// 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 SYM = RANGE("ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz_")
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))
}

