// A parser and interpreter for the While language

// 

import scala.language.implicitConversions

import scala.language.reflectiveCalls

// more convenience for the semantic actions later on

case class ~[+A, +B](_1: A, _2: B)

type IsSeq[A] = A => Seq[_]

abstract class Parser[I : IsSeq, T] {

  def parse(ts: I): Set[(T, I)]

  def parse_all(ts: I) : Set[T] =

    for ((head, tail) <- parse(ts); if tail.isEmpty) yield head

}

class SeqParser[I : IsSeq, T, S](p: => Parser[I, T], q: => Parser[I, S]) extends Parser[I, ~[T, S]] {

  def parse(sb: I) = 

    for ((head1, tail1) <- p.parse(sb); 

         (head2, tail2) <- q.parse(tail1)) yield (new ~(head1, head2), tail2)

}

class AltParser[I : IsSeq, T](p: => Parser[I, T], q: => Parser[I, T]) extends Parser[I, T] {

  def parse(sb: I) = p.parse(sb) ++ q.parse(sb)   

}

class FunParser[I : IsSeq, T, S](p: => Parser[I, T], f: T => S) extends Parser[I, S] {

  def parse(sb: I) = 

    for ((head, tail) <- p.parse(sb)) yield (f(head), tail)

}

case class StringParser(s: String) extends Parser[String, String] {

  def parse(sb: String) = {

    val (prefix, suffix) = sb.splitAt(s.length)

    if (prefix == s) Set((prefix, suffix)) else Set()

  }

}

case object NumParser extends Parser[String, Int] {

  val reg = "[0-9]+".r

  def parse(sb: String) = reg.findPrefixOf(sb) match {

    case None => Set()

    case Some(s) => {

      val (head, tail) = sb.splitAt(s.length)

      Set((head.toInt, tail)) 

    }

  }

}

implicit def string2parser(s : String) = StringParser(s)

implicit def ParserOps[I : IsSeq, T](p: Parser[I, T]) = 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)

}

implicit def StringOps(s: String) = new {

  def ||(q : => Parser[String, String]) = new AltParser[String, String](s, q)

  def ||(r: String) = new AltParser[String, String](s, r)

  def ==>[S] (f: => String => S) = new FunParser[String, String, S](s, f)

  def ~[S](q : => Parser[String, S]) = 

    new SeqParser[String, String, S](s, q)

  def ~(r: String) = 

    new SeqParser[String, String, String](s, r)

}

// the abstract syntax trees for the WHILE language

abstract class Stmt

abstract class AExp

abstract class BExp 

type Block = List[Stmt]

case object Skip extends Stmt

case class If(a: BExp, bl1: Block, bl2: Block) extends Stmt

case class While(b: BExp, bl: Block) extends Stmt

case class Assign(s: String, a: AExp) extends Stmt

case class Write(s: String) extends Stmt

case class Var(s: String) extends AExp

case class Num(i: Int) extends AExp

case class Aop(o: String, a1: AExp, a2: AExp) extends AExp

case object True extends BExp

case object False extends BExp

case class Bop(o: String, a1: AExp, a2: AExp) extends BExp

case class And(b1: BExp, b2: BExp) extends BExp

case class Or(b1: BExp, b2: BExp) extends BExp

case object IdParser extends Parser[String, String] {

  val reg = "[a-z][a-z,0-9]*".r

  def parse(sb: String) = reg.findPrefixOf(sb) match {

    case None => Set()

    case Some(s) => Set(sb.splitAt(s.length))

  }

}

// arithmetic expressions

lazy val AExp: Parser[String, AExp] = 

  (Te ~ "+" ~ AExp) ==> { case x ~ _ ~ z => Aop("+", x, z): AExp } ||

  (Te ~ "-" ~ AExp) ==> { case x ~ _ ~ z => Aop("-", x, z): AExp } || Te 

lazy val Te: Parser[String, AExp] = 

  (Fa ~ "*" ~ Te) ==> { case x ~ _ ~ z => Aop("*", x, z): AExp } || 

  (Fa ~ "/" ~ Te) ==> { case x ~ _ ~ z => Aop("/", x, z): AExp } || Fa  

lazy val Fa: Parser[String, AExp] = 

   ("(" ~ AExp ~ ")") ==> { case _ ~ y ~ _ => y } || 

   IdParser ==> Var || 

   NumParser ==> Num

// boolean expressions with some simple nesting

lazy val BExp: Parser[String, BExp] = 

   (AExp ~ "==" ~ AExp) ==> { case x ~ _ ~ z => Bop("==", x, z): BExp } || 

   (AExp ~ "!=" ~ AExp) ==> { case x ~ _ ~ z => Bop("!=", x, z): BExp } || 

   (AExp ~ "<" ~ AExp) ==> { case x ~ _ ~ z => Bop("<", x, z): BExp } || 

   (AExp ~ ">" ~ AExp) ==> { case x ~ _ ~ z => Bop(">", x, z): BExp } ||

   ("(" ~ BExp ~ ")" ~ "&&" ~ BExp) ==> { case _ ~ y ~ _ ~ _ ~ v => And(y, v): BExp } ||

   ("(" ~ BExp ~ ")" ~ "||" ~ BExp) ==> { case _ ~ y ~ _ ~ _ ~ v => Or(y, v): BExp } ||

   ("true" ==> (_ => True: BExp )) || 

   ("false" ==> (_ => False: BExp )) ||

   ("(" ~ BExp ~ ")") ==> { case _ ~ x ~ _ => x }

// statement / statements

lazy val Stmt: Parser[String, Stmt] =

  (("skip" ==> (_ => Skip: Stmt)) ||

   (IdParser ~ ":=" ~ AExp) ==> { case x ~ _ ~ z => Assign(x, z): Stmt } ||

   ("write(" ~ IdParser ~ ")") ==> { case _ ~ y ~ _ => Write(y): Stmt } ||

   ("if" ~ BExp ~ "then" ~ Block ~ "else" ~ Block) ==>

    { case _ ~ y ~ _ ~ u ~ _ ~ w => If(y, u, w): Stmt } ||

   ("while" ~ BExp ~ "do" ~ Block) ==> { case _ ~ y ~ _ ~ w => While(y, w) }) 

lazy val Stmts: Parser[String, Block] =

  (Stmt ~ ";" ~ Stmts) ==> { case x ~ _ ~ z => x :: z : Block } ||

  (Stmt ==> ( s => List(s) : Block))

// blocks (enclosed in curly braces)

lazy val Block: Parser[String, Block] =

  (("{" ~ Stmts ~ "}") ==> { case _ ~ y ~ _ => y } || 

   (Stmt ==> (s => List(s))))

Stmts.parse_all("x2:=5+3;")

Block.parse_all("{x:=5;y:=8}")

Block.parse_all("if(false)then{x:=5}else{x:=10}")

val fib = """n := 10;

             minus1 := 0;

             minus2 := 1;

             temp := 0;

             while (n > 0) do {

                 temp := minus2;

                 minus2 := minus1 + minus2;

                 minus1 := temp;

                 n := n - 1

             };

             result := minus2""".replaceAll("\\s+", "")

Stmts.parse_all(fib)

// an interpreter for the WHILE language

type Env = Map[String, Int]

def eval_aexp(a: AExp, env: Env) : Int = a match {

  case Num(i) => i

  case Var(s) => env(s)

  case Aop("+", a1, a2) => eval_aexp(a1, env) + eval_aexp(a2, env)

  case Aop("-", a1, a2) => eval_aexp(a1, env) - eval_aexp(a2, env)

  case Aop("*", a1, a2) => eval_aexp(a1, env) * eval_aexp(a2, env)

  case Aop("/", a1, a2) => eval_aexp(a1, env) / eval_aexp(a2, env)

}

def eval_bexp(b: BExp, env: Env) : Boolean = b match {

  case True => true

  case False => false

  case Bop("==", a1, a2) => eval_aexp(a1, env) == eval_aexp(a2, env)

  case Bop("!=", a1, a2) => !(eval_aexp(a1, env) == eval_aexp(a2, env))

  case Bop(">", a1, a2) => eval_aexp(a1, env) > eval_aexp(a2, env)

  case Bop("<", a1, a2) => eval_aexp(a1, env) < eval_aexp(a2, env)

  case And(b1, b2) => eval_bexp(b1, env) && eval_bexp(b2, env)

  case Or(b1, b2) => eval_bexp(b1, env) || eval_bexp(b2, env)

}

def eval_stmt(s: Stmt, env: Env) : Env = s match {

  case Skip => env

  case Assign(x, a) => env + (x -> eval_aexp(a, env))

  case If(b, bl1, bl2) => if (eval_bexp(b, env)) eval_bl(bl1, env) else eval_bl(bl2, env) 

  case While(b, bl) => 

    if (eval_bexp(b, env)) eval_stmt(While(b, bl), eval_bl(bl, env))

    else env

  case Write(x) => { println(env(x)) ; env }  

}

def eval_bl(bl: Block, env: Env) : Env = bl match {

  case Nil => env

  case s::bl => eval_bl(bl, eval_stmt(s, env))

}

def eval(bl: Block) : Env = eval_bl(bl, Map())

// parse + evaluate fib program; then lookup what is

// stored under the variable result 

println(eval(Stmts.parse_all(fib).head)("result"))

// more examles

// calculate and print all factors bigger 

// than 1 and smaller than n

println("Factors")

val factors =  

   """n := 12;

      f := 2;

      while (f < n / 2 + 1) do {

        if ((n / f) * f == n) then  { write(f) } else { skip };

        f := f + 1

      }""".replaceAll("\\s+", "")

eval(Stmts.parse_all(factors).head)

// calculate all prime numbers up to a number 

println("Primes")

val primes =  

   """end := 100;

      n := 2;

      while (n < end) do {

        f := 2;

        tmp := 0;

        while ((f < n / 2 + 1) && (tmp == 0)) do {

          if ((n / f) * f == n) then  { tmp := 1 } else { skip };

          f := f + 1

        };

        if (tmp == 0) then { write(n) } else { skip };

        n  := n + 1

      }""".replaceAll("\\s+", "")

eval(Stmts.parse_all(primes).head)