// Parser Combinators:

// Simple Version for WHILE-language

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

//

// with some added convenience for

// map-parsers and grammar rules

//

// call with

//

//    amm comb2.sc

// more convenience for the map parsers later on;

// it allows writing nested patterns as

// case x ~ y ~ z => ...

case class ~[+A, +B](x: A, y: B)

// constraint for the input

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

abstract class Parser[I : IsSeq, T]{

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

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

    for ((hd, tl) <- parse(in); 

        if tl.isEmpty) yield hd

}

// parser combinators

// sequence parser

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

                                 q: => Parser[I, S]) extends Parser[I, ~[T, S]] {

  def parse(in: I) = 

    for ((hd1, tl1) <- p.parse(in); 

         (hd2, tl2) <- q.parse(tl1)) yield (new ~(hd1, hd2), tl2)

}

// alternative parser

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

                              q: => Parser[I, T]) extends Parser[I, T] {

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

}

// map parser

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

                                 f: T => S) extends Parser[I, S] {

  def parse(in: I) = for ((hd, tl) <- p.parse(in)) yield (f(hd), tl)

}

// atomic parser for (particular) strings

case class StrParser(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()

  }

}

// atomic parser for identifiers (variable names)

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))

  }

}

// atomic parser for numbers (transformed into ints)

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 (hd, tl) = sb.splitAt(s.length)

      Set((hd.toInt, tl)) 

    }

  }

}

// the following string interpolation allows us to write 

// StrParser(_some_string_) more conveniently as 

//

// p"<_some_string_>" 

implicit def parser_interpolation(sc: StringContext) = new {

    def p(args: Any*) = StrParser(sc.s(args:_*))

}    

// more convenient syntax for parser combinators

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

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

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

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

}

// 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

// arithmetic expressions

lazy val AExp: Parser[String, AExp] = 

  (Te ~ p"+" ~ AExp).map[AExp]{ case x ~ _ ~ z => Aop("+", x, z) } ||

  (Te ~ p"-" ~ AExp).map[AExp]{ case x ~ _ ~ z => Aop("-", x, z) } || Te

lazy val Te: Parser[String, AExp] = 

  (Fa ~ p"*" ~ Te).map[AExp]{ case x ~ _ ~ z => Aop("*", x, z) } || 

  (Fa ~ p"/" ~ Te).map[AExp]{ case x ~ _ ~ z => Aop("/", x, z) } || Fa  

lazy val Fa: Parser[String, AExp] = 

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

   IdParser.map(Var) || 

   NumParser.map(Num)

// boolean expressions with some simple nesting

lazy val BExp: Parser[String, BExp] = 

   (AExp ~ p"==" ~ AExp).map[BExp]{ case x ~ _ ~ z => Bop("==", x, z) } || 

   (AExp ~ p"!=" ~ AExp).map[BExp]{ case x ~ _ ~ z => Bop("!=", x, z) } || 

   (AExp ~ p"<" ~ AExp).map[BExp]{ case x ~ _ ~ z => Bop("<", x, z) } || 

   (AExp ~ p">" ~ AExp).map[BExp]{ case x ~ _ ~ z => Bop(">", x, z) } ||

   (p"(" ~ BExp ~ p")" ~ p"&&" ~ BExp).map[BExp]{ case _ ~ y ~ _ ~ _ ~ v => And(y, v) } ||

   (p"(" ~ BExp ~ p")" ~ p"||" ~ BExp).map[BExp]{ case _ ~ y ~ _ ~ _ ~ v => Or(y, v) } ||

   (p"true".map[BExp]{ _ => True }) || 

   (p"false".map[BExp]{ _ => False }) ||

   (p"(" ~ BExp ~ p")").map[BExp]{ case _ ~ x ~ _ => x }

// a single statement 

lazy val Stmt: Parser[String, Stmt] =

  ((p"skip".map[Stmt]{_ => Skip }) ||

   (IdParser ~ p":=" ~ AExp).map[Stmt]{ case x ~ _ ~ z => Assign(x, z) } ||

   (p"write(" ~ IdParser ~ p")").map[Stmt]{ case _ ~ y ~ _ => Write(y) } ||

   (p"if" ~ BExp ~ p"then" ~ Block ~ p"else" ~ Block)

     .map[Stmt]{ case _ ~ y ~ _ ~ u ~ _ ~ w => If(y, u, w) } ||

// statements

lazy val Stmts: Parser[String, Block] =

  (Stmt ~ p";" ~ Stmts).map[Block]{ case x ~ _ ~ z => x :: z } ||

  (Stmt.map[Block]{ s => List(s) })

// blocks (enclosed in curly braces)

lazy val Block: Parser[String, Block] =

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

   (Stmt.map(s => List(s))))

// Examples

Stmt.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+", "")

println(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+", "")

println(eval(Stmts.parse_all(primes).head))