import scala.language.implicitConversions    

import scala.language.reflectiveCalls

// Rexp

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

case class RANGE(s: Set[Char]) extends Rexp

case class PLUS(r: Rexp) extends Rexp

case class OPTIONAL(r: Rexp) extends Rexp

case class NTIMES(r: Rexp, n: Int) extends Rexp 

// 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

// Convenience typing

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)

}

// nullable

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)

  case RANGE(_) => false

  case PLUS(r1) => nullable(r1)

  case OPTIONAL(_) => true

  case NTIMES(r1, i) => if (i == 0) true else nullable(r1)

}

// der

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)

  case RANGE(s) => if (s.contains(c)) ONE else ZERO 

  case PLUS(r1) => SEQ(der(c, r1), STAR(r1))

  case OPTIONAL(r1) => ALT(der(c, r1), ZERO)

  case NTIMES(r, i) => 

    if (i == 0) ZERO else SEQ(der(c, r), NTIMES(r, i - 1))

}

// Flatten

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)

}

// Env

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)

}

// Mkeps

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))

  case PLUS(r) => Stars(List(mkeps(r)))   // the first copy must match the empty string

  case OPTIONAL(r) => Right(Empty)

  case NTIMES(r, i) => Stars(List.fill(i)(mkeps(r)))

}

// Inj

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))

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

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

  case (OPTIONAL(r), Left(v1)) => Left(inj(r, c, v1))

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

}

// Rectification functions

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")

// Simp

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

  case ALT(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 (ALT (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 r => (r, F_ID)

}

// Lex

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

  case Nil => if (nullable(r)) mkeps(r) else 

    { throw new Exception("lexing error") } 

  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) = env(lex_simp(r, s.toList))

// Language specific code

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

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

val LET: Rexp = RANGE(('A' to 'Z').toSet ++ ('a' to 'z'))

val SYM : Rexp = (LET | RANGE(Set('.', '_', '>', '<', '=', ';', ',', ':')))

val PARENS : Rexp = "(" | "{" | ")" | "}"

val SEMI : Rexp = ";"

val WHITESPACE : Rexp = PLUS(" ") | "\n" | "\t" | "\r"

val DIGIT : Rexp = RANGE(('0' to '9').toSet)

val DIGIT1 : Rexp = RANGE(('1' to '9').toSet)

val STRING : Rexp = "\"" ~ (SYM | " " | "\\n" | DIGIT).% ~ "\""

val ID : Rexp = LET ~ (LET | "_" | DIGIT).%

val NUM : Rexp = "0" | (DIGIT1 ~ DIGIT.%)

val EOL : Rexp = "\n" | "\r\n"

val COMMENT : Rexp = "//" ~ (SYM | PARENS | " " | DIGIT).% ~ EOL 

val WHILE_REGS = (("k" $ KEYWORD) | 

                  ("o" $ OP) | 

                  ("str" $ STRING) |

                  ("p" $ PARENS) |

                  ("s" $ SEMI) | 

                  ("w" $ WHITESPACE) | 

                  ("i" $ ID) | 

                  ("n" $ NUM) |

		  ("c" $ COMMENT)).%

// Token

abstract class Token extends Serializable 

case class T_KEYWORD(s: String) extends Token

case class T_OP(s: String) extends Token

case class T_STRING(s: String) extends Token

case class T_PAREN(s: String) extends Token

case object T_SEMI extends Token

case class T_ID(s: String) extends Token

case class T_NUM(n: Int) extends Token

val token : PartialFunction[(String, String), Token] = {

  case ("k", s) => T_KEYWORD(s)

  case ("o", s) => T_OP(s)

  case ("str", s) => T_STRING(s)

  case ("p", s) => T_PAREN(s)

  case ("s", _) => T_SEMI

  case ("i", s) => T_ID(s)

  case ("n", s) => T_NUM(s.toInt)

}

// Tokenise

def tokenise(s: String) : List[Token] = 

  lexing_simp(WHILE_REGS, s).collect(token)

val fact = """

write "Input n please";

read n;

write "The factors of n are";

f := 2;

while n != 1 do {

    while (n / f) * f == n do {

        write f;

        n := n / f

    };

    f := f + 1

}

"""

println(tokenise(fact))