// 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"))
}