// Author: Zhuo Ying Jiang Li

// Starting code by Dr Christian Urban

// lexer

//

// Use this command to print the list of tokens:

// amm fun_token.sc <name>.fun

//

type Token = (String, String)

type Tokens = List[Token]

// regular expressions including records

abstract class Rexp

case object ZERO extends Rexp

case object ONE extends Rexp

case class CHAR(c: Char) extends Rexp

case class RANGE(chars: List[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 OPTIONAL(r: Rexp) extends Rexp

case class PLUS(r: Rexp) extends Rexp

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

case class RECD(x: String, r: Rexp) extends Rexp  // records for extracting strings or tokens

// 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::vs => SEQ(CHAR(c), charlist2rexp(vs))

}

implicit def string2rexp(s : String) : Rexp = 

  charlist2rexp(s.toList)

extension (r: Rexp) {

  def | (s: Rexp) = ALT(r, s)

  def % = STAR(r)

  def + = PLUS(r)

  def ~ (s: Rexp) = SEQ(r, s)

}

extension (s: String) {

  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)

}

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

  case ZERO => false

  case ONE => true

  case CHAR(_) => false

  case RANGE(_) => false

  case ALT(r1, r2) => nullable(r1) || nullable(r2)

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

  case STAR(_) => true

  case OPTIONAL(r1) => true

  case PLUS(r1) => nullable(r1)

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

  case RECD(_, r1) => nullable(r1)

}

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 RANGE(chars) => if (chars.contains(c)) 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 OPTIONAL(r) => der(c, r)

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

  case NTIMES(r1, n) => if (n == 0) ZERO else SEQ(der(c, r1), NTIMES(r1, n - 1))

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

}

// extracts a string from a 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 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;

// used for tokenising a string

def env(v: Val) : Tokens = 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)

}

// The injection and mkeps part of the lexer

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

// 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) => if (nullable(r)) Stars(List(mkeps(r))) else Stars(Nil)

  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), v1) => Stars(List(inj(r, c, v1)))

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

}

// 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_ERROR(v: Val): Val = throw new Exception("error")

// simplification

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)

}

// lexing functions including simplification

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))

// FUN language lexer

val DIGIT = RANGE("0123456789".toList)

val LOWERCASE = RANGE("abcdefghijklmnopqrstuvwxyz".toList)

val UPPERCASE = RANGE("ABCDEFGHIJKLMNOPQRSTUVWXYZ".toList)

val SYM = RANGE("!\"#$%&'()*+,-./:;<>=?`@[]\\^_{}|~".toList)  // I referenced the CPP ASCII table https://en.cppreference.com/w/cpp/language/ascii

val KEYWORD : Rexp = "val" | "if" | "then" | "else" | "def" | "skip" // "skip" is hardcoded because hanoi.fun calls skip() without parentheses

val TYPE : Rexp = "Int" | "Double" | "Void"

val GLOBAL_ID : Rexp = UPPERCASE ~ ("_" | LOWERCASE | DIGIT | UPPERCASE).% // start with capital letter and followed by any case

val ID : Rexp = LOWERCASE ~ ("_" | UPPERCASE | LOWERCASE | DIGIT).% // start with lowercase 

val SEMI : Rexp = ";"

val COLON : Rexp = ":"

val OP : Rexp = "=" | "==" | "-" | "+" | "*" | "!=" | "<" | ">" | "<=" | ">=" | "%" | "/" // no && and || operators

val INT : Rexp = DIGIT.+

val DOUBLE : Rexp = DIGIT.+ ~ "." ~ DIGIT.+  // negative numbers sign is lexed as operator, but the parser will identify negative numbers

val COMMA : Rexp = "," 

val WHITESPACES: Rexp = (" " | "\n" | "\t" | "\r").+ // whitespaces are either " " or \n or \t or \r

val LPAREN : Rexp = RANGE("({".toList)

val RPAREN : Rexp = RANGE(")}".toList)

val CH : Rexp = "'" ~ (LOWERCASE | UPPERCASE | DIGIT | SYM | " " | "\\n" | "\\t" | "\\r") ~ "'"  // \n, \t and \r should also be tokenized, any character should be, whitespaces too

val COMMENT : Rexp = ("//" ~ (LOWERCASE | UPPERCASE | SYM | DIGIT | RANGE(" \t\r".toList)).% ~ "\n") | ("/*" ~ (LOWERCASE | UPPERCASE | SYM | DIGIT | RANGE(" \n\t\r".toList)).% ~ "*/")

val FUN_REGS = (("keyword" $ KEYWORD) |

                ("type" $ TYPE) |

                ("global" $ GLOBAL_ID) |

                ("id" $ ID) |

                ("op" $ OP) |

                ("double" $ DOUBLE) |

                ("int" $ INT) |

                ("semi" $ SEMI) |

                ("colon" $ COLON) |

                ("comma" $ COMMA) |

                ("ch" $ CH) |

                ("par" $ (LPAREN | RPAREN)) |

                COMMENT | WHITESPACES).%

def fun_lex(program: String) : Tokens = {

  lexing_simp(FUN_REGS, program)

}

def tokenise(program: String) : Tokens = {

  lexing_simp(FUN_REGS, program)

}

import scala.io.Source._

@main

def lex(filename: String) = {

  // read file

  val fun_code = fromFile(filename).getLines.mkString("\n")

  // print tokens to screen

  println(fun_lex(fun_code).mkString("\n"))

}