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
case class CRANGE(cs: String) extends Rexp
case class PLUS(r: Rexp) extends Rexp
case class OPT(r: Rexp) extends Rexp
case class NTIMES(r: Rexp, n: Int) extends Rexp

abstract class Val
case object Empty extends Val
case class Chr(c: Char) extends Val
case class Seq(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 => 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)
}

// 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(_, r) => nullable(r)
  case CRANGE(_) => false
  case PLUS(r) => nullable(r)
  case OPT(_) => true
  case NTIMES(r, n) => if (n == 0) true else nullable(r)
}

// 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)
  case CRANGE(cs) => if (cs.contains(c)) EMPTY else NULL
  case PLUS(r) => SEQ(der(c, r), STAR(r))
  case OPT(r) => ALT(der(c, r), NULL)
  case NTIMES(r, n) => if (n == 0) NULL else der(c, SEQ(r, NTIMES(r, n - 1)))
}

// 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 Empty => ""
  case Chr(c) => c.toString
  case Left(v) => flatten(v)
  case Right(v) => flatten(v)
  case Seq(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 Seq(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 EMPTY => Empty
  case ALT(r1, r2) => 
    if (nullable(r1)) Left(mkeps(r1)) else Right(mkeps(r2))
  case SEQ(r1, r2) => Seq(mkeps(r1), mkeps(r2))
  case STAR(r) => Stars(Nil)
  case RECD(x, r) => Rec(x, mkeps(r))
  case PLUS(r) => Stars(List(mkeps(r)))
  case OPT(_) => Right(Empty)
  case NTIMES(r, n) => if (n == 0) Stars(Nil) else Stars(Nil.padTo(n, mkeps(r)))
  case _ => { println ("r : " + r.toString); 
              throw new Exception("mkeps error")}
}


def inj(r: Rexp, c: Char, v: Val) : Val = (r, v) match {
  case (STAR(r), Seq(v1, Stars(vs))) => Stars(inj(r, c, v1)::vs)
  case (SEQ(r1, r2), Seq(v1, v2)) => Seq(inj(r1, c, v1), v2)
  case (SEQ(r1, r2), Left(Seq(v1, v2))) => Seq(inj(r1, c, v1), v2)
  case (SEQ(r1, r2), Right(v2)) => Seq(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(_), Empty) => Chr(c) 
  case (CRANGE(_), Empty) => Chr(c) 
  case (RECD(x, r1), _) => Rec(x, inj(r1, c, v))
  case (PLUS(r), Seq(v1, Stars(vs))) => Stars(inj(r, c, v1)::vs)
  case (OPT(r), Left(v1)) => Left(inj(r, c, v1))
  case (NTIMES(r, n), Seq(v1, Stars(vs))) => Stars(inj(r, c, v1)::vs)
  case (NTIMES(r, n), Left(Seq(v1, Stars(vs)))) => Stars(inj(r, c, v1)::vs)
  case (NTIMES(r, n), Right(Stars(v::vs))) => Stars(mkeps(r)::inj(r, c, v)::vs)
  case _ => { println ("r : " + r.toString + "  v: " + v.toString); 
              throw new Exception("inj error")}
}

// 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(("ab" | "ab") ~ ("b" | EMPTY), "ab")

lexing(OPT("ab"), "ab")

lexing(NTIMES("1", 3), "111")
lexing(NTIMES("1" | EMPTY, 3), "11")

// 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 Seq(v1, v2) => Seq(f1(v1), f2(v2))
}
def F_SEQ_Empty1(f1: Val => Val, f2: Val => Val) = 
  (v:Val) => Seq(f1(Empty), f2(v))
def F_SEQ_Empty2(f1: Val => Val, f2: Val => Val) = 
  (v:Val) => Seq(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 ALT(r1, r2) => {
    val (r1s, f1s) = simp(r1)
    val (r2s, f2s) = simp(r2)
    (r1s, r2s) match {
      case (NULL, _) => (r2s, F_RIGHT(f2s))
      case (_, NULL) => (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 (NULL, _) => (NULL, F_ERROR)
      case (_, NULL) => (NULL, F_ERROR)
      case (EMPTY, _) => (r2s, F_SEQ_Empty1(f1s, f2s))
      case (_, EMPTY) => (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 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)

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

lexing_simp(OPT("ab"), "ab")

// Lexing Rules for a Small While Language

val SYM = CRANGE("abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ")
val DIGIT = CRANGE("0123456789")
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)).%

// filters out all white spaces
def tokenise(r: Rexp, s: String) = 
  env(lexing_simp(r, s)).filterNot { (s) => s._1 == "w"}

//   Testing
//============

def time[T](code: => T) = {
  val start = System.nanoTime()
  val result = code
  val end = System.nanoTime()
  println((end - start)/1.0e9)
  result
}

println(lexing_simp(OPT("1"), "1"))
println(lexing_simp(OPT("1"), ""))
println(ders("111".toList, NTIMES("1",3)))
println(lexing_simp(NTIMES("1",3), "111"))

val r1 = ("a" | "ab") ~ ("bcd" | "c")
println(lexing(r1, "abcd"))

val r2 = ("" | "a") ~ ("ab" | "b")
println(lexing(r2, "ab"))


// Two Simple While Tests
//========================
println("prog0 test")

val prog0 = """read n"""
println(env(lexing_simp(WHILE_REGS, prog0)))

println("prog1 test")

val prog1 = """read  n; write (n)"""
println(env(lexing_simp(WHILE_REGS, prog1)))


// Big Test
//==========

def escape(raw: String): String = {
  import scala.reflect.runtime.universe._
  Literal(Constant(raw)).toString
}

val prog2 = """
write "Fib";
read n;
minus1 := 0;
minus2 := 1;
while n > 0 do {
  temp := minus2;
  minus2 := minus1 + minus2;
  minus1 := temp;
  n := n - 1
};
write "Result";
write minus2
"""

val prog3 = """
start := 1000;
x := start;
y := start;
z := start;
while 0 < x do {
 while 0 < y do {
  while 0 < z do {
    z := z - 1
  };
  z := start;
  y := y - 1
 };     
 y := start;
 x := x - 1
}
"""


println("Tokens")
println(tokenise(WHILE_REGS, prog2).mkString("\n"))

val fib_tokens = tokenise(WHILE_REGS, prog2)
fib_tokens.map{case (s1, s2) => (escape(s1), escape(s2))}.mkString(",\n")


val test_tokens = tokenise(WHILE_REGS, prog3)
test_tokens.map{case (s1, s2) => (escape(s1), escape(s2))}.mkString(",\n")


/*
for (i <- 1 to 120 by 10) {
  print(i.toString + ":  ")
  time(lexing_simp(WHILE_REGS, prog2 * i))
}
*/

val toks_fib = 
  List(("k","write"),
       ("str","Fib"),
       ("s",";"),
       ("k","read"),
       ("i","n"),
       ("s",";"),
       ("i","minus1"),
       ("o",":="),
       ("n","0"),
       ("s",";"),
       ("i","minus2"),
       ("o",":="),
       ("n","1"),
       ("s",";"),
       ("k","while"),
       ("i","n"),
       ("o",">"),
       ("n","0"),
       ("k","do"),
       ("b","{"),
       ("i","temp"),
       ("o",":="),
       ("i","minus2"),
       ("s",";"),
       ("i","minus2"),
       ("o",":="),
       ("i","minus1"),
       ("o","+"),
       ("i","minus2"),
       ("s",";"),
       ("i","minus1"),
       ("o",":="),
       ("i","temp"),
       ("s",";"),
       ("i","n"),
       ("o",":="),
       ("i","n"),
       ("o","-"),
       ("n","1"),
       ("b","}"),
       ("s",";"),
       ("k","write"),
       ("str","Result"),
       ("s",";"),
       ("k","write"),
       ("i","minus2"))

val toks_test =
  List(("i","start"),
       ("o",":="),
       ("n","1000"),
       ("s",";"),
       ("i","x"),
       ("o",":="),
       ("i","start"),
       ("s",";"),
       ("i","y"),
       ("o",":="),
       ("i","start"),
       ("s",";"),
       ("i","z"),
       ("o",":="),
       ("i","start"),
       ("s",";"),
       ("k","while"),
       ("n","0"),
       ("o","<"),
       ("i","x"),
       ("k","do"),
       ("b","{"),
       ("k","while"),
       ("n","0"),
       ("o","<"),
       ("i","y"),
       ("k","do"),
       ("b","{"),
       ("k","while"),
       ("n","0"),
       ("o","<"),
       ("i","z"),
       ("k","do"),
       ("b","{"),
       ("i","z"),
       ("o",":="),
       ("i","z"),
       ("o","-"),
       ("n","1"),
       ("b","}"),
       ("s",";"),
       ("i","z"),
       ("o",":="),
       ("i","start"),
       ("s",";"),
       ("i","y"),
       ("o",":="),
       ("i","y"),
       ("o","-"),
       ("n","1"),
       ("b","}"),
       ("s",";"),
       ("i","y"),
       ("o",":="),
       ("i","start"),
       ("s",";"),
       ("i","x"),
       ("o",":="),
       ("i","x"),
       ("o","-"),
       ("n","1"),
       ("b","}"))
