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Lecture Programming languages (2/e): Chapter 2b - Tucker, Noonan

A grammar can be used to define associativity and precedence among the operators in an expression. A grammar is ambiguous if one of its strings has two or more diffferent parse trees. Chapter 2b provides knowledge of grammars: Associativity and precedence, ambiguous grammars. | Programming Languages 2nd edition Tucker and Noonan Chapter 2 Syntax A language that is simple to parse for the compiler is also simple to parse for the human programmer. N. Wirth Contents 2.1 Grammars 2.1.1 Backus-Naur Form 2.1.2 Derivations 2.1.3 Parse Trees 2.1.4 Associativity and Precedence 2.1.5 Ambiguous Grammars 2.2 Extended BNF 2.3 Syntax of a Small Language: Clite 2.3.1 Lexical Syntax 2.3.2 Concrete Syntax 2.4 Compilers and Interpreters 2.5 Linking Syntax and Semantics 2.5.1 Abstract Syntax 2.5.2 Abstract Syntax Trees 2.5.3 Abstract Syntax of Clite 2.1.4 Associativity and Precedence A grammar can be used to define associativity and precedence among the operators in an expression. E.g., + and - are left-associative operators in mathematics; * and / have higher precedence than + and - . Consider the more interesting grammar G1: Expr -> Expr + Term | Expr – Term | Term Term -> Term * Factor | Term / Factor | Term % Factor | Factor Factor -> Primary ** Factor | Primary Primary -> 0 | . | 9 | ( Expr ) Parse of 4**2**3+5*6+7 for Grammar G1 Figure 2.3 Precedence Associativity Operators 3 right ** 2 left * / % 1 left + - Note: These relationships are shown by the structure of the parse tree: highest precedence at the bottom, and left-associativity on the left at each level. Associativity and Precedence for Grammar G1 Table 2.1 2.1.5 Ambiguous Grammars A grammar is ambiguous if one of its strings has two or more diffferent parse trees. E.g., Grammar G1 above is unambiguous. C, C++, and Java have a large number of operators and precedence levels Instead of using a large grammar, we can: Write a smaller ambiguous grammar, and Give separate precedence and associativity (e.g., Table 2.1) An Ambiguous Expression Grammar G2 Expr -> Expr Op Expr | ( Expr ) | Integer Op -> + | - | * | / | % | ** Notes: G2 is equivalent to G1. I.e., its language is the same. G2 has fewer productions and nonterminals than G1. However, G2 is ambiguous. Ambiguous Parse of 5-4+3 Using Grammar | Programming Languages 2nd edition Tucker and Noonan Chapter 2 Syntax A language that is simple to parse for the compiler is also simple to parse for the human programmer. N. Wirth Contents 2.1 Grammars 2.1.1 Backus-Naur Form 2.1.2 Derivations 2.1.3 Parse Trees 2.1.4 Associativity and Precedence 2.1.5 Ambiguous Grammars 2.2 Extended BNF 2.3 Syntax of a Small Language: Clite 2.3.1 Lexical Syntax 2.3.2 Concrete Syntax 2.4 Compilers and Interpreters 2.5 Linking Syntax and Semantics 2.5.1 Abstract Syntax 2.5.2 Abstract Syntax Trees 2.5.3 Abstract Syntax of Clite 2.1.4 Associativity and Precedence A grammar can be used to define associativity and precedence among the operators in an expression. E.g., + and - are left-associative operators in mathematics; * and / have higher precedence than + and - . Consider the more interesting grammar G1: Expr -> Expr + Term | Expr – Term | Term Term -> Term * Factor | Term / Factor | Term % Factor | Factor Factor -> Primary ** Factor | Primary Primary ->