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Programming Languages Third Edition

Programming Languages Third Edition. Chapter 6 Part II Syntax / Grammars and Parsing. Objectives. Understand context-free grammars and BNFs Become familiar with parse trees Understand ambiguity, associativity, and precedence Read Sections 6.2 – 6.4, pp. 204-220.

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Programming Languages Third Edition

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  1. Programming LanguagesThird Edition Chapter 6 Part II Syntax / Grammars and Parsing

  2. Objectives • Understand context-free grammars and BNFs • Become familiar with parse trees • Understand ambiguity, associativity, and precedence • Read Sections 6.2 – 6.4, pp. 204-220 Programming Languages, Third Edition

  3. ParsingContext-Free Grammars and BNFs • Context-free grammar: consists of • a series of grammar rules (Productions) • Each rule has a single phrase structure name on the left, then a ::= metasymbol, followed by a sequence of symbols or other phrase structure names on the right • Nonterminals: names for phrase structures, since they are broken down into further phrase structures • Start symbol: one of the Nonterminals • Terminals: words or token symbols that cannot be broken down further Programming Languages, Third Edition

  4. Example 1: Unsigned Integers <num> ::= <digit> | <num> <digit> <digit> ::= 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 Terminals: 0, 1, … , 9 Nonterminals: <num> , <digit> Start Symbol: <num> Productions: there are 12 Metasymbols: “::=“ , “|” Programming Languages, Third Edition

  5. Example 1 (cont’d) • Derivation: the process of building in a language by beginning with the start symbol and replacing left-hand sides by choices of right-hand sides in the rules • Let’s derive the number 123 (on board) • Parse tree: graphical depiction of the replacement process in a derivation • Let’s draw parse tree for 123 (on board) Programming Languages, Third Edition

  6. Example 1 (cont’d) <num> ::= <digit> | <num> <digit> <digit> ::= 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 • Notice recursion in one of rules • Notice recursive symbol is on left • This is a left-recursive grammar • This is a left-associative grammar • Notice how parse tree cascades to left Programming Languages, Third Edition

  7. Example 2: Unsigned Integers <num> ::= <digit> | <digit> <num> <digit> ::= 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 Only made one change, so now grammar is • Right-recursive • Right-associative • Let’s draw parse tree for 123 Programming Languages, Third Edition

  8. Ex 3: Simple Expression Grammar <expr> ::= <expr> + <expr> | <expr> * <expr> | ( <expr> ) | <num> <num> ::= <digit> | <num> <digit> <digit> ::= 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 Let’s derive parse tree for: 3 + 4 + 5 Programming Languages, Third Edition

  9. Ex 3 (cont’d) <expr> ::= <expr> + <expr> | <expr> * <expr> | ( <expr> ) | <num> <num> ::= <digit> | <num> <digit> <digit> ::= 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 Is there another parse tree for: 3 + 4 + 5 Programming Languages, Third Edition

  10. Ex 3 (cont’d) <expr> ::= <expr> + <expr> | <expr> * <expr> | ( <expr> ) | <num> <num> ::= <digit> | <num> <digit> <digit> ::= 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 A grammar is ambiguous if there are two parse trees for the same string Programming Languages, Third Edition

  11. Ex 3 (cont’d) <expr> ::= <expr> + <expr> | <expr> * <expr> | ( <expr> ) | <num> <num> ::= <digit> | <num> <digit> <digit> ::= 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 Ambiguity is undesirable Let’s see why it’s undesirable: Derive parse trees for 3 + 4 * 5 Programming Languages, Third Edition

  12. Ex 3 (cont’d) <expr> ::= <expr> + <expr> | <expr> * <expr> | ( <expr> ) | <num> <num> ::= <digit> | <num> <digit> <digit> ::= 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 So what was the problem? Which tree provides correct arithmetic interpretation? Programming Languages, Third Edition

  13. Ex 3 (cont’d) Can we modify the grammar to “fix” the problem? YES! Add more levels of productions: <expr> ::= <expr> + <term> | <term> <term> ::= <term> * <factor> | <factor> <factor> ::= ( <expr> ) | <num> <num> ::= <digit> | <num> <digit> <digit> ::= 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 Programming Languages, Third Edition

  14. Ex 3 (cont’d) <expr> ::= <expr> + <term> | <term> <term> ::= <term> * <factor> | <factor> <factor> ::= ( <expr> ) | <num> <num> ::= <digit> | <num> <digit> <digit> ::= 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 Redraw parse trees for 3 + 4 + 5 and 3 + 4 * 5 Programming Languages, Third Edition

  15. Chapter 6Final Thoughts • A grammar is context-free when nonterminals appear singly on the left sides of productions • There is no context under which only certain replacements can occur • Anything not expressible using context-free grammars is a semantic, not a syntactic, issue • BNF form of language syntax makes it easier to write translators • Parsing stage can be automated (e.g. yacc tool in Unix, Python) Programming Languages, Third Edition

  16. Chapter 6Final Thoughts • Syntax establishes structure, not meaning • But meaning is related to syntax • Syntax-directed semantics: process of associating the semantics of a construct to its syntactic structure • Must construct the syntax so that it reflects the semantics to be attached later Programming Languages, Third Edition

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