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))

def distinctBy[B, C](xs: List[B], f: B => C, acc: List[C] = Nil): List[B] = xs match {
  case Nil => Nil
  case (x::xs) => {
    val res = f(x)
    if (acc.contains(res)) distinctBy(xs, f, acc)  
    else x::distinctBy(xs, f, res::acc)
  }
} 

abstract class Bit
case object Z extends Bit
case object S extends Bit
case class C(c: Char) extends Bit

type Bits = List[Bit]

// usual regular expressions
abstract class Rexp 
case object ZERO extends Rexp
case object ONE extends Rexp
case class PRED(f: Char => Boolean, s: String = "_") 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 CHAR(c: Char) = PRED(_ == c, c.toString)
def ALT(r1: Rexp, r2: Rexp) = ALTS(List(r1, r2))
def PLUS(r: Rexp) = SEQ(r, STAR(r))

// annotated regular expressions
abstract class ARexp 
case object AZERO extends ARexp
case class AONE(bs: Bits) extends ARexp
case class APRED(bs: Bits, f: Char => Boolean, s: String = "_") extends ARexp
case class AALTS(bs: Bits, rs: List[ARexp]) extends ARexp 
case class ASEQ(bs: Bits, r1: ARexp, r2: ARexp) extends ARexp 
case class ASTAR(bs: Bits, r: ARexp) extends ARexp 

// abbreviations
def AALT(bs: Bits, r1: ARexp, r2: ARexp) = AALTS(bs, 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 PRED(_, s) => s
  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)})"
}

// string of an annotated regular expressions - for testing purposes

def astring(a: ARexp): String = a match {
  case AZERO => "0"
  case AONE(_) => "1"
  case APRED(_, _, s) => s
  case AALTS(_, rs) => rs.map(astring).mkString("[", "|", "]")
  case ASEQ(_, r1, r2) => s"(${astring(r1)} ~ ${astring(r2)})"
  case ASTAR(_, r) => s"{${astring(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 PRED(_, _) => 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 PRED(f, _) => if (f(c)) 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 (PRED(_, _), 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 

var profile_simp : Int = 0

def simp(r: Rexp): (Rexp, Val => Val) = {
  profile_simp =  profile_simp + 1
  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)

//--------------------------------------------------------------------------------------------------------
// BITCODED PART


def fuse(bs: Bits, r: ARexp) : ARexp = r match {
  case AZERO => AZERO
  case AONE(cs) => AONE(bs ++ cs)
  case APRED(cs, f, s) => APRED(bs ++ cs, f, s)
  case AALTS(cs, rs) => AALTS(bs ++ cs, rs)
  case ASEQ(cs, r1, r2) => ASEQ(bs ++ cs, r1, r2)
  case ASTAR(cs, r) => ASTAR(bs ++ cs, r)
}

// translation into ARexps
def internalise(r: Rexp) : ARexp = r match {
  case ZERO => AZERO
  case ONE => AONE(Nil)
  case PRED(f, s) => APRED(Nil, f, s)
  case ALTS(List(r1, r2)) => 
    AALTS(Nil, List(fuse(List(Z), internalise(r1)), fuse(List(S), internalise(r2))))
  case ALTS(r1::rs) => {
     val AALTS(Nil, rs2) = internalise(ALTS(rs))
     AALTS(Nil, fuse(List(Z), internalise(r1)) :: rs2.map(fuse(List(S), _)))
  }
  case SEQ(r1, r2) => ASEQ(Nil, internalise(r1), internalise(r2))
  case STAR(r) => ASTAR(Nil, internalise(r))
  case RECD(x, r) => internalise(r)
}

internalise(("a" | "ab") ~ ("b" | ""))

// decoding of values from bit sequences
def decode_aux(r: Rexp, bs: Bits) : (Val, Bits) = (r, bs) match {
  case (ONE, bs) => (Empty, bs)
  case (PRED(f, _), C(c)::bs) => (Chr(c), bs)
  case (ALTS(r::Nil), bs) => decode_aux(r, bs)
  case (ALTS(rs), bs) => bs match {
    case Z::bs1 => {
      val (v, bs2) = decode_aux(rs.head, bs1)
      (Left(v), bs2)
    }
    case S::bs1 => {
      val (v, bs2) = decode_aux(ALTS(rs.tail), bs1)
      (Right(v), bs2)			
    }
  }
  case (SEQ(r1, r2), bs) => {
    val (v1, bs1) = decode_aux(r1, bs)
    val (v2, bs2) = decode_aux(r2, bs1)
    (Sequ(v1, v2), bs2)
  }
  case (STAR(r1), S::bs) => {
    val (v, bs1) = decode_aux(r1, bs)
    val (Stars(vs), bs2) = decode_aux(STAR(r1), bs1)
    (Stars(v::vs), bs2)
  }
  case (STAR(_), Z::bs) => (Stars(Nil), bs)
  case (RECD(x, r1), bs) => {
    val (v, bs1) = decode_aux(r1, bs)
    (Rec(x, v), bs1)
  }
}

def decode(r: Rexp, bs: Bits) = decode_aux(r, bs) match {
  case (v, Nil) => v
  case _ => throw new Exception("Not decodable")
}


//erase function: extracts a Rexp from Arexp
def erase(r: ARexp) : Rexp = r match{
  case AZERO => ZERO
  case AONE(_) => ONE
  case APRED(bs, f, s) => PRED(f, s)
  case AALTS(bs, rs) => ALTS(rs.map(erase(_)))
  case ASEQ(bs, r1, r2) => SEQ (erase(r1), erase(r2))
  case ASTAR(cs, r)=> STAR(erase(r))
}


// bnullable function: tests whether the aregular 
// expression can recognise the empty string
def bnullable (r: ARexp) : Boolean = r match {
  case AZERO => false
  case AONE(_) => true
  case APRED(_,_,_) => false
  case AALTS(_, rs) => rs.exists(bnullable)
  case ASEQ(_, r1, r2) => bnullable(r1) && bnullable(r2)
  case ASTAR(_, _) => true
}

def bmkeps(r: ARexp) : Bits = r match {
  case AONE(bs) => bs
  case AALTS(bs, rs) => {
    val n = rs.indexWhere(bnullable)
    bs ++ bmkeps(rs(n))
  }
  case ASEQ(bs, r1, r2) => bs ++ bmkeps(r1) ++ bmkeps(r2)
  case ASTAR(bs, r) => bs ++ List(Z)
}

// derivative of a regular expression w.r.t. a character
def bder(c: Char, r: ARexp) : ARexp = r match {
  case AZERO => AZERO
  case AONE(_) => AZERO
  case APRED(bs, f, _) => if (f(c)) AONE(bs:::List(C(c))) else AZERO
  case AALTS(bs, rs) => AALTS(bs, rs.map(bder(c, _)))
  case ASEQ(bs, r1, r2) => 
    if (bnullable(r1)) AALT(bs, ASEQ(Nil, bder(c, r1), r2), fuse(bmkeps(r1), bder(c, r2)))
    else ASEQ(bs, bder(c, r1), r2)
  case ASTAR(bs, r) => ASEQ(bs, fuse(List(S), bder(c, r)), ASTAR(Nil, r))
}


// derivative w.r.t. a string (iterates bder)
@tailrec
def bders (s: List[Char], r: ARexp) : ARexp = s match {
  case Nil => r
  case c::s => bders(s, bder(c, r))
}


def inc_profile(m: Map[ARexp, Int], a: ARexp) : Map[ARexp, Int] = {
  val current =  m.getOrElse(a, 0) 
  m + (a -> (current + 1))
}

var profile_bsimp_args : Map[ARexp, Int] = Map()
var profile_bsimp : Int = 0
var profile_flats : Int = 0


def flats(rs: List[ARexp]): List[ARexp] = {
  profile_flats = profile_flats + 1
  rs match {
    case Nil => Nil
    case AZERO :: rs1 => flats(rs1)
    case AALTS(bs, rs1) :: rs2 => rs1.map(fuse(bs, _)) ::: flats(rs2)
    case r1 :: rs2 => r1 :: flats(rs2)
}}

def bsimp(r: ARexp): ARexp = {
  //profile_bsimp = inc_profile(profile_bsimp, r)
  profile_bsimp = profile_bsimp + 1
  r match {
  case ASEQ(bs1, r1, r2) => (bsimp(r1), bsimp(r2)) match {
      case (AZERO, _) => AZERO
      case (_, AZERO) => AZERO
      case (AONE(bs2), r2s) => fuse(bs1 ++ bs2, r2s)
      case (r1s, r2s) => ASEQ(bs1, r1s, r2s)
  }
  case AALTS(bs1, rs) => distinctBy(flats(rs.map(bsimp)), erase) match {
    case Nil => AZERO
    case r :: Nil => fuse(bs1, r)
    case rs => AALTS(bs1, rs)  
  }
  //case ASTAR(bs1, r1) => ASTAR(bs1, bsimp(r1))
  case r => r
  }
}




def bders_simp (s: List[Char], r: ARexp) : ARexp = s match {
  case Nil => r
  case c::s => bders_simp(s, bsimp(bder(c, r)))
}

def blex_simp(r: ARexp, s: List[Char]) : Bits = s match {
  case Nil => if (bnullable(r)) bmkeps(r)
	      else throw new Exception("Not matched")
  case c::cs => blex_simp(bsimp(bder(c, r)), cs)
}


def blexing_simp(r: Rexp, s: String) : Val = 
 decode(r, blex_simp(internalise(r), s.toList))


def btokenise_simp(r: Rexp, s: String) = env(blexing_simp(r, s)).map(esc2)



// INCLUDING SIMPLIFICATION UNDER STARS

def bsimp_full(r: ARexp): ARexp = r match {
  case ASEQ(bs1, r1, r2) => (bsimp_full(r1), bsimp_full(r2)) match {
      case (AZERO, _) => AZERO
      case (_, AZERO) => AZERO
      case (AONE(bs2), r2s) => fuse(bs1 ++ bs2, r2s)
      case (r1s, r2s) => ASEQ(bs1, r1s, r2s)
  }
  case AALTS(bs1, rs) => distinctBy(flats(rs.map(bsimp_full)), erase) match {
    case Nil => AZERO
    case r :: Nil => fuse(bs1, r)
    case rs => AALTS(bs1, rs)  
  }
  case ASTAR(bs1, r1) => ASTAR(bs1, bsimp_full(r1))
  case r => r
}

def bders_simp_full(s: List[Char], r: ARexp) : ARexp = s match {
  case Nil => r
  case c::s => bders_simp_full(s, bsimp_full(bder(c, r)))
}

def blex_simp_full(r: ARexp, s: List[Char]) : Bits = s match {
  case Nil => if (bnullable(r)) bmkeps(r)
	      else throw new Exception("Not matched")
  case c::cs => blex_simp_full(bsimp_full(bder(c, r)), cs)
}


def blexing_simp_full(r: Rexp, s: String) : Val = 
 decode(r, blex_simp_full(internalise(r), s.toList))


def btokenise_simp_full(r: Rexp, s: String) = env(blexing_simp_full(r, s)).map(esc2)



//   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 PRED(_,_) => 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)
}

def asize(a: ARexp) = size(erase(a))


// Lexing Rules for a Small While Language

//symbols
val SYM = PRED("abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ".contains(_), "SYM")
//digits
val DIGIT = PRED("0123456789".contains(_), "NUM")
//identifiers
val ID = SYM ~ (SYM | DIGIT).% 
//numbers
val NUM = STAR(DIGIT)
//keywords
val KEYWORD : Rexp = "skip" | "while" | "do" | "if" | "then" | "else" | "read" | "write" | "true" | "false"
//semicolons
val SEMI: Rexp = ";"
//operators
val OP: Rexp = ":=" | "==" | "-" | "+" | "*" | "!=" | "<" | ">" | "<=" | ">=" | "%" | "/"
//whitespaces
val WHITESPACE = PLUS(" " | "\n" | "\t")
//parentheses
val RPAREN: Rexp = ")"
val LPAREN: Rexp = "("
val BEGIN: Rexp = "{"
val END: Rexp = "}"
//strings...but probably needs not
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)).%

// Bigger Tests
//==============


val fib_prog = """
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
"""




profile_simp = 0
profile_bsimp = 0
profile_flats = 0

println("Original " + size(WHILE_REGS))
println("Size Bit  " + asize(bders_simp((fib_prog * 20).toList, internalise(WHILE_REGS))) + "  " + profile_bsimp +  " + " + profile_flats)
println("Size Old  " + size(ders_simp((fib_prog * 20).toList, WHILE_REGS)) + "  " + profile_simp)

System.exit(0)

println("Internal sizes test OK or strange")

def perc(p1: Double, p2: Double) : String =
  f"${(((p1 - p2) / p2) * 100.0) }%5.0f" + "%"

def ders_test(n: Int, s: List[Char], r: Rexp, a: ARexp) : (Rexp, ARexp) = s match {
  case Nil => (r, a)
  case c::s => {
    // derivative 
    val (rd1, tr1) = timeR(der(c, r))
    val (ad1, ta1) = timeR(bder(c, a))
    val trs1 = f"${tr1}%.5f"
    val tas1 = f"${ta1}%.5f"
    if (tr1 < ta1) println(s"Time strange der  (step) ${n} ${perc(ta1, tr1)} sizes  der ${size(rd1)} ${asize(ad1)}")
    //simplification
    val (rd, tr) = timeR(simp(rd1)._1)
    val (ad, ta) = timeR(bsimp(ad1))
    val trs = f"${tr}%.5f"
    val tas = f"${ta}%.5f"
    //full simplification
    val (adf, taf) = timeR(bsimp_full(ad1))
    if (tr < ta) println(s"Time strange simp (step) ${n} ${perc(ta, tr)} sizes simp ${size(rd)} ${asize(ad)}")
    if (n == 1749 || n == 1734) {
      println{s"Aregex before bder (size: ${asize(a)})\n ${string(erase(a))}"}
      println{s"Aregex after bder (size: ${asize(ad1)})\n ${string(erase(ad1))}"}
      println{s"Aregex after bsimp (size: ${asize(ad)})\n ${string(erase(ad))}"}
      println{s"Aregex after bsimp_full (size: ${asize(adf)})\n ${string(erase(adf))}"}
    }
    ders_test(n + 1, s, rd, ad)
  }
}

val prg = (fib_prog * 10).toList
ders_test(0, prg, WHILE_REGS, internalise(WHILE_REGS))