// A Small Compiler for a Simple Functional Language

// (includes a lexer and a parser)

case object ZERO extends Rexp

case object ONE extends Rexp

case class RECD(x: String, r: Rexp) extends Rexp

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

def charlist2rexp(s : List[Char]): Rexp = s match {

  case Nil => ONE

implicit def string2rexp(s : String) : Rexp = 

  charlist2rexp(s.toList)

implicit def RexpOps(r: Rexp) = new {

implicit def stringOps(s: String) = new {

  def $ (r: Rexp) = RECD(s, r)

  case ZERO => false

  case ONE => true

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

  case ZERO => ZERO

  case ONE => ZERO

  case CHAR(d) => if (c == d) ONE else ZERO

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

}

// extracts a string from 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 tokenise 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 Part of the lexer

// calculates a value for how a nullable regex 

// matches the empty string 

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))

}

// injects back a character into a value

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))

// 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 returns now also 

// an rectification function; no simplification under STAR 

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 RECD(x, r1) => {

    val (r1s, f1s) = simp(r1)

    (RECD(x, r1s), F_RECD(f1s))

  }

  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 { println ("Lexing Error") ; sys.exit(-1) } 

  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))

// The Lexing Rules for the Fun Language

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

val SYM = "a" | "b" | "c" | "d" | "e" | "f" | "g" | "h" | "i" | "j" | "k" | 

          "l" | "m" | "n" | "o" | "p" | "q" | "r" | "s" | "t" | "u" | "v" | 

          "w" | "x" | "y" | "z" | "T" | "_"

val DIGIT = "0" | "1" | "2" | "3" | "4" | "5" | "6" | "7" | "8" | "9"

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

val COMMA: Rexp = ","

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

                  ("i" $ ID) | 

                  ("o" $ OP) | 

                  ("n" $ NUM) | 

                  ("s" $ SEMI) | 

                  ("c" $ COMMA) |

                  ("pl" $ LPAREN) |

                  ("pr" $ RPAREN) |

                  ("w" $ (WHITESPACE | COMMENT))).%

// The tokens for the While language

case class T_NUM(n: Int) extends Token

val token : PartialFunction[(String, String), Token] = {

  case ("k", s) => T_KWD(s)

  case ("i", s) => T_ID(s)

  case ("o", s) => T_OP(s)

  case ("n", s) => T_NUM(s.toInt)

  case ("s", _) => T_SEMI

  case ("c", _) => T_COMMA

  case ("pl", _) => T_LPAREN

  case ("pr", _) => T_RPAREN

}

def tokenise(s: String) : List[Token] = 

  lexing_simp(WHILE_REGS, s).collect(token)

case class Sequence(e1: Exp, e2: Exp) extends Exp

  case Sequence(e1, e2) => List(max_stack_exp(e1), max_stack_exp(e2)).max

abstract class Parser[I, T](implicit ev: I => Seq[_]) {

    case _ => { println ("Parse Error\n") ; sys.exit(-1) }

class SeqParser[I, T, S](p: => Parser[I, T], 

                         q: => Parser[I, S])(implicit ev: I => Seq[_]) extends Parser[I, (T, S)] {

class AltParser[I, T](p: => Parser[I, T], 

                      q: => Parser[I, T])(implicit ev: I => Seq[_]) extends Parser[I, T] {

class FunParser[I, T, S](p: => Parser[I, T], 

                         f: T => S)(implicit ev: I => Seq[_]) extends Parser[I, S] {

implicit def ParserOps[I, T](p: Parser[I, T])(implicit ev: I => Seq[_]) = new {

  def || (q : => Parser[I, T]) = new AltParser[I, T](p, q)

  def ==>[S] (f: => T => S) = new FunParser[I, T, S](p, f)

  def ~[S] (q : => Parser[I, S]) = new SeqParser[I, T, S](p, q)

}

def ListParser[I, T, S](p: => Parser[I, T], 

                        q: => Parser[I, S])(implicit ev: I => Seq[_]): Parser[I, List[T]] = {

  (p ~ q ~ ListParser(p, q)) ==> { case ((x, y), z) => x :: z : List[T] } ||

  (p ==> ((s) => List(s)))

}

implicit def TokOps(t: Token) = new {

  def || (q : => Parser[List[Token], Token]) = new AltParser[List[Token], Token](t, q)

  def ==>[S] (f: => Token => S) = new FunParser[List[Token], Token, S](t, f)

  def ~[S](q : => Parser[List[Token], S]) = new SeqParser[List[Token], Token, S](t, q)

}

    case T_NUM(n)::ts => Set((n, ts)) 

// Grammar Rules

// arithmetic expressions

  (M ~ T_SEMI ~ Exp) ==> { case ((x, y), z) => Sequence(x, z): Exp } || M

// convenient string interpolations 

// for instructions, labels and methods

import scala.language.implicitConversions

import scala.language.reflectiveCalls

implicit def sring_inters(sc: StringContext) = new {

    def i(args: Any*): String = "   " ++ sc.s(args:_*) ++ "\n"

    def l(args: Any*): String = sc.s(args:_*) ++ ":\n"

    def m(args: Any*): String = sc.s(args:_*) ++ "\n"

}

type Env = Map[String, Int]

// compile expressions

def compile_exp(a: Exp, env : Env) : String = a match {

  case Num(i) => i"ldc $i"

  case Var(s) => i"iload ${env(s)}"

  case Aop("+", a1, a2) => compile_exp(a1, env) ++ compile_exp(a2, env) ++ i"iadd"

  case Aop("-", a1, a2) => compile_exp(a1, env) ++ compile_exp(a2, env) ++ i"isub"

  case Aop("*", a1, a2) => compile_exp(a1, env) ++ compile_exp(a2, env) ++ i"imul"

  case Aop("/", a1, a2) => compile_exp(a1, env) ++ compile_exp(a2, env) ++ i"idiv"

  case Aop("%", a1, a2) => compile_exp(a1, env) ++ compile_exp(a2, env) ++ i"irem"

    i"goto $if_end" ++

    l"$if_else" ++

    l"$if_end"

  case Call(name, args) => {

    args.map(a => compile_exp(a, env)).mkString ++

    i"invokestatic XXX/XXX/$name($is)I"

  case Sequence(a1, a2) => {

    compile_exp(a1, env) ++ i"pop" ++ compile_exp(a2, env)

    i"dup" ++

    i"invokestatic XXX/XXX/write(I)V"

// compile boolean expressions

def compile_bexp(b: BExp, env : Env, jmp: String) : String = b match {

    compile_exp(a1, env) ++ compile_exp(a2, env) ++ i"if_icmpne $jmp"

    compile_exp(a1, env) ++ compile_exp(a2, env) ++ i"if_icmpeq $jmp"

    compile_exp(a1, env) ++ compile_exp(a2, env) ++ i"if_icmpge $jmp"

    compile_exp(a1, env) ++ compile_exp(a2, env) ++ i"if_icmpgt $jmp"

// compile function for declarations and main

def compile_decl(d: Decl) : String = d match {

    m".method public static $name($is)I" ++

    m".limit locals ${args.length.toString}" ++

    m".limit stack ${1 + max_stack_exp(a)}" ++

    l"${name}_Start" ++