// A simple lexer inspired by work of Sulzmann & Lu

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

//

// 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 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  

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

}

implicit def string2rexp(s : String) : Rexp = 

  charlist2rexp(s.toList)

val HELLO : Rexp = "hello"

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)

}

val TEST = ("ab" | "ba").%

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

  case ZERO => false

  case ONE => 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)

}

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 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)

}

// 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) : 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)

}

// The injection and mkeps part of the lexer

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

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))

}

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))

}

// lexing functions including simplification

def lex(r: Rexp, s: List[Char]) : Val = s match {

  case Nil => if (nullable(r)) mkeps(r) else 

    { throw new Exception("lexing error") } 

  case c::cs => inj(r, c, lex(der(c, r), cs))

}

def lexing(r: Rexp, s: String) = 

  env(lex(r, s.toList))

// The Lexing Rules for the WHILE Language

def PLUS(r: Rexp) = r ~ r.%

def Range(s : List[Char]) : Rexp = s match {

  case Nil => ZERO

  case c::Nil => CHAR(c)

  case c::s => ALT(CHAR(c), Range(s))

}

def RANGE(s: String) = Range(s.toList)

val DIGIT = RANGE("0123456789")

val ID = SYM ~ (SYM | DIGIT).% 

val NUM = PLUS(DIGIT)

val KEYWORD : Rexp = "skip" | "while" | "do" | "if" | "then" | "else" | "read" | "write" 

val SEMI: Rexp = ";"

val OP: Rexp = ":=" | "=" | "-" | "+" | "*" | "!=" | "<" | ">"

val WHITESPACE = PLUS(" " | "\n" | "\t")

val RPAREN: Rexp = "}"

val LPAREN: Rexp = "{"

val STRING: Rexp = "\"" ~ SYM.% ~ "\""

val WHILE_REGS = (("k" $ KEYWORD) | 

                  ("i" $ ID) | 

                  ("o" $ OP) | 

                  ("n" $ NUM) | 

                  ("s" $ SEMI) | 

                  ("str" $ STRING) |

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

                  ("w" $ WHITESPACE)).%

val KY : Rexp = "if" | "read" | "write"

val WH : Rexp = " " | "\n"

val TRIV_REGS = (("k" $ KY) | 

                  ("w" $ WHITESPACE)).%

// Two Simple While Tests

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

@doc("small tests")

@main

def small() = {

  val prog0 = """if"""

  println(s"test: $prog0")

  println(lexing(WHILE_REGS, prog0))

  val prog1 = """iffoo"""

  println(s"test: $prog1")

  println(lexing(WHILE_REGS, prog1))

  val prog2 = """read  n; write n"""  

  println(s"test: $prog2")

  println(lexing(WHILE_REGS, prog2))

}