lecture08 - CS 143 Lecture 8 1 Bottom-Up Par sing I I...

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Unformatted text preview: CS 143 Lecture 8 1 Bottom-Up Par sing I I Lecture 8 CS 143 Lecture 8 2 Review: Shift-Reduce Par sing Bottom-up parsing uses two actions: Shift ABC | xyz ⇒ ABCx | yz Reduce Cbxy | ijk ⇒ CbA | ijk CS 143 Lecture 8 3 Recall: The Stack • Left string can be implemented by a stack – Top of the stack is the | • Shift pushes a terminal on the stack • Reduce – pops 0 or more symbols off of the stack • production rhs – pushes a non-terminal on the stack • production lhs CS 143 Lecture 8 4 Key I ssue • How do we decide when to shift or reduce? • Example grammar: E → T + E | T T → int * T | int | (E) • Consider step int | * int + int – We could reduce by T → int giving T | * int + int – A fatal mistake! • No way to reduce to the start symbol E CS 143 Lecture 8 5 H andles • I ntuition: Want to reduce only if the result can still be reduced to the start symbol • Assume a rightmost derivation S → * α X ϖ → αβϖ • Then αβ is a handle of αβϖ CS 143 Lecture 8 6 H andles (Cont.) • Handles formalize the intuition – A handle is a string that can be reduced and also allows further reductions back to the start symbol • We only want to reduce at handles • Note: We have said what a handle is, not how to find handles CS 143 Lecture 8 7 I mpor tant Fact #2 I mportant Fact #2 about bottom-up parsing: I n shift-reduce parsing, handles appear only at the top of the stack, never inside CS 143 Lecture 8 8 Why? • I nformal induction on # of reduce moves: • True initially, stack is empty • I mmediately after reducing a handle – right-most non-terminal on top of the stack – next handle must be to right of right-most non- terminal, because this is a right-most derivation – Sequence of shift moves reaches next handle CS 143 Lecture 8 9 Summar y of H andles • I n shift-reduce parsing, handles always appear at the top of the stack • Handles are never to the left of the rightmost non-terminal – Therefore, shift-reduce moves are sufficient; the | need never move left • Bottom-up parsing algorithms are based on recognizing handles CS 143 Lecture 8 10 Conflicts Again • Generic shift-reduce strategy: – I f there is a handle on top of the stack, reduce – Otherwise, shift • But what if there is a choice? – I f it is legal to shift or reduce, there is a shift-reduce conflict – I f it is legal to reduce by two different productions, there is a reduce-reduce conflict CS 143 Lecture 8 11 Sour ce of Conflicts • Ambiguous grammars always cause conflicts • But beware, so do many non-ambiguous grammars CS 143 Lecture 8 12 Conflict Example Consider our favorite ambiguous grammar: E → E + E | E * E | (E) | int CS 143 Lecture 8 13 One Shift-Reduce Par se | int * int + int shift . . . . . ....
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lecture08 - CS 143 Lecture 8 1 Bottom-Up Par sing I I...

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