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Chapter 3

Chapter 3. Context-Free Grammars and Parsing. parser. syntax tree. sequence of tokens. The Parsing Process. Duties of parser: Determine correct syntax Build Syntax Tree (if necessary) Error reporting and recovery. Context-Free Grammars. Specification of programming language

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Chapter 3

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  1. Chapter 3 Context-Free Grammars and Parsing

  2. parser syntax tree sequence of tokens The Parsing Process • Duties of parser: • Determine correct syntax • Build Syntax Tree (if necessary) • Error reporting and recovery

  3. Context-Free Grammars • Specification of programming language • Somewhat like regular expressionsExcept… • Definitions can be recursive • No meta-symbol for repetition

  4. Context-Free GrammarExample exp  exp op exp | ( exp ) | num op  +|-|*

  5. Derivations and Languages • Context-free grammar rules determine the set of legal strings of token symbols for the structures defined by the rules. • Example: “(34-3)*42” corresponds to(num – num) * num • Example: “(34-3*42” is not a legal expression • Grammar rules determine the legal strings of token symbols by means of derivations

  6. Derivation • A derivation is a sequence of replacements of structure names by choices on the right-hand side of grammar rules.

  7. Derivation Example • exp  exp op exp [exp  exp op exp] •  exp op num [exp  num] •  exp * num [op  *] •  (exp) * num [exp  (exp)] •  (exp op exp) * num [exp  exp op exp] •  (exp op num) * num [exp  num] •  (exp – num) * num [op  -] •  (num – num) * num [exp  num]

  8. Other Context-Free Grammars • E  (E) | a • E  E +a • statement  if-stmt | otherif-stmt  if (exp) statement |if (exp) statement else statementexp  0 | 1

  9. Right recursive and Left recursive • Consider the grammarA  A a | a • A  Aa  Aaa  Aaaa … • Conversely considerA  A a | a • A  aA  aaA  aaaA • The first grammar is left recursiveThe second is right recursive

  10. empty • ‘ε’ matches the empty string • so the regular expression: a*Looks like A  Aa | ε • What does the following grammar doA  (A)A | ε

  11. Another Example • statement  if-stmt | otherif-stmt  if (exp) statement |if (exp) statement else-partelse-part  else statement | εexp  0 | 1

  12. Another Example • stmt-sequence  stmt; stmt-sequence | stmtstmt  s • stmt-sequence  stmt; stmt-sequence | εstmt  s Notice any differences??

  13. Parse Trees • Consider the string of tokens( num – num ) * num • How many derivations are there?? • Parse-Trees show the derivation without worrying about ordering

  14. Parse Trees • A parse tree corresponding to a derivation • labeled tree • interior nodes are • labeled by nonterminals • leaf nodes are • labeled by terminals • children of each internal node • represent the replacement of the associated nonterminal • one step of the derivation

  15. exp exp exp op number + number Parse-Tree exp  exp op exp | ( exp ) | num op  +|-|* what is the corresponding derivation?

  16. Left-most derivation • A left-most derivation is a derivation in which the leftmost nonterminal is replaced at each step in the derivation.

  17. exp exp exp op number + number Parse-Tree exp  exp op exp | ( exp ) | num op  +|-|* what is the corresponding left-most derivation?

  18. Abstract Syntax Trees • parse trees contain more information than is absolutely necessary for a compiler to produce executable code • A shorthand notation for a parse tree is called an abstract syntax tree

  19. exp exp exp op number + number Example If the string to parse was “3+4” + 3 4 The parse tree The abstract syntax tree tree

  20. Other Examples • What about parse trees and abstract syntax trees for the following grammar? • statement  if-stmt | otherif-stmt  if (exp) statement |if (exp) statement else statementexp  0 | 1

  21. Other Examples • What about parse trees and abstract syntax trees for this grammar? • stmt-sequence  stmt; stmt-sequence | stmtstmt  s

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