" | "."

val atTheRate = "@"

val period = "."

val optionSet3 = "," | ";"

val whitespace = " "

val re01 = reWordPlus

val re02 = STAR(optionSet1 ~ reWordPlus)

val re03 = atTheRate

val re04 = reWordPlus

val re05 = STAR(optionSet2 ~ reWordPlus)

val re06 = period

val re07 = reWordPlus

val re08 = re05

val re09 = optionSet3

val re10 = STAR(whitespace)

val re11 = reWordPlus

val re12 = re02

val re13 = atTheRate

val re14 = reWordPlus

val re15 = re05

val re16 = period

val re17 = reWordPlus

val re18 = re05

val re01_08 = SEQS(re01, re02, re03, re04, re05, re06, re07, re08)

val re09_10 = re09 ~ re10

val re11_18 = re01_08

val re = re01_08 ~ STAR(re09_10 ~ re11_18)

def process(s: String, i: Int) : Unit = {

  println(i + " " + "%.5f".format(time_needed(1, lexing(re, s))))

}

val filename = "../tests/emails.txt"

val filelines = Source.fromFile(filename).getLines.take(22).zipWithIndex

filelines.foreach({ case (s: String, i: Int) => process(s, i) })

// test: ("a" | "aa")*

val EVIL3 = STAR(ALT(CHAR('a'), SEQ(CHAR('a'), CHAR('a'))))

for (i <- 1 to 29 by 1) {

  println(i + " " + "%.5f".format(time_needed(2, matcher(EVIL3, "a" * i))) + 

	  " size: " + size(ders(("a" * i).toList, EVIL3)))

}