import scala.language.implicitConversions    

import scala.language.reflectiveCalls

import scala.annotation.tailrec   

import scala.util.Try

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))

// usual regular expressions

abstract class Rexp 

case object ZERO extends Rexp

case object ONE extends Rexp

case class CHAR(c: Char) 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 ALT(r1: Rexp, r2: Rexp) = ALTS(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

// 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 expressions - for testing purposes

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

  case ZERO => "0"

  case ONE => "1"

  case CHAR(c) => c.toString

  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)})"

}

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

// START OF NON-BITCODE PART

//

// 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 ALTS(rs) => rs.exists(nullable)

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

  case STAR(_) => true

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

}

// 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 ALTS(List(r1, r2)) => ALTS(List(der(c, r1), der(c, r2)))

  case SEQ(r1, r2) => 

    if (nullable(r1)) ALTS(List(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)

}

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 ALTS(List(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 (ALTS(List(r1, r2)), Left(v1)) => Left(inj(r1, c, v1))

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

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

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

}

// lexing without simplification

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) : Val = lex(r, s.toList)

//println(lexing(("ab" | "ab") ~ ("b" | ONE), "ab"))

// some "rectification" functions for simplification

def F_ID(v: Val): Val = v

def F_RIGHT(f: Val => Val) = (v:Val) => Right(f(v))

def F_LEFT(f: Val => Val) = (v:Val) => Left(f(v))

def F_ALT(f1: Val => Val, f2: Val => Val) = (v:Val) => v match {

  case Right(v) => Right(f2(v))

  case Left(v) => Left(f1(v))

}

def F_SEQ(f1: Val => Val, f2: Val => Val) = (v:Val) => v match {

  case Sequ(v1, v2) => Sequ(f1(v1), f2(v2))

}

def F_SEQ_Empty1(f1: Val => Val, f2: Val => Val) = 

  (v:Val) => Sequ(f1(Empty), f2(v))

def F_SEQ_Empty2(f1: Val => Val, f2: Val => Val) = 

  (v:Val) => Sequ(f1(v), f2(Empty))

def F_RECD(f: Val => Val) = (v:Val) => v match {

  case Rec(x, v) => Rec(x, f(v))

}

def F_ERROR(v: Val): Val = throw new Exception("error")

// simplification of regular expressions returning also an

// rectification function; no simplification under STAR 

def simp(r: Rexp): (Rexp, Val => Val) = r match {

  case ALTS(List(r1, r2)) => {

    val (r1s, f1s) = simp(r1)

    val (r2s, f2s) = simp(r2)

    (r1s, r2s) match {

      case (ZERO, _) => (r2s, F_RIGHT(f2s))

      case (_, ZERO) => (r1s, F_LEFT(f1s))

      case _ => if (r1s == r2s) (r1s, F_LEFT(f1s))

                else (ALTS(List(r1s, r2s)), F_ALT(f1s, f2s)) 

    }

  }

  case SEQ(r1, r2) => {

    val (r1s, f1s) = simp(r1)

    val (r2s, f2s) = simp(r2)

    (r1s, r2s) match {

      case (ZERO, _) => (ZERO, F_ERROR)

      case (_, ZERO) => (ZERO, F_ERROR)

      case (ONE, _) => (r2s, F_SEQ_Empty1(f1s, f2s))

      case (_, ONE) => (r1s, F_SEQ_Empty2(f1s, f2s))

      case _ => (SEQ(r1s,r2s), F_SEQ(f1s, f2s))

    }

  }

  case RECD(x, r1) => {

    val (r1s, f1s) = simp(r1)

    (RECD(x, r1s), F_RECD(f1s))

  }

  case r => (r, F_ID)

}

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

  case Nil => r

  case c::s => ders_simp(s, simp(der(c, r))._1)

}

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

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

  case c::cs => {

    val (r_simp, f_simp) = simp(der(c, r))

    inj(r, c, f_simp(lex_simp(r_simp, cs)))

  }

}

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

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

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

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

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

// Partial Derivatives

def pder(c: Char, r: Rexp): Set[Rexp] = r match {

  case ZERO => Set()

  case ONE => Set()

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

  case ALTS(rs) => rs.toSet.flatMap(pder(c, _))

  case SEQ(r1, r2) =>

    (for (pr1 <- pder(c, r1)) yield SEQ(pr1, r2)) ++

    (if (nullable(r1)) pder(c, r2) else Set())

  case STAR(r1) =>

    for (pr1 <- pder(c, r1)) yield SEQ(pr1, STAR(r1))

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

}

def pders(cs: List[Char], r: Rexp): Set[Rexp] = cs match {

  case Nil => Set(r)

  case c::cs => pder(c, r).flatMap(pders(cs, _))

}

def pders_simp(cs: List[Char], r: Rexp): Set[Rexp] = cs match {

  case Nil => Set(r)

  case c::cs => pder(c, r).flatMap(pders_simp(cs, _)).map(simp(_)._1)

}

def psize(rs: Set[Rexp])  = 

  rs.map(size).sum

// A simple parser for regexes

case class Parser(s: String) {

  var i = 0

  def peek() = s(i)

  def eat(c: Char) = 

    if (c == s(i)) i = i + 1 else throw new Exception("Expected " + c + " got " + s(i))

  def next() = { i = i + 1; s(i - 1) }

  def more() = s.length - i > 0

  def Regex() : Rexp = {

    val t = Term();

    if (more() && peek() == '|') {

      eat ('|') ; 

      ALT(t, Regex()) 

    } 

    else t

  }

  def Term() : Rexp = {

    var f : Rexp = 

      if (more() && peek() != ')' && peek() != '|') Factor() else ONE;

    while (more() && peek() != ')' && peek() != '|') {

      f = SEQ(f, Factor()) ;

    }

    f

  }

  def Factor() : Rexp = {

    var b = Base();

    while (more() && peek() == '*') {

      eat('*') ;

      b = STAR(b) ;

    }

    while (more() && peek() == '?') {

      eat('?') ;

      b = ALT(b, ONE) ;

    }

    while (more() && peek() == '+') {

      eat('+') ;

      b = SEQ(b, STAR(b)) ;

    }

    b

  }

  def Base() : Rexp = {

    peek() match {

      case '(' => { eat('(') ; val r = Regex(); eat(')') ; r }   // if groups should be groups RECD("",r) }

      case _ => CHAR(next())

    }

  }

}

// two simple examples for the regex parser

println("two simple examples for the regex parser")

println(string(Parser("a|(bc)*").Regex()))

println(string(Parser("(a|b)*(babab(a|b)*bab|bba(a|b)*bab)(a|b)*").Regex()))

//System.exit(0)

//   Testing

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

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

  val start = System.nanoTime()

  val result = code

  val end = System.nanoTime()

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

  //result

}

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 Aregx for testing purposes 

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

  case ZERO => 1

  case ONE => 1

  case CHAR(_) => 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)

}

//enumerates strings of length n over alphabet cs

def strs(n: Int, cs: String) : Set[String] = {

  if (n == 0) Set("")

  else {

    val ss = strs(n - 1, cs)

    ss ++

    (for (s <- ss; c <- cs.toList) yield c + s)

  }

}

def enum(n: Int, s: String) : Stream[Rexp] = n match {

  case 0 => ZERO #:: ONE #:: s.toStream.map(CHAR)

  case n => {  

    val rs = enum(n - 1, s)

    rs #:::

    (for (r1 <- rs; r2 <- rs) yield ALT(r1, r2)) #:::

    (for (r1 <- rs; r2 <- rs) yield SEQ(r1, r2)) #:::

    (for (r1 <- rs) yield STAR(r1))

  }

}

println("Antimirov Example 5.5")

val antimirov = Parser("(a|b)*(babab(a|b)*bab|bba(a|b)*bab)(a|b)*").Regex()

val strings = strs(6, "ab")

val pds = strings.flatMap(s => pders(s.toList, antimirov))

val pds_simplified = pds.map(simp(_)._1)

println("Unsimplified set")

println(pds.map(string).mkString("\n"))

println("Number of pds  " +  pds.size)

println("\nSimplified set")

println(pds_simplified.map(string).mkString("\n"))

println("Number of pds  " +  pds_simplified.size)

def fact(n: Int) : Int = 

  if (n == 0) 1 else n *  fact(n - 1)