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![LL Parsing
Parser Combinators
39
type Parser = String -> Tree
type Parser = String -> [(Tree, String)]
type Parser = String -> (Tree, String)
Returns either a singleton or
an empty list!](https://image.slidesharecdn.com/cc-ll-parsing-170116135709/85/LL-Parsing-62-320.jpg)
![LL Parsing
Parser Combinators
40
type Parser = String -> Tree
type Parser = String -> [(Tree, String)]
A parser p returns either a singleton list [(a, String)] indicating
success, or an empty list [] indicating failure. Returning a list of
results, also allow to express ambiguities.
type Parser = String -> (Tree, String)
type Parser a = String -> [(a, String)]](https://image.slidesharecdn.com/cc-ll-parsing-170116135709/85/LL-Parsing-63-320.jpg)
![LL Parsing
Primitive Parsers
41
success success :: a -> Parser a
success v = inp -> [(v, inp)]
success :: a String -> [(a, String)]
success v inp -> [(v, inp)]
fail
match
match :: Parser Char
match = inp -> case inp of
[] -> []
(x:xs) -> [(x,xs)]
fail :: Parser a
fail = inp -> []
or](https://image.slidesharecdn.com/cc-ll-parsing-170116135709/85/LL-Parsing-64-320.jpg)
![LL Parsing
Parser Combinators
42
alternation
sequencing
alt :: Parser a -> Parser a -> Parser a
p 'alt' q = inp -> (p inp ++ q inp)
seq :: Parser a -> Parser b -> Parser (a, b)
p ‘seq‘ q = inp -> [((v,w), inp’’) | (v, inp’) <- p inp
, (w, inp’’) <- q inp’]](https://image.slidesharecdn.com/cc-ll-parsing-170116135709/85/LL-Parsing-65-320.jpg)
Uploaded byEelco Visser
LL Parsing
This document provides an overview of LL parsing algorithms. It begins with a recap of formal language theory concepts like regular grammars, regular expressions, finite state automata, context-free grammars, derivation, and language generation. It then discusses predictive (recursive descent) parsing and LL parsing in particular. Key concepts covered include LL(k) grammars, filling the LL parsing table based on FIRST and FOLLOW sets, and using the table to perform LL parsing. An example grammar and its parsing table are provided to illustrate the process.
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LL Parsing
- 1. Challenge the future Delft Universityof Technology Course IN4303 Compiler Construction Eduardo Souza, Guido Wachsmuth, Eelco Visser LL Parsing Traditional Parsing Algorithms
- 2. lessons learned LL Parsing Recap:Lexical Analysis What are the formalisms to describe regular languages? • regular grammars • regular expressions • finite state automata Why are these formalisms equivalent? • constructive proofs How can we generate compiler tools from that? • implement DFAs • generate transition tables 2
- 3.
- 4. today’s lecture LL Parsing Overview efficientparsing algorithms • predictive/recursive descent parsing • LL parsing 3
- 5. today’s lecture LL Parsing Overview efficientparsing algorithms • predictive/recursive descent parsing • LL parsing grammar classes • LL(k) grammars • LR(k) grammars 3
- 6. today’s lecture LL Parsing Overview efficientparsing algorithms • predictive/recursive descent parsing • LL parsing grammar classes • LL(k) grammars • LR(k) grammars more top-down parsing algorithms • Parser Combinators • Parsing Expression Grammars • ALL(*) 3
- 7. LL Parsing Predictive (RecursiveDescent) Parsing I 4
- 8. formal languages LL Parsing5 Recap: A Theory of Language
- 9. formal languages LL Parsing vocabularyΣ finite, nonempty set of elements (words, letters) alphabet 5 Recap: A Theory of Language
- 10. formal languages LL Parsing vocabularyΣ finite, nonempty set of elements (words, letters) alphabet string over Σ finite sequence of elements chosen from Σ word, sentence, utterance 5 Recap: A Theory of Language
- 11. formal languages LL Parsing vocabularyΣ finite, nonempty set of elements (words, letters) alphabet string over Σ finite sequence of elements chosen from Σ word, sentence, utterance formal language λ set of strings over a vocabulary Σ λ ⊆ Σ* 5 Recap: A Theory of Language
- 12. formal grammars LL Parsing6 Recap: A Theory of Language
- 13. formal grammars LL Parsing formalgrammar G = (N, Σ, P, S) nonterminal symbols N terminal symbols Σ production rules P ⊆ (N∪Σ)* N (N∪Σ)* × (N∪Σ)* start symbol S∈N 6 Recap: A Theory of Language
- 14. formal grammars LL Parsing formalgrammar G = (N, Σ, P, S) nonterminal symbols N terminal symbols Σ production rules P ⊆ (N∪Σ)* N (N∪Σ)* × (N∪Σ)* start symbol S∈N 6 Recap: A Theory of Language nonterminal symbol
- 15. formal grammars LL Parsing formalgrammar G = (N, Σ, P, S) nonterminal symbols N terminal symbols Σ production rules P ⊆ (N∪Σ)* N (N∪Σ)* × (N∪Σ)* start symbol S∈N 6 Recap: A Theory of Language context
- 16. formal grammars LL Parsing formalgrammar G = (N, Σ, P, S) nonterminal symbols N terminal symbols Σ production rules P ⊆ (N∪Σ)* N (N∪Σ)* × (N∪Σ)* start symbol S∈N 6 Recap: A Theory of Language replacement
- 17. formal grammars LL Parsing formalgrammar G = (N, Σ, P, S) nonterminal symbols N terminal symbols Σ production rules P ⊆ (N∪Σ)* N (N∪Σ)* × (N∪Σ)* start symbol S∈N grammar classes type-0, unrestricted type-1, context-sensitive: (a A c, a b c) type-2, context-free: P ⊆ N × (N∪Σ)* type-3, regular: (A, x) or (A, xB) 6 Recap: A Theory of Language
- 18. formal languages LL Parsing7 Recap: A Theory of Language
- 19. formal languages LL Parsing formalgrammar G = (N, Σ, P, S) 7 Recap: A Theory of Language
- 20. formal languages LL Parsing formalgrammar G = (N, Σ, P, S) derivation relation G ⊆ (N∪Σ)* × (N∪Σ)* w G w’ ∃(p, q)∈P: ∃u,v∈(N∪Σ)* : w=u p v ∧ w’=u q v 7 Recap: A Theory of Language
- 21. formal languages LL Parsing formalgrammar G = (N, Σ, P, S) derivation relation G ⊆ (N∪Σ)* × (N∪Σ)* w G w’ ∃(p, q)∈P: ∃u,v∈(N∪Σ)* : w=u p v ∧ w’=u q v formal language L(G) ⊆ Σ* L(G) = {w∈Σ* | S G * w} 7 Recap: A Theory of Language
- 22. formal languages LL Parsing formalgrammar G = (N, Σ, P, S) derivation relation G ⊆ (N∪Σ)* × (N∪Σ)* w G w’ ∃(p, q)∈P: ∃u,v∈(N∪Σ)* : w=u p v ∧ w’=u q v formal language L(G) ⊆ Σ* L(G) = {w∈Σ* | S G * w} classes of formal languages 7 Recap: A Theory of Language
- 23. recursive descent LL Parsing8 Exp → “while” Exp “do” Exp Predictive parsing public void parseExp() { consume(WHILE); parseExp(); consume(DO); parseExp(); }
- 24. look ahead LL Parsing9 Exp → “while” Exp “do” Exp Exp → “if” Exp “then” Exp “else” Exp Predictive parsing public void parseExp() { switch current() { case WHILE: consume(WHILE); parseExp(); ...; break; case IF : consume(IF); parseExp(); ...; break; default : error(); } }
- 25. parse table LL Parsing10 rows • nonterminal symbols N • symbol to parse columns • terminal symbols Σk • look ahead k entries • production rules P • possible conflicts Predictive parsing T1 T2 T3 ... N1 N1 →... N1 →... N2 N2 →... N3 N3 →... N3 →... N4 N4 →... N5 N5 →... N6 N6 →... N6 →... N7 N7 →... N8 N8 →... N8 →... N8 →... ...
- 26. automaton LL Parsing Predictive parsing 11 …tn $t1 $ S input parse table stack
- 27.
- 28.
- 29. automaton LL Parsing Predictive parsing 13 x… $ $ Xi x Xi Xi → Y1... Yk …
- 30. automaton LL Parsing Predictive parsing 13 x… $ $ x Xi Xi → Y1... Yk … Yk … Y1
- 31. LL Parsing LL ParseTables II 14
- 32. entry (X, w)∈Pat row X and column T T∈ FIRST(w) nullable(w) ∧ T∈ FOLLOW(X) filling the table LL Parsing 15 Predictive parsing
- 33. entry (X, w)∈Pat row X and column T T∈ FIRST(w) nullable(w) ∧ T∈ FOLLOW(X) filling the table LL Parsing 15 Predictive parsing letters that w can start with
- 34. entry (X, w)∈Pat row X and column T T∈ FIRST(w) nullable(w) ∧ T∈ FOLLOW(X) filling the table LL Parsing 15 Predictive parsing w G * ε
- 35. entry (X, w)∈Pat row X and column T T∈ FIRST(w) nullable(w) ∧ T∈ FOLLOW(X) filling the table LL Parsing 15 Predictive parsing letters that can follow X
- 36. nullable LL Parsing nullable(X) (X, ε)∈ P nullable(X) (X0, X1 … Xk)∈P ∧ nullable(X1) ∧ … ∧ nullable(Xk) nullable(X0) nullable(w) nullable(ε) nullable(X1 … Xk) = nullable(X1) ∧ … ∧ nullable(Xk) 16 Predictive parsing
- 37. first sets LL Parsing FIRST(X) X∈Σ: FIRST(X) = {X} (X0, X1 … Xi … Xk)∈P ∧ nullable(X1 … Xi) FIRST(X0) ⊇ FIRST(Xi+1) FIRST(w) FIRST(ε) = {} ¬nullable(X) FIRST(Xw) = FIRST(X) nullable(X) FIRST(Xw) = FIRST(X) ∪ FIRST(w) 17 Predictive parsing
- 38. follow sets LL Parsing FOLLOW(X) (X0,X1 … Xi … Xk)∈P ∧ nullable(Xi+1 … Xk) FOLLOW(Xi) ⊇ FOLLOW(X0) (X0, X1 … Xi … Xk)∈P FOLLOW(Xi) ⊇ FIRST(Xi+1 … Xk) 18 Predictive parsing
- 39. LL Parsing 19 Example nullableFIRST FOLLOW Start Exp Exp’ Term Term’ Fact p0: Start → Exp EOF p1: Exp → Term Exp’ p2: Exp’ → “+” Term Exp’ p3: Exp’ → p4: Term → Fact Term’ p5: Term’ → “*” Fact Term’ p6: Term’ → p7: Fact → Num p8: Fact → “(” Exp “)”
- 40. nullable LL Parsing 20 Example (X,ε) ∈ P nullable(X) (X0, X1 … Xk)∈P ∧ nullable(X1) ∧ … ∧ nullable(Xk) nullable(X0) nullable FIRST FOLLOW Start Exp Exp’ Term Term’ Fact p0: Start → Exp EOF p1: Exp → Term Exp’ p2: Exp’ → “+” Term Exp’ p3: Exp’ → p4: Term → Fact Term’ p5: Term’ → “*” Fact Term’ p6: Term’ → p7: Fact → Num p8: Fact → “(” Exp “)”
- 41. nullable LL Parsing 21 Example (X,ε) ∈ P nullable(X) (X0, X1 … Xk)∈P ∧ nullable(X1) ∧ … ∧ nullable(Xk) nullable(X0) p0: Start → Exp EOF p1: Exp → Term Exp’ p2: Exp’ → “+” Term Exp’ p3: Exp’ → p4: Term → Fact Term’ p5: Term’ → “*” Fact Term’ p6: Term’ → p7: Fact → Num p8: Fact → “(” Exp “)” nullable FIRST FOLLOW Start no Exp no Exp’ yes Term no Term’ yes Fact no
- 42. FIRST sets LL Parsing22 Example (X0, X1 … Xi … Xk)∈P ∧ nullable(X1 … Xi) FIRST(X0) ⊇ FIRST(Xi+1) p0: Start → Exp EOF p1: Exp → Term Exp’ p2: Exp’ → “+” Term Exp’ p3: Exp’ → p4: Term → Fact Term’ p5: Term’ → “*” Fact Term’ p6: Term’ → p7: Fact → Num p8: Fact → “(” Exp “)” nullable FIRST FOLLOW Start no Exp no Exp’ yes Term no Term’ yes Fact no
- 43. FIRST sets LL Parsing23 Example (X0, X1 … Xi … Xk)∈P ∧ nullable(X1 … Xi) FIRST(X0) ⊇ FIRST(Xi+1) p0: Start → Exp EOF p1: Exp → Term Exp’ p2: Exp’ → “+” Term Exp’ p3: Exp’ → p4: Term → Fact Term’ p5: Term’ → “*” Fact Term’ p6: Term’ → p7: Fact → Num p8: Fact → “(” Exp “)” nullable FIRST FOLLOW Start no Num ( Exp no Num ( Exp’ yes + Term no Num ( Term’ yes * Fact no Num (
- 44. FOLLOW sets LL Parsing24 Example (X0, X1 … Xi … Xk)∈P ∧ nullable(Xi+1 … Xk) FOLLOW(Xi) ⊇ FOLLOW(X0) (X0, X1 … Xi … Xk)∈P FOLLOW(Xi) ⊇ FIRST(Xi+1 … Xk) nullable FIRST FOLLOW Start no Num ( Exp no Num ( Exp’ yes + Term no Num ( Term’ yes * Fact no Num ( p0: Start → Exp EOF p1: Exp → Term Exp’ p2: Exp’ → “+” Term Exp’ p3: Exp’ → p4: Term → Fact Term’ p5: Term’ → “*” Fact Term’ p6: Term’ → p7: Fact → Num p8: Fact → “(” Exp “)”
- 45. FOLLOW sets LL Parsing25 Example (X0, X1 … Xi … Xk)∈P ∧ nullable(Xi+1 … Xk) FOLLOW(Xi) ⊇ FOLLOW(X0) (X0, X1 … Xi … Xk)∈P FOLLOW(Xi) ⊇ FIRST(Xi+1 … Xk) p0: Start → Exp EOF p1: Exp → Term Exp’ p2: Exp’ → “+” Term Exp’ p3: Exp’ → p4: Term → Fact Term’ p5: Term’ → “*” Fact Term’ p6: Term’ → p7: Fact → Num p8: Fact → “(” Exp “)” nullable FIRST FOLLOW Start no Num ( Exp no Num ( ) EOF Exp’ yes + ) EOF Term no Num ( + ) EOF Term’ yes * + ) EOF Fact no Num ( * + ) EOF
- 46. LL parse table LLParsing 26 Example entry (X, w)∈P at row X and column T T∈ FIRST(w) nullable(w) ∧ T∈ FOLLOW(X) + * Num ( ) EOF Start Exp Exp’ Term Term’ Fact p0: Start → Exp EOF p1: Exp → Term Exp’ p2: Exp’ → “+” Term Exp’ p3: Exp’ → p4: Term → Fact Term’ p5: Term’ → “*” Fact Term’ p6: Term’ → p7: Fact → Num p8: Fact → “(” Exp “)”
- 47. LL parse table LLParsing 27 Example entry (X, w)∈P at row X and column T T∈ FIRST(w) nullable(w) ∧ T∈ FOLLOW(X) p0: Start → Exp EOF p1: Exp → Term Exp’ p2: Exp’ → “+” Term Exp’ p3: Exp’ → p4: Term → Fact Term’ p5: Term’ → “*” Fact Term’ p6: Term’ → p7: Fact → Num p8: Fact → “(” Exp “)” + * Num ( ) EOF Start p0 p0 Exp p1 p1 Exp’ p2 p3 p3 Term p4 p4 Term’ p6 p5 p6 p6 Fact p7 p8
- 48. parsing (4+3)*6 EOF LLParsing 28 Example p0: Start → Exp EOF p1: Exp → Term Exp’ p2: Exp’ → “+” Term Exp’ p3: Exp’ → p4: Term → Fact Term’ p5: Term’ → “*” Fact Term’ p6: Term’ → p7: Fact → Num p8: Fact → “(” Exp “)” + * Num ( ) EOF Start p0 p0 Exp p1 p1 Exp’ p2 p3 p3 Term p4 p4 Term’ p6 p5 p6 p6 Fact p7 p8
- 49.
- 50. LL Parsing Grammar classes 29 context-freegrammars LL(0)
- 51. LL Parsing Grammar classes 29 context-freegrammars LL(1) LL(0)
- 52. LL Parsing Grammar classes 29 context-freegrammars LL(k) LL(1) LL(0)
- 53. encoding precedence LL Parsing30 Exp → Num Exp → “(” Exp “)” Exp → Exp “*” Exp Exp → Exp “+” Exp Predictive parsing Fact → Num Fact → “(” Exp “)” Term → Term “*” Fact Term → Fact Exp → Exp “+” Term Exp → Term
- 54. eliminating left recursion LLParsing 31 Term → Term “*” Fact Term → Fact Exp → Exp “+” Term Exp → Term Predictive parsing Term’ → “*” Fact Term’ Term’ → Term → Fact Term’ Exp’ → “+” Term Exp’ Exp’ → Exp → Term Exp’
- 55. left factoring LL Parsing32 Exp → “if” Exp “then” Exp “else” Exp Exp → “if” Exp “then” Exp Predictive parsing Exp → “if” Exp “then” Exp Else Else → “else” Exp Else →
- 56.
- 57. LL Parsing Parser Combinators 34 •Parsers are modeled as functions, and larger parsers are built from smaller ones using higher-order functions. • Can be implemented in any lazy functional language with higher-order style type system (e.g. Haskell, Scala). • Parser combinators enable a recursive descent parsing strategy that facilitates modular piecewise construction and testing.
- 58. LL Parsing Parser Combinators 35 typeParser = String -> Tree
- 59. LL Parsing Parser Combinators 36 typeParser = String -> Tree What about intermediate parsers?
- 60. LL Parsing Parser Combinators 37 typeParser = String -> (Tree, String) type Parser = String -> Tree Return the remainder of the input!
- 61. LL Parsing Parser Combinators 38 typeParser = String -> (Tree, String) type Parser = String -> Tree WWhat about parsers that fail?
- 62. LL Parsing Parser Combinators 39 typeParser = String -> Tree type Parser = String -> [(Tree, String)] type Parser = String -> (Tree, String) Returns either a singleton or an empty list!
- 63. LL Parsing Parser Combinators 40 typeParser = String -> Tree type Parser = String -> [(Tree, String)] A parser p returns either a singleton list [(a, String)] indicating success, or an empty list [] indicating failure. Returning a list of results, also allow to express ambiguities. type Parser = String -> (Tree, String) type Parser a = String -> [(a, String)]
- 64. LL Parsing Primitive Parsers 41 successsuccess :: a -> Parser a success v = inp -> [(v, inp)] success :: a String -> [(a, String)] success v inp -> [(v, inp)] fail match match :: Parser Char match = inp -> case inp of [] -> [] (x:xs) -> [(x,xs)] fail :: Parser a fail = inp -> [] or
- 65. LL Parsing Parser Combinators 42 alternation sequencing alt:: Parser a -> Parser a -> Parser a p 'alt' q = inp -> (p inp ++ q inp) seq :: Parser a -> Parser b -> Parser (a, b) p ‘seq‘ q = inp -> [((v,w), inp’’) | (v, inp’) <- p inp , (w, inp’’) <- q inp’]
- 66. LL Parsing Parser Combinators 43 •Parser combinators can use semantic actions to manipulate intermediate results, being able to produce values rather than trees. • More powerful combinators can be build to allow parsing context-sensitive languages (by passing the context together with parsing results). • Parser Combinators in Scala: A. Moors, F. Piessens, Martin Odersky. Parser combinators in Scala. Technical Report Department of Computer Science, K.U. Leuven, February 2008.
- 67. LL Parsing Parsing ExpressionGrammars IV 44
- 68. LL Parsing Parsing ExpressionGrammars (PEGs) 45 A ← e Rules are of the form: where A is a non-terminal and e is a parsing expression.
- 69.
- 70. LL Parsing Syntactic Predicates 47 &eand !e : preserves the knowledge whether e fails or not. Comment ← '//' (!EndOfLine .)* EndOfLine
- 71. LL Parsing Parsing ExpressionGrammars 48 S ← a b / a S ← a / a b • Prioritized choice '/'.
- 72. LL Parsing Parsing ExpressionGrammars 49 S ← a b / a ≠ S ← a / a b • Prioritized choice '/'. • Backtracks when parsing an alternative fails. • Uses memoization of intermediate results to parse in linear time, called packrat parsing. • Does not allow left-recursion.
- 73. LL Parsing ANTLR /ALL(*) V 50
- 74. LL Parsing LL(*) 51 • ParsesLL-regular grammars: for any given non-terminal, parsers can use the entire remaining of the input to differentiate the alternative productions. • Statically builds a DFA from the grammar productions to recognize lookahead. • When in conflict, chooses the first alternative and backtracks when DFA lookahead recognition fails.
- 75. LL Parsing LL(*) GrammarAnalysis 52 S : ID | ID = E | unsigned* int ID | unsigned* ID ID
- 76. LL Parsing LL(*) GrammarAnalysis 53 S : ID | ID = E | unsigned* int ID | unsigned* ID ID (1) (2) (3) (4) augmented recursive transition network (ATN) s11 s s1 s3 ε s7 ε ε ε s2 s4 s’ s8 s5 s10s9 s12 s14s13 ID ID ID IDint unsigned unsigned ε ε ID = s6 E ε ε ε ε terminals: ID, =, int, unsigned
- 77. LL Parsing LL(*) GrammarAnalysis 54 S : ID | ID = E | unsigned* int ID | unsigned* ID ID (1) (2) (3) (4) terminals: ID, =, int, unsigned converts ATN to DFA s11 s s1 s3 ε s7 ε ε ε s2 s4 s’ s8 s5 s10s9 s12 s14s13 ID ID ID IDint unsigned unsigned ε ε ID = s6 E ε ε ε ε (i) Initial state = closure(s); (ii) Create a final state for each production; (iii) While DFA state contains ATN states from multiple paths, create transitions with terminals (or EOF if DFA contains s’); (iv) If DFA state contain ATN states from a single path, add transition to corresponding final DFA state;
- 78. s0’ s1’ s2’ s3’ => 2 s4’ => 1 s5’ =>4 s6’ => 3 ID = EOF ID ID int unsigned unsigned int LL Parsing LL(*) Grammar Analysis 55 (1) (2) (3) (4) S : ID | ID = E | unsigned* int ID | unsigned* ID ID s11 s s1 s3 ε s7 ε ε ε s2 s4 s’ s8 s5 s10s9 s12 s14s13 ID ID ID IDint unsigned unsigned ε ε ID = s6 E ε ε ε ε terminals: ID, =, int, unsigned
- 79. LL Parsing Adaptive LL(*) 56 S: E = E ; | E ; E : E * E | E + E | E ( E ) | ID void S() { switch (adaptivePredict("S", callStack)){ case 1 : E(); match('='); E(); match(‘;'); break; case 2: E(); match(';'); break; } }
- 80. LL Parsing Adaptive LL(*) 57 Dynamicallybuilds the lookahead DFA. S : E = E ; | E ; E : E * E | E + E | E ( E ) | ID terminals: =, ;, *, +, (, ), ID s6 s8 E s s1 ε ε s2 s’ s3 E = s4 E ε ε s5 ; s7 ;
- 81. LL Parsing Adaptive LL(*) 58 D0s1 ID :1 = s2 s4s3 :2 ( ID ) ; D0 s1 ID :1 = After parsing: x = y; f(x); Dynamically builds the lookahead DFA.
- 82. LL Parsing Adaptive LL(*) 59 S: x B | y C B : A a C : A b a A : b | ε parse: yba
- 83. LL Parsing Adaptive LL(*) 60 S: x B | y C B : A a C : A b a A : b | ε input: yba stack: S
- 84. LL Parsing Adaptive LL(*) 61 S: x B | y C B : A a C : A b a A : b | ε input: yba stack: yC
- 85. LL Parsing Adaptive LL(*) 62 S: x B | y C B : A a C : A b a A : b | ε input: ba stack: C
- 86. LL Parsing Adaptive LL(*) 63 S: x B | y C B : A a C : A b a A : b | ε input: ba stack: A ba
- 87. LL Parsing Adaptive LL(*) 64 S: x B | y C B : A a C : A b a A : b | ε input: ba stack: A ba b in First(A) b in Follow(A) A1 or A2? A1 A2
- 88. LL Parsing Adaptive LL(*) 65 •Tries to parse using strong LL (without looking at the call stack), when there are multiple alternatives, splits the parser to try all possibilities. • Parsing continues with a graph, handling multiple stacks in paralell to explore all alternatives. • Eventually, if the grammar is unambiguous, only one stack "survives". If multiple stacks survive, an ambiguty has been found and the parser picks the production with lower value.
- 89. LL Parsing ANTLR 4 66 •Accepts as input any context-free grammar that does not contain indirect or hidden left-recursion. • Generates ALL(*) parses in Java or C#. • Grammars contain lexical and syntactic rules and generate a lexer and a parser. • ANTLR4 grammars can be scannerless and composable by using individual characters as input symbols.
- 90.
- 91.
- 92. lessons learned LL Parsing Summary Howcan we parse context-free languages effectively? • predictive parsing algorithms 68
- 93. lessons learned LL Parsing Summary Howcan we parse context-free languages effectively? • predictive parsing algorithms Which grammar classes are supported by these algorithms? • LL(k) grammars, LL(k) languages 68
- 94. lessons learned LL Parsing Summary Howcan we parse context-free languages effectively? • predictive parsing algorithms Which grammar classes are supported by these algorithms? • LL(k) grammars, LL(k) languages How can we generate compiler tools from that? • implement automaton • generate parse tables 68
- 95. lessons learned LL Parsing Summary Howcan we parse context-free languages effectively? • predictive parsing algorithms Which grammar classes are supported by these algorithms? • LL(k) grammars, LL(k) languages How can we generate compiler tools from that? • implement automaton • generate parse tables What are other techniques for implementing top-down parsers? • Parser Combinators • PEGs • ALL(*) 68
- 96.
- 97. learn more LL Parsing Literature formallanguages Noam Chomsky: Three models for the description of language. 1956 J. E. Hopcroft, R. Motwani, J. D. Ullman: Introduction to Automata Theory, Languages, and Computation. 2006 69
- 98. learn more LL Parsing Literature formallanguages Noam Chomsky: Three models for the description of language. 1956 J. E. Hopcroft, R. Motwani, J. D. Ullman: Introduction to Automata Theory, Languages, and Computation. 2006 syntactical analysis Andrew W. Appel, Jens Palsberg: Modern Compiler Implementation in Java, 2nd edition. 2002 Alfred V. Aho, Ravi Sethi, Jeffrey D. Ullman, Monica S. Lam: Compilers: Principles, Techniques, and Tools, 2nd edition. 2006 69
- 99.
- 100. learn more LL Parsing Literature ALL(*) TerenceJohn Parr, Sam Harwell, Kathleen Fisher. Adaptive LL(*) parsing: the power of dynamic analysis. In OOPSLA 2014. 70
- 101. learn more LL Parsing Literature ALL(*) TerenceJohn Parr, Sam Harwell, Kathleen Fisher. Adaptive LL(*) parsing: the power of dynamic analysis. In OOPSLA 2014. Parsing Expression Grammars Bryan Ford. Parsing Expression Grammars: a recognition-based syntactic foundation. In POPL 2004. 70
- 102. learn more LL Parsing Literature ALL(*) TerenceJohn Parr, Sam Harwell, Kathleen Fisher. Adaptive LL(*) parsing: the power of dynamic analysis. In OOPSLA 2014. Parsing Expression Grammars Bryan Ford. Parsing Expression Grammars: a recognition-based syntactic foundation. In POPL 2004. Parser Combinators Graham Hutton. Higher-Order Functions for Parsing. Journal of Functional Programming, 1992. A. Moors, F. Piessens, Martin Odersky. Parser combinators in Scala. Technical Report Department of Computer Science, K.U. Leuven, February 2008. 70
- 103.
- 104.
- 105. copyrights LL Parsing Pictures Slide 1:Book Scanner by Ben Woosley, some rights reserved Slides 5-7: Noam Chomsky by Fellowsisters, some rights reserved Slide 8, 9, 26-28: Tiger by Bernard Landgraf, some rights reserved Slide 32: Ostsee by Mario Thiel, some rights reserved 73