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Practical, General Parser Combinators Anastasia Izmaylova, Ali Afroozeh and Tijs van der Storm

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Trade-offs Flexibility Expressivity Performance

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Performance Compiler construction DSLs Reverse Engineering Speed Natural grammars Modularity

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Performance Compiler construction DSLs Reverse Engineering Speed Natural grammars Modularity

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Performance Compiler construction DSLs Reverse Engineering Speed Natural grammars Modularity General parsing technology

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Performance O(n) O(n3) Deterministic Highly Ambiguous

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E ::= '-' E | E '*' E | E '+' E | Num '*' > '+' Expressivity

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E ::= '-' E | E '*' E | E '+' E | Num E ::= E '+' T | T T ::= T '*' F | F F ::= '-' F | Num '*' > '+' Expressivity

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E ::= '-' E | E '*' E | E '+' E | Num E ::= E '+' T | T T ::= T '*' F | F F ::= '-' F | Num E ::= T E1 E1 ::= '+' T E1 | ε T ::= F T1 T1 ::= '*' F | ε F ::= '-' F | Num '*' > '+' Expressivity

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E ::= '-' E | E '*' E | E '+' E | Num E ::= E '+' T | T T ::= T '*' F | F F ::= '-' F | Num E ::= T E1 E1 ::= '+' T E1 | ε T ::= F T1 T1 ::= '*' F | ε F ::= '-' F | Num '*' > '+' Expressivity

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E ::= '-' E | E '*' E | E '+' E | Num E ::= E '+' T | T T ::= T '*' F | F F ::= '-' F | Num E ::= T E1 E1 ::= '+' T E1 | ε T ::= F T1 T1 ::= '*' F | ε F ::= '-' F | Num '*' > '+' Expressivity

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E ::= '-' E | E '*' E | E '+' E | Num E ::= E '+' T | T T ::= T '*' F | F F ::= '-' F | Num E ::= T E1 E1 ::= '+' T E1 | ε T ::= F T1 T1 ::= '*' F | ε F ::= '-' F | Num '*' > '+' Expressivity

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Flexibility def Primary = ( PrimaryNoNewArray | ArrayCreationExpression ) def PrimaryNoNewArray = ( Literal | Type ~ "." ~ "class" | "void" ~ "." ~ "class" | "this" | ClassName ~ "." ~ "this" | "(" ~ Expression ~ ")" | ClassInstanceCreationExpression | FieldAccess | MethodInvocation | ArrayAccess ) def Literal = ( IntegerLiteral | FloatingPointLiteral | BooleanLiteral | CharacterLiteral | StringLiteral | NullLiteral ) primary : '(' primaryNoNewArray ')'
 | arrayCreationExpression
 ; 
 primaryNoNewArray : literal
 | type '.' 'class' | 'void' '.' 'class' | 'this' | className '.' 'this' | '(' type ')' | '(' expression ')' | classInstanceCreationExpression | fieldAccess | methodInvocation | arrayAccess
 ; literal : integerLiteral
 | floatingPointLiteral | booleanLiteral | characterLiteral | stringLiteral | nullLiteral
 ;

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General top-down parsing

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Recursive-descent parsing

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Recursive-descent parsing Memoization in CFGs Norvig 91

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Recursive-descent parsing Memoization in CFGs Norvig 91 Memoization in CPS Johnson 91

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Recursive-descent parsing Memoization in CFGs Norvig 91 Memoization in CPS Johnson 91 LR Parsing Knuth 65

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Recursive-descent parsing Memoization in CFGs Norvig 91 Memoization in CPS Johnson 91 Recursive-ascent parsing Penello 86 LR Parsing Knuth 65

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Recursive-descent parsing Memoization in CFGs Norvig 91 Memoization in CPS Johnson 91 Recursive-ascent parsing Penello 86 LR Parsing Knuth 65 GLR Parsing Tomita 85

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Recursive-descent parsing Memoization in CFGs Norvig 91 Memoization in CPS Johnson 91 Recursive-ascent parsing Penello 86 LR Parsing Knuth 65 GLR Parsing Tomita 85 RNGLR Parsing Scott and Johnstone 06

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Recursive-descent parsing Memoization in CFGs Norvig 91 Memoization in CPS Johnson 91 Recursive-ascent parsing Penello 86 LR Parsing Knuth 65 GLR Parsing Tomita 85 RNGLR Parsing Scott and Johnstone 06 GLR with reduced stack Aycock and Horspool 99

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Recursive-descent parsing Memoization in CFGs Norvig 91 Memoization in CPS Johnson 91 Recursive-ascent parsing Penello 86 LR Parsing Knuth 65 GLR Parsing Tomita 85 RNGLR Parsing Scott and Johnstone 06 GLR with reduced stack Aycock and Horspool 99 RIGLR Scott and Johnstone 05

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Recursive-descent parsing Memoization in CFGs Norvig 91 Memoization in CPS Johnson 91 Recursive-ascent parsing Penello 86 LR Parsing Knuth 65 GLR Parsing Tomita 85 RNGLR Parsing Scott and Johnstone 06 GLR with reduced stack Aycock and Horspool 99 RIGLR Scott and Johnstone 05 GLL Parsing Scott and Johnstone 13

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Recursive-descent parsing Memoization in CFGs Norvig 91 Memoization in CPS Johnson 91 Recursive-ascent parsing Penello 86 LR Parsing Knuth 65 GLR Parsing Tomita 85 RNGLR Parsing Scott and Johnstone 06 GLR with reduced stack Aycock and Horspool 99 RIGLR Scott and Johnstone 05 GLL Parsing Scott and Johnstone 13 GLL parsing with a different GSS Afroozeh and Izmaylova 15

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Recursive-descent parsing Memoization in CFGs Norvig 91 Memoization in CPS Johnson 91 Recursive-ascent parsing Penello 86 LR Parsing Knuth 65 GLR Parsing Tomita 85 RNGLR Parsing Scott and Johnstone 06 GLR with reduced stack Aycock and Horspool 99 RIGLR Scott and Johnstone 05 GLL Parsing Scott and Johnstone 13 GLL parsing with a different GSS Afroozeh and Izmaylova 15 This work

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Basic RD recognizers

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Basic RD recognizers Memorized CPS recognizers Memorization in top-down parsing Johnson '91

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Basic RD recognizers Cubic CPS recognizers Memorized CPS recognizers Memorization in top-down parsing Johnson '91

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Basic RD recognizers Cubic CPS recognizers Binarized SPPFs Memorized CPS recognizers Memorization in top-down parsing Johnson '91 BRNGLR, Scott & Johnstone ’07 GLL Parsing, Scott & Johnstone '13

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Basic RD recognizers Cubic CPS recognizers Binarized SPPFs Memorized CPS recognizers Memorization in top-down parsing Johnson '91 BRNGLR, Scott & Johnstone ’07 GLL Parsing, Scott & Johnstone '13 Cubic CPS parsers

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Basic recursive-descent recognizers type Result[T] = Option[T]
 def success[T](t: T) = Some(t)
 def failure[T] = None

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Basic recursive-descent recognizers type Result[T] = Option[T]
 def success[T](t: T) = Some(t)
 def failure[T] = None type Recognizer = Int => Result[Int]


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Basic recursive-descent recognizers type Result[T] = Option[T]
 def success[T](t: T) = Some(t)
 def failure[T] = None type Recognizer = Int => Result[Int]
 def epsilon: Recognizer =
 i => success(i)

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Basic recursive-descent recognizers type Result[T] = Option[T]
 def success[T](t: T) = Some(t)
 def failure[T] = None type Recognizer = Int => Result[Int]
 def epsilon: Recognizer =
 i => success(i) def terminal(t: String): Recognizer =
 i => if(input.startsWith(t, i)) success(i + t.length) else failure

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Basic recursive-descent recognizers type Result[T] = Option[T]
 def success[T](t: T) = Some(t)
 def failure[T] = None type Recognizer = Int => Result[Int]
 def epsilon: Recognizer =
 i => success(i) def terminal(t: String): Recognizer =
 i => if(input.startsWith(t, i)) success(i + t.length) else failure def seq(rs: Recognizer*): Recognizer =
 rs.reduceLeft((cur, r) => (i => cur(i).flatMap(r)))

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Basic recursive-descent recognizers type Result[T] = Option[T]
 def success[T](t: T) = Some(t)
 def failure[T] = None type Recognizer = Int => Result[Int]
 def epsilon: Recognizer =
 i => success(i) def terminal(t: String): Recognizer =
 i => if(input.startsWith(t, i)) success(i + t.length) else failure def seq(rs: Recognizer*): Recognizer =
 rs.reduceLeft((cur, r) => (i => cur(i).flatMap(r))) 
 
 
 
 
 
 def rule(nt: String, alts: Recognizer*): Recognizer =
 alts.reduce((cur, alt) => i => cur(i).orElse(alt(i)))

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Full backtracking

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Full backtracking trait MonadPlus[T, M[_] <: MonadPlus[_, M]] {
 def map[U](f: T => U): M[U]
 def flatMap[U](f: T => M[U]): M[U]
 def orElse(r: => M[T]): M[T]
 }

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Full backtracking trait MonadPlus[T, M[_] <: MonadPlus[_, M]] {
 def map[U](f: T => U): M[U]
 def flatMap[U](f: T => M[U]): M[U]
 def orElse(r: => M[T]): M[T]
 } type Result[T] <: MonadPlus[T, Result]

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Full backtracking trait MonadPlus[T, M[_] <: MonadPlus[_, M]] {
 def map[U](f: T => U): M[U]
 def flatMap[U](f: T => M[U]): M[U]
 def orElse(r: => M[T]): M[T]
 } type Result[T] <: MonadPlus[T, Result] type K[T] = T => Unit
 
 trait Result[T] extends (K[T] => Unit) with MonadPlus[T, Result]

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Full backtracking r1 = i => k => if (input.charAt(i) == 'a') k(i+1) r2 = i => k => if (input.charAt(i) == 'b') k(i+1) k0: Int => Unit = println(“Success”) r1(i).flatMap(r2): i => k => r1(i)(j => r2(j)(k))

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Left recursion & memoization

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Left recursion & memoization def memo[T](f: Int => Result[T]): Int => Result[T] = {
 val table: Map[Int, Result[T]] = HashMap.empty
 i => table.getOrElseUpdate(i, memo_result(f(i)))
 }

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Left recursion & memoization def memo[T](f: Int => Result[T]): Int => Result[T] = {
 val table: Map[Int, Result[T]] = HashMap.empty
 i => table.getOrElseUpdate(i, memo_result(f(i)))
 }

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Left recursion & memoization def memo[T](f: Int => Result[T]): Int => Result[T] = {
 val table: Map[Int, Result[T]] = HashMap.empty
 i => table.getOrElseUpdate(i, memo_result(f(i)))
 } def memo_result[T](res: => Result[T]): Result[T] = {
 val Rs: MutableList[T] = MutableList.empty
 val Ks: MutableList[K[T]] = MutableList.empty
 return result(k =>
 if(Ks.isEmpty) {
 Ks += k
 val k_i: K[T] = t => if (!Rs.contains(t)) { 
 Rs += t; for(kt <- Ks) kt(t) 
 }
 res(k_i)
 } else {
 Ks += k
 for(t <- Rs) k(t)
 })
 }

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Left recursion & memoization def memo[T](f: Int => Result[T]): Int => Result[T] = {
 val table: Map[Int, Result[T]] = HashMap.empty
 i => table.getOrElseUpdate(i, memo_result(f(i)))
 } def memo_result[T](res: => Result[T]): Result[T] = {
 val Rs: MutableList[T] = MutableList.empty
 val Ks: MutableList[K[T]] = MutableList.empty
 return result(k =>
 if(Ks.isEmpty) {
 Ks += k
 val k_i: K[T] = t => if (!Rs.contains(t)) { 
 Rs += t; for(kt <- Ks) kt(t) 
 }
 res(k_i)
 } else {
 Ks += k
 for(t <- Rs) k(t)
 })
 }

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Left recursion & memoization def memo[T](f: Int => Result[T]): Int => Result[T] = {
 val table: Map[Int, Result[T]] = HashMap.empty
 i => table.getOrElseUpdate(i, memo_result(f(i)))
 } def memo_result[T](res: => Result[T]): Result[T] = {
 val Rs: MutableList[T] = MutableList.empty
 val Ks: MutableList[K[T]] = MutableList.empty
 return result(k =>
 if(Ks.isEmpty) {
 Ks += k
 val k_i: K[T] = t => if (!Rs.contains(t)) { 
 Rs += t; for(kt <- Ks) kt(t) 
 }
 res(k_i)
 } else {
 Ks += k
 for(t <- Rs) k(t)
 })
 }

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Left recursion & memoization def memo[T](f: Int => Result[T]): Int => Result[T] = {
 val table: Map[Int, Result[T]] = HashMap.empty
 i => table.getOrElseUpdate(i, memo_result(f(i)))
 } def memo_result[T](res: => Result[T]): Result[T] = {
 val Rs: MutableList[T] = MutableList.empty
 val Ks: MutableList[K[T]] = MutableList.empty
 return result(k =>
 if(Ks.isEmpty) {
 Ks += k
 val k_i: K[T] = t => if (!Rs.contains(t)) { 
 Rs += t; for(kt <- Ks) kt(t) 
 }
 res(k_i)
 } else {
 Ks += k
 for(t <- Rs) k(t)
 })
 }

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Memoization on continutations S ::= S S S | S S | b

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Memoization on continutations S ::= S S S | S S | b Multiple calls at the same input position

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Memoization on continutations S ::= S S S | S S | b Multiple calls at the same input position def memo_k[T](f: T => Unit): T => Unit = {
 val s: Set[T] = HashSet.empty
 return t => if(!s.contains(t)) { s += t; f(t) }
 }

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S ::= a S b S | a S | s Input: aasb

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S, 0, 4 a, 0, 1 S, 1, 3 b, 3, 4 a, 1, 2 S, 2, 3 s, 2, 3 S, 1, 4 S, 0, 4 a, 0, 1 S, 2, 3 s, 2, 3 a, 1, 2 b, 3, 4 a (a) Parse tree 1 (b) Parse tree 2 S, 0, 4 a, 0, 1 S, 1, 3 b, 3, 4 a, 1, 2 S, 2, 3 s, 2, 3 S, 1, 4 S, 0, 4 a, 0, 1 S, 2, 3 s, 2, 3 a, 1, 2 b, 3, 4 (a) Parse tree 1 (b) Parse tree 2 S ::= a S b S | a S | s Input: aasb

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S, 0, 4 a, 0, 1 S, 1, 3 b, 3, 4 a, 1, 2 S, 2, 3 s, 2, 3 S, 1, 4 S, 0, 4 a, 0, 1 S, 2, 3 s, 2, 3 a, 1, 2 b, 3, 4 a (a) Parse tree 1 (b) Parse tree 2 S, 0, 4 a, 0, 1 S, 1, 3 b, 3, 4 a, 1, 2 S, 2, 3 s, 2, 3 S, 1, 4 S, 0, 4 a, 0, 1 S, 2, 3 s, 2, 3 a, 1, 2 b, 3, 4 (a) Parse tree 1 (b) Parse tree 2 , 0, 4 , 1, 3 b, 3, 4 S, 2, 3 s, 2, 3 S, 1, 4 S, 0, 4 a, 0, 1 S, 2, 3 s, 2, 3 a, 1, 2 b, 3, 4 S, 0, 4 a, 0, 1 S, 1, 3 b, 3, 4 a, 1, 2 S, 2, 3 s, 2, 3 S, 1, 4 a, 0, 1 S, 1, 3 a, 1, 2 S ::= a S . b, 0, 3 (S ::= aSb., 3) rse tree 1 (b) Parse tree 2 (c) SPPF (d) B S ::= a S b S | a S | s Input: aasb

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S, 0, 4 a, 0, 1 S, 1, 3 b, 3, 4 a, 1, 2 S, 2, 3 s, 2, 3 S, 1, 4 S, 0, 4 a, 0, 1 S, 2, 3 s, 2, 3 a, 1, 2 b, 3, 4 a (a) Parse tree 1 (b) Parse tree 2 S, 0, 4 a, 0, 1 S, 1, 3 b, 3, 4 a, 1, 2 S, 2, 3 s, 2, 3 S, 1, 4 S, 0, 4 a, 0, 1 S, 2, 3 s, 2, 3 a, 1, 2 b, 3, 4 (a) Parse tree 1 (b) Parse tree 2 S ::= a S b S | a S | s 4 3 b, 3, 4 S, 0, 4 a, 0, 1 S, 1, 3 b, 3, 4 a, 1, 2 S, 2, 3 s, 2, 3 S, 1, 4 S, 0, 4 a, 0, 1 S, 1, 3 b, 3, 4 a, 1, 2 S, 2, 3 s, 2, 3 S, 1, 4 S ::= a S . b, 0, 3 S ::= a S . b, 1, 3 (S ::= aSb., 3) (S ::= aS., 1) ee 2 (c) SPPF (d) Binarized SPPF Input: aasb

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Cubic CPS parsers type Parser = Int => Result[SPPFNode]

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Cubic CPS parsers type Parser = Int => Result[SPPFNode] def terminal(t: String): Parser = i => if(input.startsWith(t, i)) success(sppf.getTerminalNode(t, i, i + t.length)) else failure
 def epsilon: Parser = i => success(sppf.getEpsilonNode(i))

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Cubic CPS parsers type Parser = Int => Result[SPPFNode] def terminal(t: String): Parser = i => if(input.startsWith(t, i)) success(sppf.getTerminalNode(t, i, i + t.length)) else failure
 def epsilon: Parser = i => success(sppf.getEpsilonNode(i)) def seq(ps: Parser*): Parser = ps.reduceLeft(seq2) def seq2(p1: Parser, p2: Parser) = fix(q => i => p1(i).flatMap(t1 => p2(t1.rightExtent).map(t2 => sppf.getIntermediateNode(q, t1, t2))))

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Cubic CPS parsers type Parser = Int => Result[SPPFNode] def terminal(t: String): Parser = i => if(input.startsWith(t, i)) success(sppf.getTerminalNode(t, i, i + t.length)) else failure
 def epsilon: Parser = i => success(sppf.getEpsilonNode(i)) def seq(ps: Parser*): Parser = ps.reduceLeft(seq2) def seq2(p1: Parser, p2: Parser) = fix(q => i => p1(i).flatMap(t1 => p2(t1.rightExtent).map(t2 => sppf.getIntermediateNode(q, t1, t2)))) def rule(nt: String, alts: Parser*): Parser = alts.map(rule1(nt, _)).reduce((cur, p) => i => cur(i).orElse(p(i))) def rule1(nt: String, p: Parser): Parser = fix(q => i => p(i).map(t => sppf.getNonterminalNode(nt, q, t)))

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Highly-ambiguous grammar 0 100 200 300 400 500 0 2000 6000 10000 Size (#characters) CPU time (ms) ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● y = 0.000064 x3 + 0.0137 x2 − 2.8824 x 91.2971 R2 = 0.9998 Regression line S ::= SSS | SS | b

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Pragmatics

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Pragmatics • Lexical disambiguation filters

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Pragmatics • Lexical disambiguation filters • Layout (whitespace/comment) insertion

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Pragmatics • Lexical disambiguation filters • Layout (whitespace/comment) insertion • Semantic actions and terms

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Pragmatics • Lexical disambiguation filters • Layout (whitespace/comment) insertion • Semantic actions and terms See our ScalaDays 2015 talk!

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Java 3 4 5 0 1 2 3 Size (#characters) in log10 CPU time (ms) in log10 y = 1.138201 x − 8.696786 R2 = 0.9828 Regression line 7449 Java source files from JDK 1.7.0_60-b19

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Operator Precedence val E: OperatorNonterminal = syn ( right{ E ~ "^" ~ E } |> "-" ~ E |> left ( E ~ "*" ~ E | E ~ "/" ~ E ) |> left ( E ~ "+" ~ E | E ~ "-" ~ E ) | "(" ~ E ~ ")" | "[0-9]".r )

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val Primary: Nonterminal = syn ( PrimaryNoNewArray | ArrayCreationExpression ) val PrimaryNoNewArray: Nonterminal = syn ( Literal | Type ~ "." ~ "class" | "void" ~ "." ~ "class" | "this" | ClassName ~ "." ~ "this" | "(" ~ Expression ~ ")" | ClassInstanceCreationExpression | FieldAccess | MethodInvocation | ArrayAccess ) val Literal: Nonterminal = syn ( IntegerLiteral | FloatingPointLiteral | BooleanLiteral | CharacterLiteral | StringLiteral | NullLiteral ) val IntegerLiteral: Nonterminal = syn ( DecimalIntegerLiteral.!>>(".") | HexIntegerLiteral.!>>(".") | OctalIntegerLiteral | BinaryIntegerLiteral ) val FloatingPointLiteral: Nonterminal = syn ( DecimalFloatingPointLiteral | HexadecimalFloatingPointLiteral ) val ClassInstanceCreationExpression: Nonterminal = syn ( "new" ~ TypeArguments.? ~ TypeDeclSpecifier ~ TypeArguments | (Primary | QualifiedIdentifier).! ~ "." ~ "new" ~ TypeArgum ) val TypeArgumentsOrDiamond: Nonterminal = syn ( "<" ~ ">" | TypeArguments ) val ArgumentList: Nonterminal = syn (Expression.+(",")) val ArrayCreationExpression: Nonterminal = syn ( "new" ~ (PrimitiveType | ReferenceType).! ~ DimExpr.+ ~ ("[ val Expression: OperatorNonterminal = syn ( Expression ~ "." ~ Identifier | Expression ~ "." ~ "this" | Expression ~ "." ~ "new" ~ TypeArguments.? ~ Identifier ~ TypeArgumentsOrDiamond.? ~ "(" ~ ArgumentList.? ~ ")" ~ ClassBody.? | Expression ~ "." ~ NonWildTypeArguments ~ ExplicitGenericInvocationSuffix | Expression ~ "." ~ "super" ~ ("." ~ Identifier).!.? ~ Arguments | Type ~ "." ~ "class" | "void" ~ "." ~ "class" | Expression ~ "(" ~ ArgumentList.? ~ ")" | Expression ~ "[" ~ Expression ~ "]" |> Expression ~ "++" | Expression ~ "--" |> "+".!>>("+") ~ Expression | "-".!>>("-") ~ Expression | "++" ~ Expression | "--" ~ Expression | "!" ~ Expression | "~" ~ Expression | "new" ~ ClassInstanceCreationExpression | "new" ~ ArrayCreationExpression | "(" ~ PrimitiveType ~ ")" ~ Expression | "(" ~ ReferenceType ~ ")" ~ Expression |> left ( Expression ~ "*" ~ Expression | Expression ~ "/" ~ Expression | Expression ~ "%" ~ Expression ) |> left ( Expression ~ "+".!>>("+") ~ Expression | Expression ~ "-".!>>("-") ~ Expression ) |> left ( Expression ~ "<<" ~ Expression | Expression ~ ">>".!>>(">") ~ Expression | Expression ~ ">>>" ~ Expression ) |> left ( Expression ~ "<".!>>("[=<]".r) ~ Expression | Expression ~ ">".!>>("[=>]".r) ~ Expression | Expression ~ "<=" ~ Expression | Expression ~ ">=" ~ Expression | Expression ~ "instanceof" ~ Type ) |> left ( Expression ~ "==" ~ Expression | Expression ~ "!=" ~ Expression ) |> Expression ~ "&".!>>("&") ~ Expression |> Expression ~ "^" ~ Expression |> Expression ~ "|".!>>("|") ~ Expression |> Expression ~ "&&" ~ Expression |> Expression ~ "||" ~ Expression |> Expression ~ "?" ~ Expression ~ ":" ~ Expression |> Expression ~ AssignmentOperator ~ Expression | "(" ~ Expression ~ ")" | Primary)

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) val InclusiveOrExpression: Nonterminal = syn ( ExclusiveOrExpression | InclusiveOrExpression ~ "|" ~ ExclusiveOrExpression ) val ConditionalAndExpression: Nonterminal = syn ( InclusiveOrExpression | ConditionalAndExpression ~ "&&" ~ InclusiveOrExpression ) val ConditionalOrExpression: Nonterminal = syn ( ConditionalAndExpression | ConditionalOrExpression ~ "||" ~ ConditionalAndExpression ) val ConditionalExpression: Nonterminal = syn ( ConditionalOrExpression | ConditionalOrExpression ~ "?" ~ Expression ~ ":" ~ Conditio ) val AssignmentExpression: Nonterminal = syn ( ConditionalExpression | Assignment ) val Assignment: Nonterminal = syn ( LeftHandSide ~ AssignmentOperator ~ AssignmentExpression ) val LeftHandSide: Nonterminal = syn ( ExpressionName | "(" ~ LeftHandSide ~ ")" | FieldAccess | ArrayAccess ) val AssignmentOperator: Nonterminal = syn ( "=" | "+=" | "-=" | "*=" | "/=" | "&=" | "|=" | "^=" | "%=" | "<<=" | ">>=" | ">>>=" ) val Expression: Nonterminal = syn ( AssignmentExpression ) val Expression: OperatorNonterminal = syn ( Expression ~ "." ~ Identifier | Expression ~ "." ~ "this" | Expression ~ "." ~ "new" ~ TypeArguments.? ~ Identifier ~ TypeArgumentsOrDiamond.? ~ "(" ~ ArgumentList.? ~ ")" ~ ClassBody.? | Expression ~ "." ~ NonWildTypeArguments ~ ExplicitGenericInvocationSuffix | Expression ~ "." ~ "super" ~ ("." ~ Identifier).!.? ~ Arguments | Type ~ "." ~ "class" | "void" ~ "." ~ "class" | Expression ~ "(" ~ ArgumentList.? ~ ")" | Expression ~ "[" ~ Expression ~ "]" |> Expression ~ "++" | Expression ~ "--" |> "+".!>>("+") ~ Expression | "-".!>>("-") ~ Expression | "++" ~ Expression | "--" ~ Expression | "!" ~ Expression | "~" ~ Expression | "new" ~ ClassInstanceCreationExpression | "new" ~ ArrayCreationExpression | "(" ~ PrimitiveType ~ ")" ~ Expression | "(" ~ ReferenceType ~ ")" ~ Expression |> left ( Expression ~ "*" ~ Expression | Expression ~ "/" ~ Expression | Expression ~ "%" ~ Expression ) |> left ( Expression ~ "+".!>>("+") ~ Expression | Expression ~ "-".!>>("-") ~ Expression ) |> left ( Expression ~ "<<" ~ Expression | Expression ~ ">>".!>>(">") ~ Expression | Expression ~ ">>>" ~ Expression ) |> left ( Expression ~ "<".!>>("[=<]".r) ~ Expression | Expression ~ ">".!>>("[=>]".r) ~ Expression | Expression ~ "<=" ~ Expression | Expression ~ ">=" ~ Expression | Expression ~ "instanceof" ~ Type ) |> left ( Expression ~ "==" ~ Expression | Expression ~ "!=" ~ Expression ) |> Expression ~ "&".!>>("&") ~ Expression |> Expression ~ "^" ~ Expression |> Expression ~ "|".!>>("|") ~ Expression |> Expression ~ "&&" ~ Expression |> Expression ~ "||" ~ Expression |> Expression ~ "?" ~ Expression ~ ":" ~ Expression |> Expression ~ AssignmentOperator ~ Expression | "(" ~ Expression ~ ")" | Primary)

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Meerkat Parsers Anastasia Izmaylova @IAnastassija & Ali Afroozeh @afruze https://github.com/meerkat-parser