06-ParseRecursiveGram

06-ParseRecursiveGram - Discussion#6 Parsing Recursive...

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Discussion #6 Chapter 10, Section 2 1/16 Discussion #6 Parsing Recursive Grammars
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Discussion #6 Chapter 10, Section 2 2/16 Topics Tail recursion LL(1) with ε Table driven LL(1) with ε Lexical Analyzers
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Discussion #6 Chapter 10, Section 2 3/16 Motivating Example Let’s use integers instead of digits in our prefix language. What’s the problem with *2+72100? Syntax error? Or is it simply ambiguous? * 2 + 7 2100 = 2 * (7 + 2100) = 4214? * 2 + 72 100 = 2 * (72+100) = 344? Solutions? Let n mark the beginning of a number e.g. * n2 + n72 n100 = 2 * (72 + 100) = 344 Strange: but you’ll soon see where we are headed and why.
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Discussion #6 Chapter 10, Section 2 4/16 E (1) N | (2) OEE O (3) + | (4) * N (5) nI I (6) D | (7) ID D (8) 0 | (9) 1 | … | (17) 9 E I D n 2 O E E N N + I n D I D I D 1 0 0 I n D I D 7 2 N O E E * Consider: * n2 + n72 n100
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Discussion #6 Chapter 10, Section 2 5/16 E (1) N | (2) OEE O (3) + | (4) * N (5) nI I (6) D | (7) ID D (8) 0 | (9) 1 | … | (17) 9 E I D n 2 O E E N N + I n ?? N O E E * * n2 + n72 n100 Question… Which rule do we choose? I (6) D or I (7) ID We don’t know without looking further ahead. Should we look further ahead, or find another way?
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Discussion #6 Chapter 10, Section 2 6/16 LL(1) with ε There is another way.
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06-ParseRecursiveGram - Discussion#6 Parsing Recursive...

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