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Understanding Attribute Grammars and Their Applications in Expression Evaluation

This article explores the concept of attribute grammars, a generalization of context-free grammars (CFG), where each grammar symbol has associated attributes. It covers both synthesized and inherited attributes, detailing their roles in computing values and expressions. The discussion includes examples such as the evaluation of arithmetic expressions and the conversion of binary numbers to decimal. Additionally, it highlights methods for computing attribute values during or after parsing, emphasizing the use of dependency graphs and rule-based techniques. This comprehensive overview aims to deepen your understanding of attribute grammars.

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Understanding Attribute Grammars and Their Applications in Expression Evaluation

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  1. Attribute Grammars • Recall the yacc program • Parse a given expression • Evaluate it expr : expr '+' expr {$$ = $1 + $3;} | expr '-' expr {$$ = $1 - $3;} | expr '*' expr {$$ = $1 * $3;} | expr '/' expr {$$ = $1 / $3;} | '(' expr ')' {$$ = $2;} | NUMBER ; by Neng-Fa Zhou

  2. Attributes and Attribute Grammars • Attributes • variables (type,offset,first or last occurrence,...) • constants (type, value, scope, ...) • Attribute grammar(Syntax-directed definition) • A generalization of CFG in which each grammar symbol has an associated set of attributes • Semantics rules for computing attribute values by Neng-Fa Zhou

  3. Synthesized Attributes • Synthesized Attributes • The value is computed from the values of attributes of the children • S-attributed grammar - synthesized attributes only • Bottom-up propagation • Example • values of expressions • types of expressions by Neng-Fa Zhou

  4. S-Attributed GrammarsExample by Neng-Fa Zhou

  5. The Annotated Parse Tree by Neng-Fa Zhou

  6. Inherited Attributes • Inherited Attributes • The value is computed from the values of attributes of the siblings and parent • Top-down propagation • Example • type information • where does a variable occurs? lhs or rhs by Neng-Fa Zhou

  7. Inherited AttributesExample by Neng-Fa Zhou

  8. The Annotated Parser Tree by Neng-Fa Zhou

  9. Converting Binary to Decimal N ::= BIN N.v = BIN.v BIN.r = 0 BIN0 ::= BIN1 B BIN1.r = BIN0.r + 1 B.r = BIN0.r BIN0.v = BIN1.v+B.v BIN ::= B BIN.v = B.v B.r = BIN.r B ::= '1' B.v = 2B.r B ::= '0' B.v = 0 by Neng-Fa Zhou

  10. Dependency Graphs • Each node represents an attribute of a node in the parse tree • Each arc represents the dependence relationship (flow of values) by Neng-Fa Zhou

  11. Computing Attribute Values • 1.Compute while parsing • Oblivious methods • Fast (one pass) • Complicated • Some attribute values cannot be computed • 2. Compute after parsing • Parse-tree methods (sort dependency graphs) • Rule-based methods (data-flow or fix-point) by Neng-Fa Zhou

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