Chapter 3 Context-Free Grammars and Parsing Ambiguous Grammar

1. Chapter 3 Context-Free Grammars and Parsing Ambiguous Grammar Gang S. Liu College of Computer Science & Technology Harbin Engineering University Samuel2005@126.com

2. Ambiguous Grammar • exp → exp op exp | (exp) | number • op → + | - | * • The string 34 – 3 * 42 has two different parse trees and syntax trees. * - 42 34 3 - 34 * 3 42 A grammar that generates a string with two distinct parse trees is called an ambiguous grammar. Samuel2005@126.com

3. Two Ways to Deal with Ambiguity • Disambiguating rule • State a rule that specifies in each ambiguous case which of the trees is correct. • It corrects the ambiguity without changing and complicating the grammar. • Syntactic structure of the language is not given by the grammar alone. • Change grammar into a form that forces the construction of a correct parse tree. • In both cases we must decide which of the trees are correct. Samuel2005@126.com

4. Ambiguous Grammar • exp → exp op exp | (exp) | number • op → + | - | * • The string 34 – 3 * 42 has two different parse trees and syntax trees. * - 42 34 3 - 34 * 3 42 √ × A grammar that generates a string with two distinct parse trees is called an ambiguous grammar. Samuel2005@126.com

5. Precedence • Some operations have precedence over other operations. • Multiplication has precedence over addition. • To handle the precedence of operations in the grammar, we group the operators into groups of equal precedence. • We must write a different rule for each precedence. Samuel2005@126.com

6. Example exp → exp op exp | (exp) | number op →+ | - | * * - 42 34 3 - 34 * 3 42 √ × exp → exp addop exp | term addop →+ | - term → term mulop term | factor mulop →* factor →(exp) | number Samuel2005@126.com

7. (34 – 3) – 42 = –11 34 – (3 – 42) = 73 Ambiguous 34 – 3 – 42 √ × (34 – 3) – 42 Samuel2005@126.com

8. Associativity • Some operation (like subtraction) are left associative. • A series of subtraction operations is performed from left to right. • exp → exp addop exp | term • Recursion on both sides of the operator allows either side to match repetitions of the operator in a derivation. • exp → exp addop term | term • The right recursion is replaced with the base case, forcing the repetitive matches on the left side • Left recursion makes addition and subtraction left associative. Samuel2005@126.com

9. Example 34 - 3 - 42has a unique parse tree Samuel2005@126.com

10. Example exp → exp addop term | term addop →+ | - term → term mulop factor | factor mulop →* factor →(exp) | number 34- 3* 42has a unique parse tree exp exp addop term term - term mulop factor factor factor * number number number Samuel2005@126.com

11. Dangling else Problem statement → if-stmt | other if-stmt → if (exp)statement | if(exp) statementelsestatement exp → 0 | 1 • if (0) if (1) other else other has two parse trees with two meaning if (0) if (1) other else otherand if (0) if (1) other else other √ × Samuel2005@126.com

12. if (0) if (1) other else other Samuel2005@126.com

13. if (0) if (1) other else other Samuel2005@126.com

14. Dangling else Problem statement → if-stmt | other if-stmt → if (exp)statement | if(exp) statementelsestatement exp → 0 | 1 • if (0) if (1) other else other has two parse trees with two meaning if (0) if (1) other else otherand if (0) if (1) other else other • Modify the grammar. • Disambiguating rule: the most closely nested rule. Samuel2005@126.com

15. Dangling else Problem if (0) if (1) other else other statement → matched-stmt | unmatched-stmt matched-stmt →if (exp) matched-stmt else matched-stmt | other unmatched-stmt → if (exp)statement | if(exp) matched-stmtelseunmatched-stmt exp → 0 | 1 Samuel2005@126.com

16. Inessential Ambiguity • Sometimes a grammar may be ambiguous and yet always produce unique abstract syntax trees. • Example: ( a + b ) + c = a + ( b + c ) Samuel2005@126.com

17. Extended BNF Notation (EBNF) • { }repetitions A → β {α} and A → {α} β Samuel2005@126.com

18. Left and Right Recursion • Left recursive grammar: • A → A α | β • Equivalent to β α* • A → β {α} • Right recursive grammar: • A → αA | β • Equivalent to α * β • A → {α} β Samuel2005@126.com

19. Extended BNF Notation (EBNF) • { }repetitions A → β {α} and A → {α} β • [ ] optional constructs statement → if-stmt | other if-stmt → if (exp)statement | if(exp) statementelsestatement exp → 0 | 1 statement → if-stmt | other if-stmt → if (exp)statement[elsestatement] exp → 0 | 1 Samuel2005@126.com

20. Syntax Diagrams • Graphical representations for visually representing EBNF rules are called syntax diagrams. • They consist of boxes representing terminals and nonterminals, arrowed lines representing sequencing and choices, and nonterminal labels for each diagram representing the grammar rule defining that nonterminal. • A round or oval box is used to indicate terminals in a diagram, while a square or rectangular box is used to indicate nonterminals. Samuel2005@126.com

21. Syntax Diagrams(cont) • As an example, consider the grammar rule • factor → ( exp ) | number • This is written as a syntax diagram in the following way: Samuel2005@126.com

22. Syntax Diagrams(cont) • Syntax diagrams are written from the EBNF rather than the BNF, so we need diagrams representing repetition and optional constructs. Given a repetition such as • A → { B } • The corresponding syntax diagram is usually drawn as follow: Samuel2005@126.com

23. Syntax Diagrams(cont) • An optional construct such as • A → [ B ] • Is drawn as: Samuel2005@126.com

24. Example exp → exp addop term | term addop →+ | – term → term mulop factor | factor mulop →* factor →(exp) | number exp → term { addop term } addop →+ | – term → factor { mulop factor } mulop →* factor →(exp) | number Samuel2005@126.com

25. Example statement → if-stmt | other if-stmt → if (exp)statement | if(exp) statementelsestatement exp → 0 | 1 statement → if-stmt | other if-stmt → if (exp)statement[elsestatement] exp → 0 | 1 Samuel2005@126.com

26. Homework Samuel2005@126.com