// Parser Combinators: Simple Version

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

//

// Call with

//

//  amm comb1.sc

//  Note, in the lectures I did not show the implicit type constraint

//  I : IsSeq, which means that the input type 'I' needs to be

//  a sequence. 

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

// 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)   

}

// 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 ((hd1, hd2), tl2)

}

// 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)

}

// an example of an atomic parser for characters

case class CharParser(c: Char) extends Parser[String, Char] {

  def parse(in: String) = 

    if (in != "" && in.head == c) Set((c, in.tail)) else Set()

}

// an atomic parser for parsing strings according to a regex

import scala.util.matching.Regex

case class RegexParser(reg: Regex) extends Parser[String, String] {

  def parse(in: String) = reg.findPrefixMatchOf(in) match {

    case None => Set()

    case Some(m) => Set((m.matched, m.after.toString))  

  }

}

// atomic parsers for numbers and "verbatim" strings 

val NumParser = RegexParser("[0-9]+".r)

def StrParser(s: String) = RegexParser(Regex.quote(s).r)

// NumParserInt transforms a "string integer" into a propper Int

// (needs "new" because MapParser is not a case class)

val NumParserInt = new MapParser(NumParser, (s: String) => s.toInt)

// 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)

}

// these implicits allow us to use an infix notation for

// sequences and alternatives; we also can write the usual

// map for a MapParser

// with this NumParserInt can now be written more conveniently

// as:

val NumParserInt2 = NumParser.map(_.toInt)

// A parser for palindromes (just returns them as string)

lazy val Pal : Parser[String, String] = {

  ((p"a" ~ Pal) ~ p"a").map{ case ((x, y), z) => s"$x$y$z" } || 

}  

// examples

Pal.parse_all("abaaaba")

Pal.parse("abaaaba")

println("Palindrome: " + Pal.parse_all("abaaaba"))

// A parser for wellnested parentheses 

//

//   P ::= ( P ) P | epsilon

//

//   (transforms '(' -> '{' , ')' -> '}' )

lazy val P : Parser[String, String] = {

  (p"(" ~ P ~ p")" ~ P).map{ case (((_, x), _), y) => "{" + x + "}" + y } ||

  p""

}  

println(P.parse_all("(((()()))())"))

println(P.parse_all("(((()()))()))"))

println(P.parse_all(")("))

println(P.parse_all("()"))

// A parser for arithmetic expressions (Terms and Factors)

lazy val E: Parser[String, Int] = {

  (T ~ p"+" ~ E).map{ case ((x, _), z) => x + z } ||

  (T ~ p"-" ~ E).map{ case ((x, _), z) => x - z } || T }

lazy val T: Parser[String, Int] = {

  (F ~ p"*" ~ T).map{ case ((x, _), z) => x * z } || F }

lazy val F: Parser[String, Int] = {

  (p"(" ~ E ~ p")").map{ case ((_, y), _) => y } || NumParserInt }

println(E.parse_all("1+3+4"))

println(E.parse("1+3+4"))

println(E.parse_all("4*2+3"))

println(E.parse_all("4*(2+3)"))

println(E.parse_all("(4)*((2+3))"))

println(E.parse_all("4/2+3"))

println(E.parse("1 + 2 * 3"))

println(E.parse_all("(1+2)+3"))

println(E.parse_all("1+2+3"))

// with parser combinators (and other parsing algorithms)

// no left-recursion is allowed, otherwise the will loop

lazy val EL: Parser[String, Int] = 

  ((EL ~ p"+" ~ EL).map{ case ((x, y), z) => x + z} || 

   (EL ~ p"*" ~ EL).map{ case ((x, y), z) => x * z} ||

   (p"(" ~ EL ~ p")").map{ case ((x, y), z) => y} ||

   NumParserInt)

// this will run forever:

//println(EL.parse_all("1+2+3"))

// non-ambiguous vs ambiguous grammars

// ambiguous

lazy val S : Parser[String, String] =

  (p"1" ~ S ~ S).map{ case ((x, y), z) => x + y + z } || p""

//println(time(S.parse("1" * 10)))

//println(time(S.parse_all("1" * 10)))

// non-ambiguous

lazy val U : Parser[String, String] =

  (p"1" ~ U).map{ case (x, y) => x + y } || p""

//println(time(U.parse("1" * 10)))

//println(time(U.parse_all("1" * 10)))

println(U.parse("1" * 25))

U.parse("11")

U.parse("11111")

U.parse("11011")

U.parse_all("1" * 100)

U.parse_all("1" * 100 + "0")

// you can see the difference in second example

//S.parse_all("1" * 100)         // succeeds

//S.parse_all("1" * 100 + "0")   // fails

// A variant which counts how many 1s are parsed

lazy val UCount : Parser[String, Int] =

  (p"1" ~ UCount).map{ case (_, y) => y + 1 } || p"".map{ _ => 0 }

println(UCount.parse("11111"))

println(UCount.parse_all("11111"))

// Two single character parsers

lazy val One : Parser[String, String] = p"a"

lazy val Two : Parser[String, String] = p"b"

One.parse("a")

One.parse("aaa")

// note how the pairs nest to the left with sequence parsers

(One ~ One).parse("aaa")

(One ~ One ~ One).parse("aaa")

(One ~ One ~ One ~ One).parse("aaaa")

(One || Two).parse("aaa")

// a problem with the arithmetic expression parser: it 

// gets very slow with deeply nested parentheses

println("Runtime problem")

println(E.parse("1"))

println(E.parse("(1)"))

println(E.parse("((1))"))

//println(E.parse("(((1)))"))

//println(E.parse("((((1))))"))

//println(E.parse("((((((1))))))"))

//println(E.parse("(((((((1)))))))"))

//println(E.parse("((((((((1)))))))"))

// runs with amm2 and amm3