Parsers Combinators in Scala, Ilya @lambdamix Kliuchnikov

Parser Combinators in Scala
Илья Ключников
@lambdamix

1

Комбинаторные библиотеки
● Actors
● Parsers
● ScalaCheck, Spesc
● Scalaz
● SBT
● EDSLs
● ...

2

33/35 11/14 8/9 4/13

3

Intro: combinators, parsers

Scala Parser Combinators from the Ground Up

How to write typical parser

33/35 11/14 Pros, cons 8/9 4/13

Advanced techniques
4

Parser?
● Трансформирует текст в структуру

+

2*3 + 4 * 3

2 3

5

Hello, parser
import scala.util.parsing.combinator._
import syntactical.StandardTokenParsers

sealed trait Expr
case class Num(i: Int) extends Expr
case class Var(n: String) extends Expr
case class Plus(e1: Expr, e2: Expr) extends Expr
case class Mult(e1: Expr, e2: Expr) extends Expr

object ArithParsers extends StandardTokenParsers with ImplicitConversions {
lexical.delimiters += ("(", ")", "+", "*")
def expr: Parser[Expr] =
term ~ ("+" ~> expr) ^^ Plus | term
def term: Parser[Expr] =
factor ~ ("*" ~> term) ^^ Mult | factor
def factor: Parser[Expr] =
numericLit ^^ { s => Num(s.toInt) } | ident ^^ Var | "(" ~> expr <~ ")"

def parseExpr(s: String) = phrase(expr)(new lexical.Scanner(s))
}

scala> ArithParsers.parseExpr("1")
res1: ArithParsers.ParseResult[parsers2.Expr] = [1.2] parsed: Num(1)

scala> ArithParsers.parseExpr("1 + 1 * 2")
res2: ArithParsers.ParseResult[parsers2.Expr] = [1.10] parsed: Plus(Num(1),Mult(Num(1),Num(2)))

scala> ArithParsers.parseExpr("a * (a * a)")
res3: ArithParsers.ParseResult[parsers2.Expr] = [1.12] parsed: Mult(Var(a),Mult(Var(a),Var(a)))
6

Example 2: Lambda calculus
t ::= terms:
x variable
λx.t abstraction
tt application

x y z = ((x y) z)
λx.λy.y = λx.(λy.y)
7

Example 2
sealed trait Term
case class Var(n: String) extends Term
case class Lam(v: Var, body: Term) extends Term
case class App(t1: Term, t2: Term) extends Term

object LamParsers extends StandardTokenParsers with ImplicitConversions with PackratParsers {
lexical.delimiters += ("(", ")", ".", "")
lazy val term: PackratParser[Term] =
appTerm | lam
lazy val vrb: PackratParser[Var] =
ident ^^ Var
lazy val lam: PackratParser[Term] =
("" ~> vrb) ~ ("." ~> term) ^^ Lam
lazy val appTerm: PackratParser[Term] =
appTerm ~ aTerm ^^ App | aTerm
lazy val aTerm: PackratParser[Term] =
vrb | "(" ~> term <~ ")"
def parseTerm(s: String) =
phrase(term)(new lexical.Scanner(s))
}

scala> LamParsers.parseTerm("x y z")
res1: LamParsers.ParseResult[parsers.Term] = [1.6] parsed: App(App(Var(x),Var(y)),Var(z))

scala> LamParsers.parseTerm("""x.y.x y""")
res2: LamParsers.ParseResult[parsers.Term] = [1.10] parsed:
Lam(Var(x),Lam(Var(y),App(Var(x),Var(y))))

scala> LamParsers.parseTerm("""(x.x x) (x. x x)""")
res3: LamParsers.ParseResult[parsers.Term] = [1.19] parsed:
App(Lam(Var(x),App(Var(x),Var(x))),Lam(Var(x),App(Var(x),Var(x)))) 8

Комбинаторные библиотеки
● Actors
● Parsers
● ScalaCheck, Spesc
● Scalaz
● SBT
● EDSLs
● ...

10

Принципы комбинаторных библиотек
● Соответствие терминологии библиотеки и
терминологии предметной области.
● Состав
● типы,
● примитивы,
● комбинаторы первого порядка,
● комбинаторы высшего порядка.
● Свойство замыкания (композиционность).
● Возможность эффективной реализации.
E. Кирпичев. Элементы функциональных языков. Практика функционального 11
программирования №3.

Предметная область
● Грамматика ● Парсеры
● Регулярная ● LL-парсеры
● Бесконтекстная ● LR-парсеры
● Леворекурсивная ● Нисходящие
● Праворекурсивная ● Восходящие
● Аттрибутная ● GLL
● Boolean ● Packrat-парсеры
● PEG ● Parsing with
● ... derivativatives
13

Предметная область

14

Подходы к созданию парсеров
● Parser-generator ● Hand-written
● Yacc ● Low-level
● Lex ● High-level
● JavaCC
● AntLR
● Rat!

15

Parsers in Scala

C9 Lectures: Dr. Erik Meijer - Functional Programming Fundamentals Chapter 8 of 13
A. Moors, F. Piessens, M. Odersky. Parser Combinators in Scala. Report CW 49 // Feb 2008
16

Scala parser combinators are
a form of recursive descent parsing
with infinite backtracking.

17

Parsers in Scala are functional
Background:
● W. Burge. Recursive Programming Techniques.
Addison-Wesley, 1975.
● Ph. Wadler. How to Replace Failure by a List of
Successes. A method for exception handling,
backtracking, and pattern matching in lazy
functional languages // 1985
● G. Hutton. Higher-order functions for parsing //
Journal of functional programming. 1992/2
● J. Fokker. Functional Parsers // 1995

18

Parser?
● Трансформирует текст в структуру

+

2*3 + 4 * 3

2 3

19

Парсер – это функция
type Parser[A] = String => A

Нет композиции функций, не обязательно парсить всю строку

type Parser[A] = String => (A, String)

Может закончиться неудачей

type Parser[A] = String => Option[(A, String)]

20

Results
trait SimpleResults {
type Input
trait Result[+T] {
def next: Input
}
case class Success[+T](result: T, next: Input) extends Result[T]
case class Failure(msg: String, next: Input) extends Result[Nothing]
}

object XParser extends SimpleResults {
type Input = String
val acceptX: Input => Result[Char] = { (in: String) =>
if (in.charAt(0) == 'x')
Success('x', in.substring(1))
else
Failure("expected an x", in)
}
}

scala> XParser.acceptX("xyz")
res0: parsers.XParser.Result[Char] = Success(x,yz)

scala> XParser.acceptX("yz")
res1: parsers.XParser.Result[Char] = Failure(expected an x,yz)

22

The basis: Parser, |, ~, accept
trait SimpleParsers extends SimpleResults {
trait Parser[+T] extends (Input => Result[T]) {
def apply(in: Input): Result[T]
def |[U >: T](p: => Parser[U]): Parser[U] = new Parser[U] {
def apply(in: Input) = Parser.this(in) match {
case Failure(_, _) => p(in)
case Success(x, n) => Success(x, n)}}

def ~[U](p: => Parser[U]): Parser[(T, U)] = new Parser[(T, U)] {
case Success(x, next) => p(next) match {
case Success(x2, next2) => Success((x, x2), next2)
case Failure(m, n) => Failure(m, n) }
case Failure(m, n) => Failure(m, n)}}
}
}

trait StringParsers extends SimpleParsers {
type Input = String
private val EOI = 0.toChar

def accept(expected: Char) = new Parser[Char] {
def apply(in: String) =
if (in == "") {
if (expected == EOI) Success(expected, "")
else Failure("no more input", in)
} else if (in.charAt(0) == expected)
Success(expected, in.substring(1))
else Failure("expected '" + expected + "'", in)
}
def eoi = accept(EOI)
}
23

The simplest parser
object OXOParser extends StringParsers {
def oxo = accept('o') ~ accept('x') ~ accept('o')
def oxos: Parser[Any] =
(oxo ~ accept(' ') ~ oxos | oxo)
}

scala> OXOParser.oxos("123")
res2: parsers.OXOParser.Result[Any] = Failure(expected 'o',123)

scala> OXOParser.oxos("oxo")
res3: parsers.OXOParser.Result[Any] = Success(((o,x),o),)

scala> OXOParser.oxos("oxo oxo")
res4: parsers.OXOParser.Result[Any] = Success(((((o,x),o), ),((o,x),o)),)

scala> OXOParser.oxos("oxo oxo 1")
res5: parsers.OXOParser.Result[Any] = Success(((((o,x),o), ),((o,x),o)), 1)

scala> (OXOParser.oxos ~ OXOParser.eoi)("oxo oxo 1")
res6: parsers.OXOParser.Result[(Any, Char)] = Failure(expected '?', 1)

24

Be careful!
def |[U >: T](p: => Parser[U]): Parser[U] = new Parser[U] { call-by-name param

def ~[U](p: => Parser[U]): Parser[(T, U)] = new Parser[(T, U)] { call-by-name param
}
}

}

25

Be careful!
def |[U >: T](p: Parser[U]): Parser[U] = new Parser[U] { call-by-value param

def ~[U](p: Parser[U]): Parser[(T, U)] = new Parser[(T, U)] { call-by-value param
}
}

}

scala> OXOParser.oxos("123")
java.lang.StackOverflowError
at parsers.OXOParser$.oxo(stepbystep.scala:67)
at parsers.OXOParser$.oxos(stepbystep.scala:69)
at parsers.OXOParser$.oxos(stepbystep.scala:69) 26
...

Attempt #2
(Factoring out Plumbing)

27

Where is a problem?

}
}

}

28

Too much “threading”

}
}

}

29

Improved Results
type Input
trait Result[+T] {
def next: Input
def map[U](f: T => U): Result[U]
def flatMapWithNext[U](f: T => Input => Result[U]): Result[U]
def append[U >: T](alt: => Result[U]): Result[U]
}
case class Success[+T](result: T, next: Input) extends Result[T] {
def map[U](f: T => U) = Success(f(result), next)
def flatMapWithNext[U](f: T => Input => Result[U]) = f(result)(next)
def append[U >: T](alt: => Result[U]) = this
}
case class Failure(msg: String, next: Input) extends Result[Nothing] {
def map[U](f: Nothing => U) = this
def flatMapWithNext[U](f: Nothing => Input => Result[U]) = this
def append[U](alt: => Result[U]) = alt
}
}

●map -...
●flatMapWithNext - ...

●append – for multiple results (we do not consider it here)

30

Parser is a function with many results
type Parser[A] = String => A

type Parser[A] = String => (A, String)

type Parser[A] = String => Option[(A, String)]

type Parser[A] = String => List[(A, String)]

31

After improving
type Input
trait Result[+T] {
def next: Input
def map[U](f: T => U): Result[U]
def flatMapWithNext[U](f: T => Input => Result[U]): Result[U]
def append[U >: T](alt: => Result[U]): Result[U]
}
case class Success[+T](result: T, next: Input) extends Result[T] {
def map[U](f: T => U) = Success(f(result), next)
def flatMapWithNext[U](f: T => Input => Result[U]) = f(result)(next)
def append[U >: T](alt: => Result[U]) = this
}
case class Failure(msg: String, next: Input) extends Result[Nothing] {
def map[U](f: Nothing => U) = this
def flatMapWithNext[U](f: Nothing => Input => Result[U]) = this
def append[U](alt: => Result[U]) = alt
}
}

abstract class Parser[+T] extends (Input => Result[T]) {
def flatMap[U](f: T => Parser[U]): Parser[U] = new Parser[U] {
def apply(in: Input) = Parser.this(in) flatMapWithNext (f)
}
def map[U](f: T => U): Parser[U] = new Parser[U] {
def apply(in: Input) = Parser.this(in) map (f)
}
def apply(in: Input) = Parser.this(in) append p(in)
}
def ~[U](p: => Parser[U]): Parser[(T, U)] =
for (a <- this; b <- p) yield (a, b)
Hey! 32
}
}

So, Parser is a Monad!!

33

Where is my “withFilter”?
● In Scala 2.10
● It was not easy...

34

Removing noise...

def Parser[T](f: Input => Result[T]) =
new Parser[T] { def apply(in: Input) = f(in) }
Removing
Boilerplate
abstract class Parser[+T] extends (Input => Result[T]) {
New Parser{apply}
def flatMap[U](f: T => Parser[U]): Parser[U] =
Parser { in => Parser.this(in) flatMapWithNext (f) }

def map[U](f: T => U): Parser[U] =
Parser { in => Parser.this(in) map (f) }

def |[U >: T](p: => Parser[U]): Parser[U] =
Parser { in => Parser.this(in) append p(in) }

def ~[U](p: => Parser[U]): Parser[(T, U)] =
for (a <- this; b <- p) yield (a, b)
}

}

35

Real Parsers
package scala.util.parsing.combinator

trait Parsers { Stream annotated with
type Elem
type Input = Reader[Elem] coordinates
sealed abstract class ParseResult[+T]
case class Success[+T](result: T, override val next: Input) extends ParseResult[T]
sealed abstract class NoSuccess(val msg: String, override val next: Input)
extends ParseResult[Nothing]
case class Failure(override val msg: String, override val next: Input)
extends NoSuccess(msg, next)
case class Error(override val msg: String, override val next: Input)
extends NoSuccess(msg, next)

...
abstract class Parser[+T] extends (Input => ParseResult[T]) { Controlling
... backtracking
}
case class ~[+a, +b](_1: a, _2: b) {
override def toString = "("+ _1 +"~"+ _2 +")"
}
Deconstructing sequencing
}

package scala.util.parsing.input

abstract class Reader[+T] {
def first: T
def rest: Reader[T] 37
}

Simplified picture

trait Parsers {
type Elem
type Input = Reader[Elem]

sealed abstract class ParseResult[+T]

abstract class Parser[+T] extends (Input => ParseResult[T]) {
combinators
}

combinators
}

38

Basic Combinators

trait Parsers {

def elem(kind: String, p: Elem => Boolean): Parser[Elem]
def elem(e: Elem): Parser[Elem]
implicit def accept(e: Elem): Parser[Elem]

abstract class Parser[+T] extends (Input => ParseResult[T]) {
def ~ [U](q: => Parser[U]): Parser[~[T, U]]
def <~ [U](q: => Parser[U]): Parser[T]
def ~! [U](p: => Parser[U]): Parser[~[T, U]]
def | [U >: T](q: => Parser[U]): Parser[U]
def ||| [U >: T](q0: => Parser[U]): Parser[U]
def ^^ [U](f: T => U): Parser[U]
def ^^^ [U](v: => U): Parser[U]
def ^? [U](f: PartialFunction[T, U], error: T => String): Parser[U]
def ^? [U](f: PartialFunction[T, U]): Parser[U]
def >>[U](fq: T => Parser[U])
def *: Parser[List[T]]
def +: Parser[List[T]]
def ?: Parser[Option[T]]
}

}

40

Swiss army knife Combinators

trait Parsers {

def commit[T](p: => Parser[T]): Parser[T]
def accept[ES <% List[Elem]](es: ES): Parser[List[Elem]]
def accept[U](expected: String, f: PartialFunction[Elem, U]): Parser[U]
def failure(msg: String): Parser[Nothing]
def err(msg: String): Parser[Nothing]
def success[T](v: T): Parser[T]
def rep[T](p: => Parser[T]): Parser[List[T]]
def repsep[T](p: => Parser[T], q: => Parser[Any]): Parser[List[T]]
def rep1[T](p: => Parser[T]): Parser[List[T]]
def rep1[T](first: => Parser[T], p0: => Parser[T]): Parser[List[T]]
def repN[T](num: Int, p: => Parser[T]): Parser[List[T]]
def rep1sep[T](p : => Parser[T], q : => Parser[Any]): Parser[List[T]]
def chainl1[T](p: => Parser[T], q: => Parser[(T, T) => T]): Parser[T]
def chainl1[T, U](first: => Parser[T], p: => Parser[U], q: => Parser[(T, U) => T]): Parser[T]
def chainr1[T, U](p: => Parser[T], q: => Parser[(T, U) => U],
combine: (T, U) => U, first: U): Parser[U]
def opt[T](p: => Parser[T]): Parser[Option[T]]
def not[T](p: => Parser[T]): Parser[Unit]
def guard[T](p: => Parser[T]): Parser[T]
def positioned[T <: Positional](p: => Parser[T]): Parser[T]
def phrase[T](p: Parser[T]): Parser[T]

}

Inpired by G. Hutton and E. Meijer. Monadic Parser Combinators.
41

Простейший (low-level) парсер
trait SimplestParsers extends Parsers {
type Elem = Char
def whitespaceChar: Parser[Char] =
elem("space char", ch => ch <= ' ' && ch != EofCh)
def letter: Parser[Char] = elem("letter", _.isLetter)

def whitespace: Parser[List[Char]] = rep(whitespaceChar)
def ident: Parser[List[Char]] = rep1(letter)

def parse[T](p: Parser[T], in: String): ParseResult[T] =
p(new CharSequenceReader(in))
}

scala> val p1 = new SimplestParsers{}
p1: java.lang.Object with parsers.SimplestParsers = $anon$1@17d59ff0

scala> import p1._
import p1._

scala> parse(letter, "foo bar")
res0: p1.ParseResult[Char] = [1.2] parsed: f

scala> parse(ident, "foo bar")
res1: p1.ParseResult[List[Char]] = [1.4] parsed: List(f, o, o)

scala> parse(ident, "123")
res2: p1.ParseResult[List[Char]] =
[1.1] failure: letter expected
43
123
^

Towards AST
trait Token
case class Id(n: String) extends Token
case class Num(n: String) extends Token
case object ErrorToken extends Token

trait TokenParsers extends Parsers {

type Elem = Char

private def whitespaceChar: Parser[Char] =
elem("space char", ch => ch <= ' ' && ch != EofCh)
def letter: Parser[Char] = elem("letter", _.isLetter)
def digit: Parser[Char] = elem("digit", _.isDigit)

def whitespace: Parser[List[Char]] = rep(whitespaceChar)
def idLit: Parser[String] = rep1(letter) ^^ { _.mkString("") }
def numLit: Parser[String] = rep1(digit) ^^ { _.mkString("") }

def id: Parser[Token] = idLit ^^ Id
def num: Parser[Token] = numLit ^^ Num

def token = id | num

def parse[T](p: Parser[T], in: String): ParseResult[T] =
p(new CharSequenceReader(in))

}

44

Lexer/Scanner
trait Scanners extends TokenParsers {
class Scanner(in: Reader[Char]) extends Reader[Token] {
def this(in: String) = this(new CharArrayReader(in.toCharArray()))
private val (tok, rest1, rest2) = whitespace(in) match {
case Success(_, in1) => token(in1) match {
case Success(tok, in2) => (tok, in1, in2)
case ns: NoSuccess => (ErrorToken, ns.next, ns.next.rest)
}
case ns: NoSuccess => (ErrorToken, ns.next, ns.next.rest)
}
def first = tok
def rest = new Scanner(rest2)
}
}

scala> val scs = new Scanners {}
scs: java.lang.Object with Scanners = $anon$1@68a750a

scala> val reader = new scs.Scanner("foo bar")
reader: scs.Scanner = Scanners$Scanner@6a75863f

scala> reader.first
res0: Token = Id(foo)

scala> reader.rest.first
res1: Num = Num(123)

scala> reader.rest.rest.first
res2: Token = ErrorToken
45

Lexing
Reader[Char] Low-level Parsing Reader[Token]

46

Parser

Implicit magic
“~” magic

50

Итак, ...
● Parsers Combinators in Scala позволяют описывать
исполняемые грамматики в виде, близком к BNF.
● Внутреннее устройство Parser Combinators - самый
настоящий Programming Pearl.
● Internal DSL for External DSLs.

51

Discussion
(Parser Combinators vs Parser Generator)

52

PROS
● Toт же язык (Scala) – не нужно учить новый
инструмент.
● Исполняемая грамматика - всегда
актуальный код.
● Краткость + богатая выразительность: LL(*) и
больше (в том числе, контекстные
грамматики).
● Можно делать fusion синтаксического
разбора и чего-нибудь еще.
● Модульность 53

CONS
● Некоторые простые вещи могут
кодироваться очень непросто.
● Performance.

54

Performance

Hand-written Lift-json is 350 times faster than version based on parser
combinators (proof link)

55

Parsing “9”: Too much backtracking
import scala.util.parsing.combinator._
import syntactical.StandardTokenParsers

sealed trait Expr
case class Num(i: Int) extends Expr
case class Var(n: String) extends Expr
case class Plus(e1: Expr, e2: Expr) extends Expr
case class Mult(e1: Expr, e2: Expr) extends Expr

object ArithParsers extends StandardTokenParsers with ImplicitConversions {
lexical.delimiters += ("(", ")", "+", "*")
def expr: Parser[Expr] =
term ~ ("+" ~> expr) ^^ Plus | term
def term: Parser[Expr] =
factor ~ ("*" ~> term) ^^ Mult | factor
def factor: Parser[Expr] =
numericLit ^^ { s => Num(s.toInt) } | ident ^^ Var | "(" ~> expr <~ ")"

def parseExpr(s: String) = phrase(expr)(new lexical.Scanner(s))
}

57

Idea: Memoization (Really, Laziness)

58

+ Left Recursion
sealed trait Term

appTerm | lam
ident ^^ Var
("" ~> vrb) ~ ("." ~> term) ^^ Lam
appTerm ~ aTerm ^^ App | aTerm
vrb | "(" ~> term <~ ")"
}

59

+ Left Recursion
sealed trait Term

appTerm | lam
ident ^^ Var
("" ~> vrb) ~ ("." ~> term) ^^ Lam
appTerm ~ aTerm ^^ App | aTerm lazy val
vrb | "(" ~> term <~ ")"
}

60

Without Left Recursion
sealed trait Term

object LamParsers extends StandardTokenParsers with ImplicitConversions {
lazy val term: Parser[Term] =
appTerm | lam
lazy val vrb: Parser[Var] =
ident ^^ Var
lazy val lam: Parser[Term] =
("" ~> vrb) ~ ("." ~> term) ^^ Lam
lazy val appTerm: Parser[Term] =
(aTerm +) ^^ { _.reduceLeft(App) }
lazy val aTerm: Parser[Term] =
vrb | "(" ~> term <~ ")"
}

61

Packrat Performance

62

Other Parsers
● Pairboled Parser (PEG parser)
● GLL parser
● Derivative combinators

http://stackoverflow.com/questions/4423514/scala-parsers-availability-differences-and-combining
63

Trends
● Merging two worlds
● Compositionality (Functional programming)
● Performance

64

https://github.com/ilya-klyuchnikov/tapl-scala

66

Parsers Combinators in Scala, Ilya @lambdamix Kliuchnikov

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