import scala.language.implicitConversions    

import scala.language.reflectiveCalls

import scala.annotation.tailrec   

abstract class Rexp 

case object NULL extends Rexp

case object EMPTY 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 Void extends Val

case class Chr(c: Char) extends Val

case class Sequ(v1: Val, v2: Val) extends Val

case class Left(n: Int, v: Val) extends Val

case class Right(n: Int, 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 => EMPTY

  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)

}

// size of a regular expressions - for testing purposes 

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

  case NULL => 1

  case EMPTY => 1

  case CHAR(_) => 1

  case ALT(r1, r2) => 1 + size(r1) + size(r2)

  case SEQ(r1, r2) => 1 + size(r1) + size(r2)

  case STAR(r) => 1 + size(r)

  case RECD(_, r) => 1 + size(r)

}

// nullable function: tests whether the regular 

// expression can recognise the empty string

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

  case NULL => false

  case EMPTY => 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 NULL => NULL

  case EMPTY => NULL

  case CHAR(d) => if (c == d) EMPTY else NULL

  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))

}

// extracts a string from value

def flatten(v: Val) : String = v match {

  case Void => ""

  case Chr(c) => c.toString

  case Left(n, v) => flatten(v)

  case Right(n, 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 Void => Nil

  case Chr(c) => Nil

  case Left(n, v) => env(v)

  case Right(n, 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)

}

def left_inc(v: Val) = v match {

  case Left(v, n) => Left(v, n + 1)

  case v => Left(v, 1)

}

def right_inc(v: Val) = v match {

  case Right(v, n) => Right(v, n + 1)

  case v => Right(v, 1)

}

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

  case EMPTY => Void

  case ALT(r1, r2) => 

    if (nullable(r1)) left_inc(mkeps(r1)) else right_inc(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), 1) => Left(inj(r1, c, v1), 1)

  case (ALT(r1, r2), Left(v1), n) => inc_left(inj(r1, c, Left(v1, n - 1)))

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

  case (CHAR(d), Void) => Chr(d) 

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

// Lexing Rules for a Small While Language

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 WHILE_REGS = (("k" $ KEYWORD) | 

                  ("i" $ ID) | 

                  ("o" $ OP) | 

                  ("n" $ NUM) | 

                  ("s" $ SEMI) | 

                  ("p" $ (LPAREN | RPAREN)) | 

                  ("b" $ (BEGIN | END)) | 

                  ("w" $ WHITESPACE)).%

*/

val WHILE_REGS = (KEYWORD | 

                  ID | 

                  OP | 

                  NUM | 

                  SEMI | 

                  LPAREN | RPAREN | 

                  BEGIN | END | 

                  WHITESPACE).%

// Some Tests

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

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

  val start = System.nanoTime()

  val result = code

  val end = System.nanoTime()

  println((end - start)/1.0e9)

  result

}

val prog0 = """read n"""

env (lexing_simp(WHILE_REGS, prog0))

println("Next test")

/*

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

env (lexing_simp(WHILE_REGS, prog1))

val prog2 = """

i := 2;

max := 100;

while i < max do {

  isprime := 1;

  j := 2;

  while (j * j) <= i + 1  do {

    if i % j == 0 then isprime := 0  else skip;

    j := j + 1

  };

  if isprime == 1 then write i else skip;

  i := i + 1

}"""

lexing_acc(WHILE_REGS, prog2)

for (i <- 1 to 228 by 1) {

  print(i.toString + ":  ")

  time(lexing_acc(WHILE_REGS, prog2 * i))

}

for (i <- 1 to 100 by 10) {

  print(i.toString + ":  ")

  time(lexing_simp(WHILE_REGS, prog2 * i))

}

*/