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Understanding Context-Free Grammar in Programming Language Syntax

Learn about the distinction between regular expressions and context-free grammars in programming languages. Explore Backus-Naur Form (BNF) and how to specify token patterns for ANTLR using Regular Expressions.

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Understanding Context-Free Grammar in Programming Language Syntax

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  1. Programming Language Syntax 2 http://flic.kr/p/zCyMp

  2. Think-Pair-Share Activity Assuming the following INTEGER regex: Try to build a regex that matches arithmetic expressions, such as: • 55 • 2 + 5 • 4 * 5 / -3 • (9 * 4)/(2 - +4) • ((4 + 7) * 10) * (69 + 7) / (44 - (22 + 66) * +5)

  3. Here’s one way • Except this isn’t a regex • Regexes cannot have recursive constructs • It’s actually a context-free grammar (CFG) • Like regexes with recursion • Expressed (more or less) in Backus-Naur Form (BNF)

  4. Recall from last time… ANTLR generates for you … But how do you tell ANTLR what your language is like?

  5. You specify token patterns usingRegular Expressions … You specify patterns of tokens using aContext-Free Grammar

  6. Important distinctions betweenregexes and CFG rules in ANTLR • Naming: • Regex names start with uppercase letter • CFG-rule names start with lowercase letter • Character versus token handling: • Regexes process stream of characters • CFG rules process stream of tokens

  7. Will this regex match these strings? “4 4 4 4”? “4444”? No Yes

  8. Will this CFG production match these strings? “4 4 4 4”? “4444”? Yes Yes

  9. Backus-Naur Form (BNF) ANTLR BNF BNF BNF

  10. Extended BNF (EBNF) ANTLR BNF Things not in BNF EBNF

  11. CFG Terminology terminals non-terminal productions

  12. CFG Derivation Series of replacement operations that shows how to derive a string of terminals from the start symbol

  13. Derivation Example CFG: String to derive:

  14. CFG: Derivation: String to derive:

  15. Parse Tree: Graphical Representation of Derivation Can you think of another possible derivation? Hint: This one is a “right-most” derivation

  16. Here’s a “left-most” derviation A grammar with multiple possible derivations is ambiguous Makes generating parser more difficult

  17. Two concepts important to expressions • Associativity: Group based on L-to-R order • 10 - 4 - 3 means (10 - 4) - 3 versus 10 - (4 - 3) • Precedence: Group based on operator • 3 + 4 * 5 means 3 + (4 * 5) versus (3 + 4) * 5

  18. Think-Pair-Share Activity • Rewrite this CFG to be unambiguous • Left associative • Multiplication/division have higher precedence than addition/subtraction

  19. Solution • Create parse tree for: • 3 + 4 * 5 • 10 - 4 - 3

  20. Parse Tree for 3 + 4 * 5

  21. Parse Tree for 10 - 4 - 3

  22. What’s next? • Homework 1 assigned!

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